diff --git "a/1hop_ProofByContra_testrandom_nodistractor_testdistractor_noadj.json" "b/1hop_ProofByContra_testrandom_nodistractor_testdistractor_noadj.json" new file mode 100644--- /dev/null +++ "b/1hop_ProofByContra_testrandom_nodistractor_testdistractor_noadj.json" @@ -0,0 +1,17302 @@ +{ + "example1": { + "in_context_example0": { + "question": "Everything that is a shumpus or a wumpus is a rompus. Polly is not a rompus.", + "query": "Prove: Polly is not a wumpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a shumpus.\n\n", + "Polly is not a wumpus and Polly is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a wumpus is a jompus. Wren is not a jompus.", + "query": "Prove: Wren is not a wumpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a wumpus.", + "Wren is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a wumpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a tumpus.\n\n", + "Wren is not a wumpus and Wren is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a dumpus or a lempus is a wumpus. Wren is not a wumpus.", + "query": "Prove: Wren is not a lempus and Wren is not a dumpus.", + "chain_of_thought": [ + "Assume Wren is a lempus.", + "Wren is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a lempus.\n\n", + "Assume Wren is a dumpus.", + "Wren is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a dumpus.\n\n", + "Wren is not a lempus and Wren is not a dumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a shumpus is a lempus. Stella is not a lempus.", + "query": "Prove: Stella is not a shumpus and Stella is not a numpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a numpus.", + "Stella is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a numpus.\n\n", + "Stella is not a shumpus and Stella is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a yumpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a yumpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a lempus.\n\n", + "Rex is not a yumpus and Rex is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a vumpus is a wumpus. Sally is not a wumpus.", + "query": "Prove: Sally is not a vumpus and Sally is not a shumpus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is a shumpus.", + "Sally is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a shumpus.\n\n", + "Sally is not a vumpus and Sally is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a lorpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a lorpus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a lorpus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a grimpus.\n\n", + "Max is not a lorpus and Max is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a numpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a numpus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a numpus.", + "Polly is an impus or a numpus.", + "Everything that is an impus or a numpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a numpus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a numpus.", + "Everything that is an impus or a numpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not an impus.\n\n", + "Polly is not a numpus and Polly is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a lempus or an impus is a jompus. Everything that is a brimpus or a tumpus is a shumpus. Everything that is a lempus or an impus is a shumpus. Fae is not a numpus. Fae is not a shumpus.", + "query": "Prove: Fae is not an impus and Fae is not a lempus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a lempus or an impus.", + "Everything that is a lempus or an impus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a lempus.", + "Fae is a lempus or an impus.", + "Everything that is a lempus or an impus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a lempus.\n\n", + "Fae is not an impus and Fae is not a lempus." + ] + } + }, + "example2": { + "in_context_example0": { + "question": "Everything that is a dumpus or a tumpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a tumpus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a dumpus.\n\n", + "Sally is not a tumpus and Sally is not a dumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a gorpus is a shumpus. Stella is not a shumpus.", + "query": "Prove: Stella is not a gorpus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not an impus.\n\n", + "Stella is not a gorpus and Stella is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a sterpus or a lempus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a lempus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a sterpus.\n\n", + "Sam is not a lempus and Sam is not a sterpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a wumpus or a gorpus is a yumpus. Polly is not a yumpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a gorpus and Polly is not a wumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lorpus or a grimpus is a lempus. Alex is not a lempus.", + "query": "Prove: Alex is not a grimpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a lorpus.\n\n", + "Alex is not a grimpus and Alex is not a lorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a yumpus or a wumpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a yumpus or a wumpus.", + "Everything that is a yumpus or a wumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a wumpus.", + "Everything that is a yumpus or a wumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a wumpus and Sam is not a yumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a zumpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a zumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a zumpus and Fae is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a gorpus is a rompus. Fae is not a rompus.", + "query": "Prove: Fae is not a gorpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a shumpus.\n\n", + "Fae is not a gorpus and Fae is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or an impus is a vumpus. Everything that is a lempus or a brimpus is a shumpus. Everything that is a lempus or a brimpus is a vumpus. Rex is not a vumpus. Rex is not a wumpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a lempus.\n\n", + "Rex is not a brimpus and Rex is not a lempus." + ] + } + }, + "example3": { + "in_context_example0": { + "question": "Everything that is a sterpus or a vumpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a vumpus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a vumpus.", + "Alex is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a vumpus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a sterpus.\n\n", + "Alex is not a vumpus and Alex is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a gorpus or a dumpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a dumpus and Sam is not a gorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or a grimpus is a numpus. Wren is not a numpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a grimpus and Wren is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a tumpus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a tumpus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a grimpus.\n\n", + "Max is not a tumpus and Max is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a shumpus or a vumpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a shumpus.\n\n", + "Polly is not a vumpus and Polly is not a shumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a rompus or a shumpus is a numpus. Sam is not a numpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a rompus.\n\n", + "Sam is not a shumpus and Sam is not a rompus." + ] + }, + "in_context_example6": { + "question": "Everything that is a tumpus or a numpus is a lorpus. Wren is not a lorpus.", + "query": "Prove: Wren is not a numpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a tumpus.\n\n", + "Wren is not a numpus and Wren is not a tumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a rompus or a jompus is a yumpus. Stella is not a yumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a jompus and Stella is not a rompus." + ] + }, + "test_example": { + "question": "Everything that is a wumpus or a tumpus is a brimpus. Everything that is a dumpus or a zumpus is a shumpus. Everything that is a dumpus or a zumpus is a brimpus. Wren is not a brimpus. Wren is not a lempus.", + "query": "Prove: Wren is not a zumpus and Wren is not a dumpus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a dumpus.", + "Wren is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a dumpus.\n\n", + "Wren is not a zumpus and Wren is not a dumpus." + ] + } + }, + "example4": { + "in_context_example0": { + "question": "Everything that is a yumpus or a tumpus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a tumpus and Sally is not a yumpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a yumpus.", + "Sally is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a yumpus.\n\n", + "Sally is not a tumpus and Sally is not a yumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or a jompus is a vumpus. Polly is not a vumpus.", + "query": "Prove: Polly is not a jompus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a vumpus.", + "Polly is a vumpus.", + "This contradicts with Polly is not a vumpus.", + "Polly is not a jompus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a vumpus.", + "Polly is a vumpus.", + "This contradicts with Polly is not a vumpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a jompus and Polly is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a vumpus or a dumpus is a gorpus. Stella is not a gorpus.", + "query": "Prove: Stella is not a dumpus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a dumpus.", + "Stella is a vumpus or a dumpus.", + "Everything that is a vumpus or a dumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a dumpus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a dumpus.", + "Everything that is a vumpus or a dumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a vumpus.\n\n", + "Stella is not a dumpus and Stella is not a vumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a brimpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a brimpus and Sally is not a jompus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a jompus.", + "Sally is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a jompus.\n\n", + "Sally is not a brimpus and Sally is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lorpus or an impus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not an impus and Fae is not a lorpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a lorpus or an impus.", + "Everything that is a lorpus or an impus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a lorpus.", + "Fae is a lorpus or an impus.", + "Everything that is a lorpus or an impus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a lorpus.\n\n", + "Fae is not an impus and Fae is not a lorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a zumpus or a lempus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a lempus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a zumpus.\n\n", + "Rex is not a lempus and Rex is not a zumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a dumpus or a yumpus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a dumpus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a dumpus.", + "Rex is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a dumpus.\n\n", + "Rex is not a yumpus and Rex is not a dumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a jompus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a jompus and Stella is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a sterpus is a vumpus. Everything that is a tumpus or a sterpus is a yumpus. Everything that is a numpus or a lempus is a vumpus. Alex is not an impus. Alex is not a vumpus.", + "query": "Prove: Alex is not a sterpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a sterpus.", + "Alex is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a sterpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a sterpus and Alex is not a tumpus." + ] + } + }, + "example5": { + "in_context_example0": { + "question": "Everything that is a zumpus or a dumpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a zumpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a zumpus.", + "Fae is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a zumpus.\n\n", + "Fae is not a dumpus and Fae is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lorpus or a dumpus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a lorpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a lorpus or a dumpus.", + "Everything that is a lorpus or a dumpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a lorpus.", + "Fae is a lorpus or a dumpus.", + "Everything that is a lorpus or a dumpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a lorpus.\n\n", + "Fae is not a dumpus and Fae is not a lorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a vumpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a vumpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a brimpus.\n\n", + "Sally is not a vumpus and Sally is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a wumpus is a jompus. Fae is not a jompus.", + "query": "Prove: Fae is not a wumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a jompus.", + "Fae is a jompus.", + "This contradicts with Fae is not a jompus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a jompus.", + "Fae is a jompus.", + "This contradicts with Fae is not a jompus.", + "Fae is not a shumpus.\n\n", + "Fae is not a wumpus and Fae is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a brimpus or a gorpus is a dumpus. Polly is not a dumpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a gorpus and Polly is not a brimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a zumpus or a lempus is an impus. Polly is not an impus.", + "query": "Prove: Polly is not a lempus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a lempus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a zumpus.\n\n", + "Polly is not a lempus and Polly is not a zumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a tumpus or a sterpus is a lorpus. Max is not a lorpus.", + "query": "Prove: Max is not a sterpus and Max is not a tumpus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a sterpus.\n\n", + "Assume Max is a tumpus.", + "Max is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a tumpus.\n\n", + "Max is not a sterpus and Max is not a tumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a gorpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a zumpus or a gorpus.", + "Everything that is a zumpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a gorpus.", + "Everything that is a zumpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a gorpus and Polly is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a rompus is a vumpus. Everything that is a gorpus or a rompus is an impus. Everything that is a brimpus or a numpus is a vumpus. Max is not a wumpus. Max is not a vumpus.", + "query": "Prove: Max is not a rompus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a rompus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a gorpus.\n\n", + "Max is not a rompus and Max is not a gorpus." + ] + } + }, + "example6": { + "in_context_example0": { + "question": "Everything that is a vumpus or a numpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a numpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a numpus.", + "Polly is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a numpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a numpus and Polly is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a gorpus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a gorpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a gorpus and Wren is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a rompus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a rompus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a rompus.", + "Rex is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a rompus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a rompus and Rex is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a jompus is a numpus. Sam is not a numpus.", + "query": "Prove: Sam is not a jompus and Sam is not a grimpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a grimpus.", + "Sam is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a grimpus.\n\n", + "Sam is not a jompus and Sam is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a lorpus is a wumpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a lorpus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a lorpus.", + "Alex is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a lorpus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not an impus.\n\n", + "Alex is not a lorpus and Alex is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a jompus is a lempus. Polly is not a lempus.", + "query": "Prove: Polly is not a jompus and Polly is not a sterpus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a jompus.\n\n", + "Assume Polly is a sterpus.", + "Polly is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a sterpus.\n\n", + "Polly is not a jompus and Polly is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a gorpus or a yumpus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a yumpus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a yumpus.", + "Max is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a yumpus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a gorpus.\n\n", + "Max is not a yumpus and Max is not a gorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a shumpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a shumpus and Rex is not a yumpus.", + "chain_of_thought": [ + "Assume Rex is a shumpus.", + "Rex is a yumpus or a shumpus.", + "Everything that is a yumpus or a shumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a shumpus.\n\n", + "Assume Rex is a yumpus.", + "Rex is a yumpus or a shumpus.", + "Everything that is a yumpus or a shumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a yumpus.\n\n", + "Rex is not a shumpus and Rex is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a dumpus or a grimpus is a numpus. Everything that is a dumpus or a grimpus is a shumpus. Everything that is a lorpus or a lempus is a numpus. Rex is not a numpus. Rex is not a yumpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a dumpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a dumpus or a grimpus.", + "Everything that is a dumpus or a grimpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a dumpus.", + "Rex is a dumpus or a grimpus.", + "Everything that is a dumpus or a grimpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a dumpus.\n\n", + "Rex is not a grimpus and Rex is not a dumpus." + ] + } + }, + "example7": { + "in_context_example0": { + "question": "Everything that is a gorpus or a lempus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a lempus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a lempus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a gorpus.\n\n", + "Max is not a lempus and Max is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a zumpus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a tumpus.\n\n", + "Sam is not a zumpus and Sam is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a shumpus is a dumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a grimpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a grimpus.", + "Sam is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a grimpus.\n\n", + "Sam is not a shumpus and Sam is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a zumpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a zumpus and Wren is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a numpus is a brimpus. Polly is not a brimpus.", + "query": "Prove: Polly is not a numpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a numpus.", + "Polly is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a numpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a lempus.\n\n", + "Polly is not a numpus and Polly is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a dumpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a dumpus and Fae is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is an impus or a zumpus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a zumpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a zumpus.", + "Sally is an impus or a zumpus.", + "Everything that is an impus or a zumpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a zumpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a zumpus.", + "Everything that is an impus or a zumpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not an impus.\n\n", + "Sally is not a zumpus and Sally is not an impus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a rompus is a jompus. Alex is not a jompus.", + "query": "Prove: Alex is not a rompus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a gorpus.\n\n", + "Alex is not a rompus and Alex is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a rompus or a grimpus is a gorpus. Everything that is a numpus or a jompus is a vumpus. Everything that is a rompus or a grimpus is a vumpus. Wren is not a vumpus. Wren is not a tumpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a rompus.\n\n", + "Wren is not a grimpus and Wren is not a rompus." + ] + } + }, + "example8": { + "in_context_example0": { + "question": "Everything that is a gorpus or a zumpus is a dumpus. Polly is not a dumpus.", + "query": "Prove: Polly is not a zumpus and Polly is not a gorpus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a gorpus.", + "Polly is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a gorpus.\n\n", + "Polly is not a zumpus and Polly is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a rompus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a rompus and Sally is not a jompus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a jompus or a rompus.", + "Everything that is a jompus or a rompus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a jompus.", + "Sally is a jompus or a rompus.", + "Everything that is a jompus or a rompus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a jompus.\n\n", + "Sally is not a rompus and Sally is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a grimpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a numpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a numpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a numpus.\n\n", + "Rex is not a grimpus and Rex is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a yumpus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a yumpus and Rex is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a gorpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a gorpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a gorpus.", + "Sam is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a gorpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not an impus.\n\n", + "Sam is not a gorpus and Sam is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a lorpus is a numpus. Max is not a numpus.", + "query": "Prove: Max is not a lorpus and Max is not a dumpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a lorpus.\n\n", + "Assume Max is a dumpus.", + "Max is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a dumpus.\n\n", + "Max is not a lorpus and Max is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a rompus or a grimpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a grimpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a grimpus.", + "Sam is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a grimpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a rompus.\n\n", + "Sam is not a grimpus and Sam is not a rompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a shumpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a shumpus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a shumpus.", + "Rex is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a shumpus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a zumpus.\n\n", + "Rex is not a shumpus and Rex is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a wumpus is an impus. Everything that is a grimpus or a rompus is a numpus. Everything that is a sterpus or a wumpus is a numpus. Sam is not a vumpus. Sam is not a numpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a wumpus and Sam is not a sterpus." + ] + } + }, + "example9": { + "in_context_example0": { + "question": "Everything that is a lorpus or a rompus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a rompus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a rompus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a lorpus.\n\n", + "Max is not a rompus and Max is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a gorpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a gorpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a gorpus.", + "Sam is a tumpus or a gorpus.", + "Everything that is a tumpus or a gorpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a gorpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a gorpus.", + "Everything that is a tumpus or a gorpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a tumpus.\n\n", + "Sam is not a gorpus and Sam is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a vumpus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not a vumpus and Max is not a numpus.", + "chain_of_thought": [ + "Assume Max is a vumpus.", + "Max is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a vumpus.\n\n", + "Assume Max is a numpus.", + "Max is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a numpus.\n\n", + "Max is not a vumpus and Max is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or a lempus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a lempus and Alex is not a rompus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a rompus.", + "Alex is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a rompus.\n\n", + "Alex is not a lempus and Alex is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a dumpus is a numpus. Polly is not a numpus.", + "query": "Prove: Polly is not a dumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a lempus.\n\n", + "Polly is not a dumpus and Polly is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a jompus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a jompus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a jompus and Fae is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a sterpus is a lorpus. Stella is not a lorpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a brimpus or a sterpus.", + "Everything that is a brimpus or a sterpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a sterpus.", + "Everything that is a brimpus or a sterpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a sterpus and Stella is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lorpus or a brimpus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a brimpus and Stella is not a lorpus.", + "chain_of_thought": [ + "Assume Stella is a brimpus.", + "Stella is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a brimpus.\n\n", + "Assume Stella is a lorpus.", + "Stella is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a lorpus.\n\n", + "Stella is not a brimpus and Stella is not a lorpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a lorpus is a lempus. Everything that is a tumpus or an impus is a sterpus. Everything that is a tumpus or an impus is a lempus. Sally is not a lempus. Sally is not a rompus.", + "query": "Prove: Sally is not an impus and Sally is not a tumpus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not an impus.\n\n", + "Assume Sally is a tumpus.", + "Sally is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a tumpus.\n\n", + "Sally is not an impus and Sally is not a tumpus." + ] + } + }, + "example10": { + "in_context_example0": { + "question": "Everything that is a rompus or a vumpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a vumpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a vumpus.", + "Wren is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a vumpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a rompus.\n\n", + "Wren is not a vumpus and Wren is not a rompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lempus or a yumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a yumpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a yumpus.", + "Sam is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a yumpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a lempus.\n\n", + "Sam is not a yumpus and Sam is not a lempus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a lempus is a dumpus. Fae is not a dumpus.", + "query": "Prove: Fae is not a lempus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a numpus.\n\n", + "Fae is not a lempus and Fae is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a shumpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a shumpus and Wren is not a jompus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a jompus.", + "Wren is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a jompus.\n\n", + "Wren is not a shumpus and Wren is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a vumpus or a tumpus is a lorpus. Max is not a lorpus.", + "query": "Prove: Max is not a tumpus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a vumpus or a tumpus.", + "Everything that is a vumpus or a tumpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or a tumpus.", + "Everything that is a vumpus or a tumpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a vumpus.\n\n", + "Max is not a tumpus and Max is not a vumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a gorpus or a lempus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a lempus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a lempus and Sam is not a gorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or an impus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not an impus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is an impus.", + "Stella is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not an impus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not an impus and Stella is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a zumpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a zumpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a wumpus.\n\n", + "Rex is not a zumpus and Rex is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a rompus or a numpus is a brimpus. Everything that is an impus or a dumpus is a brimpus. Everything that is an impus or a dumpus is a vumpus. Polly is not a brimpus. Polly is not a yumpus.", + "query": "Prove: Polly is not a dumpus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not an impus.\n\n", + "Polly is not a dumpus and Polly is not an impus." + ] + } + }, + "example11": { + "in_context_example0": { + "question": "Everything that is a jompus or a lorpus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a jompus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a jompus.", + "Wren is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a jompus.\n\n", + "Wren is not a lorpus and Wren is not a jompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a grimpus is a numpus. Sally is not a numpus.", + "query": "Prove: Sally is not a grimpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a grimpus and Sally is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a jompus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a jompus and Wren is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a wumpus or a rompus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a rompus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a rompus.", + "Rex is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a rompus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a wumpus.\n\n", + "Rex is not a rompus and Rex is not a wumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a numpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a numpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is an impus or a numpus.", + "Everything that is an impus or a numpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a numpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a numpus.", + "Everything that is an impus or a numpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not an impus.\n\n", + "Sam is not a numpus and Sam is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a dumpus is a grimpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a numpus or a dumpus.", + "Everything that is a numpus or a dumpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a dumpus.", + "Everything that is a numpus or a dumpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a numpus.\n\n", + "Fae is not a dumpus and Fae is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a rompus or a vumpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a vumpus and Fae is not a rompus.", + "chain_of_thought": [ + "Assume Fae is a vumpus.", + "Fae is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a vumpus.\n\n", + "Assume Fae is a rompus.", + "Fae is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a rompus.\n\n", + "Fae is not a vumpus and Fae is not a rompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a rompus is an impus. Alex is not an impus.", + "query": "Prove: Alex is not a rompus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a gorpus.\n\n", + "Alex is not a rompus and Alex is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a brimpus is a vumpus. Everything that is a tumpus or a brimpus is a gorpus. Everything that is a shumpus or a sterpus is a vumpus. Stella is not an impus. Stella is not a vumpus.", + "query": "Prove: Stella is not a brimpus and Stella is not a tumpus.", + "chain_of_thought": [ + "Assume Stella is a brimpus.", + "Stella is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a brimpus.\n\n", + "Assume Stella is a tumpus.", + "Stella is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a tumpus.\n\n", + "Stella is not a brimpus and Stella is not a tumpus." + ] + } + }, + "example12": { + "in_context_example0": { + "question": "Everything that is a brimpus or a gorpus is a zumpus. Max is not a zumpus.", + "query": "Prove: Max is not a gorpus and Max is not a brimpus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a zumpus.", + "Max is a zumpus.", + "This contradicts with Max is not a zumpus.", + "Max is not a gorpus.\n\n", + "Assume Max is a brimpus.", + "Max is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a zumpus.", + "Max is a zumpus.", + "This contradicts with Max is not a zumpus.", + "Max is not a brimpus.\n\n", + "Max is not a gorpus and Max is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a dumpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a jompus.\n\n", + "Sam is not a dumpus and Sam is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a jompus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not a jompus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a grimpus.\n\n", + "Fae is not a jompus and Fae is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lempus or a jompus is a wumpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a jompus and Alex is not a lempus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is a lempus.", + "Alex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a lempus.\n\n", + "Alex is not a jompus and Alex is not a lempus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a jompus is a brimpus. Alex is not a brimpus.", + "query": "Prove: Alex is not a jompus and Alex is not a lempus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is a lempus.", + "Alex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a lempus.\n\n", + "Alex is not a jompus and Alex is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a rompus or a shumpus is a gorpus. Max is not a gorpus.", + "query": "Prove: Max is not a shumpus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a shumpus.", + "Max is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a shumpus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a rompus.\n\n", + "Max is not a shumpus and Max is not a rompus." + ] + }, + "in_context_example6": { + "question": "Everything that is a gorpus or a vumpus is a tumpus. Rex is not a tumpus.", + "query": "Prove: Rex is not a vumpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a vumpus.", + "Rex is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a vumpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a vumpus and Rex is not a gorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a tumpus or a rompus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a rompus and Max is not a tumpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a rompus.\n\n", + "Assume Max is a tumpus.", + "Max is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a tumpus.\n\n", + "Max is not a rompus and Max is not a tumpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a jompus is a gorpus. Everything that is a tumpus or an impus is a gorpus. Everything that is a vumpus or a jompus is a brimpus. Stella is not a zumpus. Stella is not a gorpus.", + "query": "Prove: Stella is not a jompus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a vumpus.\n\n", + "Stella is not a jompus and Stella is not a vumpus." + ] + } + }, + "example13": { + "in_context_example0": { + "question": "Everything that is a tumpus or a shumpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a shumpus and Polly is not a tumpus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a tumpus.", + "Polly is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a tumpus.\n\n", + "Polly is not a shumpus and Polly is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or a yumpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a yumpus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a yumpus.", + "Alex is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a yumpus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a brimpus.\n\n", + "Alex is not a yumpus and Alex is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a shumpus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a shumpus and Stella is not a numpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a numpus.", + "Stella is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a numpus.\n\n", + "Stella is not a shumpus and Stella is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a gorpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a gorpus and Max is not a jompus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a jompus or a gorpus.", + "Everything that is a jompus or a gorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a gorpus.\n\n", + "Assume Max is a jompus.", + "Max is a jompus or a gorpus.", + "Everything that is a jompus or a gorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a jompus.\n\n", + "Max is not a gorpus and Max is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or an impus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not an impus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is an impus.", + "Rex is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not an impus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a tumpus.\n\n", + "Rex is not an impus and Rex is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a yumpus is a tumpus. Max is not a tumpus.", + "query": "Prove: Max is not a yumpus and Max is not a shumpus.", + "chain_of_thought": [ + "Assume Max is a yumpus.", + "Max is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a yumpus.\n\n", + "Assume Max is a shumpus.", + "Max is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a shumpus.\n\n", + "Max is not a yumpus and Max is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a jompus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a jompus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a lempus.\n\n", + "Wren is not a jompus and Wren is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a shumpus is a dumpus. Wren is not a dumpus.", + "query": "Prove: Wren is not a shumpus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a shumpus and Wren is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a tumpus is a lempus. Everything that is an impus or a tumpus is a vumpus. Everything that is a lorpus or a jompus is a lempus. Max is not a zumpus. Max is not a lempus.", + "query": "Prove: Max is not a tumpus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a tumpus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not an impus.\n\n", + "Max is not a tumpus and Max is not an impus." + ] + } + }, + "example14": { + "in_context_example0": { + "question": "Everything that is a brimpus or a lempus is a tumpus. Wren is not a tumpus.", + "query": "Prove: Wren is not a lempus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is a lempus.", + "Wren is a brimpus or a lempus.", + "Everything that is a brimpus or a lempus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not a lempus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or a lempus.", + "Everything that is a brimpus or a lempus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not a brimpus.\n\n", + "Wren is not a lempus and Wren is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a jompus is a numpus. Rex is not a numpus.", + "query": "Prove: Rex is not a jompus and Rex is not a rompus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a rompus.", + "Rex is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a rompus.\n\n", + "Rex is not a jompus and Rex is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is an impus or a yumpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a yumpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is an impus or a yumpus.", + "Everything that is an impus or a yumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a yumpus.", + "Everything that is an impus or a yumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not an impus.\n\n", + "Sally is not a yumpus and Sally is not an impus." + ] + }, + "in_context_example3": { + "question": "Everything that is a sterpus or a dumpus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a dumpus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a dumpus and Rex is not a sterpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a numpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a numpus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a numpus and Wren is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a wumpus or a zumpus is a yumpus. Fae is not a yumpus.", + "query": "Prove: Fae is not a zumpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a zumpus and Fae is not a wumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a zumpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a zumpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a zumpus and Polly is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a shumpus is a rompus. Polly is not a rompus.", + "query": "Prove: Polly is not a shumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a lempus or a shumpus.", + "Everything that is a lempus or a shumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a shumpus.", + "Everything that is a lempus or a shumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a lempus.\n\n", + "Polly is not a shumpus and Polly is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a jompus is a vumpus. Everything that is a sterpus or a jompus is a rompus. Everything that is a lempus or a dumpus is a vumpus. Fae is not a tumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not a jompus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a jompus and Fae is not a sterpus." + ] + } + }, + "example15": { + "in_context_example0": { + "question": "Everything that is a brimpus or a lorpus is a jompus. Wren is not a jompus.", + "query": "Prove: Wren is not a lorpus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a brimpus or a lorpus.", + "Everything that is a brimpus or a lorpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or a lorpus.", + "Everything that is a brimpus or a lorpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a brimpus.\n\n", + "Wren is not a lorpus and Wren is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a wumpus is a sterpus. Stella is not a sterpus.", + "query": "Prove: Stella is not a wumpus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a wumpus.", + "Stella is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a wumpus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not an impus.\n\n", + "Stella is not a wumpus and Stella is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a jompus or a tumpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a tumpus and Sally is not a jompus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a jompus.", + "Sally is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a jompus.\n\n", + "Sally is not a tumpus and Sally is not a jompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lempus or a gorpus is a zumpus. Sally is not a zumpus.", + "query": "Prove: Sally is not a gorpus and Sally is not a lempus.", + "chain_of_thought": [ + "Assume Sally is a gorpus.", + "Sally is a lempus or a gorpus.", + "Everything that is a lempus or a gorpus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a gorpus.\n\n", + "Assume Sally is a lempus.", + "Sally is a lempus or a gorpus.", + "Everything that is a lempus or a gorpus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a lempus.\n\n", + "Sally is not a gorpus and Sally is not a lempus." + ] + }, + "in_context_example4": { + "question": "Everything that is a brimpus or a yumpus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a yumpus and Fae is not a brimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or an impus is a wumpus. Sam is not a wumpus.", + "query": "Prove: Sam is not an impus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a brimpus.\n\n", + "Sam is not an impus and Sam is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a sterpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a sterpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a sterpus.", + "Sally is a brimpus or a sterpus.", + "Everything that is a brimpus or a sterpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a sterpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a sterpus.", + "Everything that is a brimpus or a sterpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a brimpus.\n\n", + "Sally is not a sterpus and Sally is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a yumpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a yumpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a yumpus.", + "Wren is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a yumpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a yumpus and Wren is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a jompus or a zumpus is a shumpus. Everything that is a yumpus or a lorpus is a gorpus. Everything that is a yumpus or a lorpus is a shumpus. Sam is not a sterpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a lorpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a yumpus or a lorpus.", + "Everything that is a yumpus or a lorpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a lorpus.", + "Everything that is a yumpus or a lorpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a lorpus and Sam is not a yumpus." + ] + } + }, + "example16": { + "in_context_example0": { + "question": "Everything that is a wumpus or an impus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not an impus and Max is not a wumpus.", + "chain_of_thought": [ + "Assume Max is an impus.", + "Max is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not an impus.\n\n", + "Assume Max is a wumpus.", + "Max is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a wumpus.\n\n", + "Max is not an impus and Max is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a numpus or a vumpus is a lempus. Polly is not a lempus.", + "query": "Prove: Polly is not a vumpus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a numpus.\n\n", + "Polly is not a vumpus and Polly is not a numpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a tumpus is a lempus. Max is not a lempus.", + "query": "Prove: Max is not a tumpus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a lorpus or a tumpus.", + "Everything that is a lorpus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a tumpus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a tumpus.", + "Everything that is a lorpus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a lorpus.\n\n", + "Max is not a tumpus and Max is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a numpus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a numpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a numpus and Wren is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a zumpus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a zumpus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a zumpus.", + "Alex is an impus or a zumpus.", + "Everything that is an impus or a zumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a zumpus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a zumpus.", + "Everything that is an impus or a zumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not an impus.\n\n", + "Alex is not a zumpus and Alex is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a grimpus or an impus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not an impus and Alex is not a grimpus.", + "chain_of_thought": [ + "Assume Alex is an impus.", + "Alex is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not an impus.\n\n", + "Assume Alex is a grimpus.", + "Alex is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a grimpus.\n\n", + "Alex is not an impus and Alex is not a grimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a gorpus or a vumpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a vumpus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a vumpus.", + "Fae is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a vumpus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a gorpus.\n\n", + "Fae is not a vumpus and Fae is not a gorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a zumpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a zumpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a zumpus and Polly is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or an impus is a jompus. Everything that is a grimpus or an impus is a numpus. Everything that is a tumpus or a lempus is a numpus. Wren is not a rompus. Wren is not a numpus.", + "query": "Prove: Wren is not an impus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a grimpus.\n\n", + "Wren is not an impus and Wren is not a grimpus." + ] + } + }, + "example17": { + "in_context_example0": { + "question": "Everything that is a shumpus or an impus is a grimpus. Stella is not a grimpus.", + "query": "Prove: Stella is not an impus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is an impus.", + "Stella is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not an impus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a shumpus.\n\n", + "Stella is not an impus and Stella is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a numpus is a yumpus. Rex is not a yumpus.", + "query": "Prove: Rex is not a numpus and Rex is not a jompus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a jompus.", + "Rex is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a jompus.\n\n", + "Rex is not a numpus and Rex is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a numpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a numpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a lempus.\n\n", + "Sam is not a numpus and Sam is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a numpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a numpus and Wren is not an impus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is an impus or a numpus.", + "Everything that is an impus or a numpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is an impus.", + "Wren is an impus or a numpus.", + "Everything that is an impus or a numpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not an impus.\n\n", + "Wren is not a numpus and Wren is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a sterpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a rompus.\n\n", + "Sam is not a sterpus and Sam is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lorpus or a gorpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a gorpus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a lorpus.\n\n", + "Wren is not a gorpus and Wren is not a lorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a jompus is a vumpus. Max is not a vumpus.", + "query": "Prove: Max is not a jompus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a jompus.", + "Max is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a jompus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a lempus.\n\n", + "Max is not a jompus and Max is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a vumpus or a grimpus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a grimpus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a vumpus.\n\n", + "Sally is not a grimpus and Sally is not a vumpus." + ] + }, + "test_example": { + "question": "Everything that is a dumpus or a numpus is a grimpus. Everything that is a wumpus or an impus is a jompus. Everything that is a dumpus or a numpus is a jompus. Wren is not a lempus. Wren is not a jompus.", + "query": "Prove: Wren is not a numpus and Wren is not a dumpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a dumpus.", + "Wren is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a dumpus.\n\n", + "Wren is not a numpus and Wren is not a dumpus." + ] + } + }, + "example18": { + "in_context_example0": { + "question": "Everything that is a zumpus or a lorpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a lorpus and Sam is not a zumpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a zumpus.", + "Sam is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a zumpus.\n\n", + "Sam is not a lorpus and Sam is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a gorpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a gorpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a gorpus and Fae is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a jompus is a lempus. Rex is not a lempus.", + "query": "Prove: Rex is not a jompus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a brimpus.\n\n", + "Rex is not a jompus and Rex is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a brimpus is a lempus. Fae is not a lempus.", + "query": "Prove: Fae is not a brimpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a brimpus.", + "Fae is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a brimpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a numpus.\n\n", + "Fae is not a brimpus and Fae is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a dumpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a tumpus or a dumpus.", + "Everything that is a tumpus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a dumpus.", + "Everything that is a tumpus or a dumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a tumpus.\n\n", + "Sam is not a dumpus and Sam is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a wumpus or an impus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not an impus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a wumpus.\n\n", + "Wren is not an impus and Wren is not a wumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a shumpus is a yumpus. Polly is not a yumpus.", + "query": "Prove: Polly is not a shumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a shumpus and Polly is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a tumpus is a vumpus. Max is not a vumpus.", + "query": "Prove: Max is not a tumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a lempus.\n\n", + "Max is not a tumpus and Max is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a jompus is a zumpus. Everything that is a sterpus or a jompus is a vumpus. Everything that is a wumpus or a dumpus is a vumpus. Rex is not a vumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a jompus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a jompus and Rex is not a sterpus." + ] + } + }, + "example19": { + "in_context_example0": { + "question": "Everything that is a jompus or a grimpus is a shumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a jompus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a jompus.", + "Rex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a jompus.\n\n", + "Rex is not a grimpus and Rex is not a jompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a brimpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a brimpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a yumpus.\n\n", + "Sam is not a brimpus and Sam is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or an impus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not an impus and Fae is not a yumpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a yumpus.", + "Fae is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a yumpus.\n\n", + "Fae is not an impus and Fae is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a jompus is a dumpus. Wren is not a dumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a tumpus.\n\n", + "Wren is not a jompus and Wren is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a yumpus or a gorpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a gorpus and Rex is not a yumpus.", + "chain_of_thought": [ + "Assume Rex is a gorpus.", + "Rex is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a gorpus.\n\n", + "Assume Rex is a yumpus.", + "Rex is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a yumpus.\n\n", + "Rex is not a gorpus and Rex is not a yumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a vumpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a vumpus and Wren is not a dumpus.", + "chain_of_thought": [ + "Assume Wren is a vumpus.", + "Wren is a dumpus or a vumpus.", + "Everything that is a dumpus or a vumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a vumpus.\n\n", + "Assume Wren is a dumpus.", + "Wren is a dumpus or a vumpus.", + "Everything that is a dumpus or a vumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a dumpus.\n\n", + "Wren is not a vumpus and Wren is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a shumpus is a grimpus. Polly is not a grimpus.", + "query": "Prove: Polly is not a shumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a shumpus and Polly is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a jompus is a lorpus. Wren is not a lorpus.", + "query": "Prove: Wren is not a jompus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a brimpus.\n\n", + "Wren is not a jompus and Wren is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a shumpus is a lorpus. Everything that is a dumpus or a yumpus is a gorpus. Everything that is an impus or a shumpus is a gorpus. Sam is not a grimpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a shumpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not an impus.\n\n", + "Sam is not a shumpus and Sam is not an impus." + ] + } + }, + "example20": { + "in_context_example0": { + "question": "Everything that is a dumpus or a zumpus is a brimpus. Stella is not a brimpus.", + "query": "Prove: Stella is not a zumpus and Stella is not a dumpus.", + "chain_of_thought": [ + "Assume Stella is a zumpus.", + "Stella is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a zumpus.\n\n", + "Assume Stella is a dumpus.", + "Stella is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a dumpus.\n\n", + "Stella is not a zumpus and Stella is not a dumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or a zumpus is a numpus. Max is not a numpus.", + "query": "Prove: Max is not a zumpus and Max is not a brimpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a brimpus.", + "Max is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a brimpus.\n\n", + "Max is not a zumpus and Max is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a vumpus is a gorpus. Alex is not a gorpus.", + "query": "Prove: Alex is not a vumpus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a vumpus.", + "Alex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a vumpus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a shumpus.\n\n", + "Alex is not a vumpus and Alex is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a brimpus or a wumpus is a lorpus. Sally is not a lorpus.", + "query": "Prove: Sally is not a wumpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a wumpus.", + "Sally is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a wumpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a brimpus.\n\n", + "Sally is not a wumpus and Sally is not a brimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a rompus is a lorpus. Alex is not a lorpus.", + "query": "Prove: Alex is not a rompus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a rompus and Alex is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a zumpus or a yumpus is an impus. Polly is not an impus.", + "query": "Prove: Polly is not a yumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a zumpus.\n\n", + "Polly is not a yumpus and Polly is not a zumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a sterpus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a sterpus and Max is not a shumpus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a sterpus.\n\n", + "Assume Max is a shumpus.", + "Max is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a shumpus.\n\n", + "Max is not a sterpus and Max is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lorpus or a sterpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a sterpus and Sam is not a lorpus." + ] + }, + "test_example": { + "question": "Everything that is a lempus or a dumpus is a tumpus. Everything that is a numpus or a gorpus is an impus. Everything that is a lempus or a dumpus is an impus. Max is not an impus. Max is not a zumpus.", + "query": "Prove: Max is not a dumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a dumpus.", + "Max is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a dumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a lempus.\n\n", + "Max is not a dumpus and Max is not a lempus." + ] + } + }, + "example21": { + "in_context_example0": { + "question": "Everything that is a sterpus or an impus is a lempus. Fae is not a lempus.", + "query": "Prove: Fae is not an impus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not an impus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a sterpus.\n\n", + "Fae is not an impus and Fae is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or a lorpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a lorpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a lorpus.", + "Polly is a brimpus or a lorpus.", + "Everything that is a brimpus or a lorpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a lorpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a lorpus.", + "Everything that is a brimpus or a lorpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a lorpus and Polly is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a jompus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a jompus and Sam is not a zumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a zumpus.", + "Sam is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a zumpus.\n\n", + "Sam is not a jompus and Sam is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a gorpus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a gorpus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not an impus.\n\n", + "Stella is not a gorpus and Stella is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a zumpus or a yumpus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a yumpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a yumpus.", + "Wren is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a yumpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a yumpus.", + "Everything that is a zumpus or a yumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a yumpus and Wren is not a zumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a jompus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a jompus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is an impus or a jompus.", + "Everything that is an impus or a jompus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a jompus.", + "Everything that is an impus or a jompus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not an impus.\n\n", + "Stella is not a jompus and Stella is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a zumpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a vumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a vumpus.", + "Sam is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a vumpus.\n\n", + "Sam is not a zumpus and Sam is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a lempus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a lempus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is an impus or a lempus.", + "Everything that is an impus or a lempus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a lempus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a lempus.", + "Everything that is an impus or a lempus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not an impus.\n\n", + "Max is not a lempus and Max is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a numpus is a rompus. Everything that is a brimpus or a numpus is a dumpus. Everything that is a tumpus or a gorpus is a dumpus. Sam is not a wumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a numpus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a brimpus or a numpus.", + "Everything that is a brimpus or a numpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a numpus.", + "Everything that is a brimpus or a numpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a brimpus.\n\n", + "Sam is not a numpus and Sam is not a brimpus." + ] + } + }, + "example22": { + "in_context_example0": { + "question": "Everything that is a zumpus or a dumpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a dumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a dumpus and Polly is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a zumpus is a jompus. Alex is not a jompus.", + "query": "Prove: Alex is not a zumpus and Alex is not a yumpus.", + "chain_of_thought": [ + "Assume Alex is a zumpus.", + "Alex is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a zumpus.\n\n", + "Assume Alex is a yumpus.", + "Alex is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a yumpus.\n\n", + "Alex is not a zumpus and Alex is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a sterpus or a jompus is a dumpus. Rex is not a dumpus.", + "query": "Prove: Rex is not a jompus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a jompus and Rex is not a sterpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a shumpus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a shumpus and Max is not a jompus.", + "chain_of_thought": [ + "Assume Max is a shumpus.", + "Max is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a shumpus.\n\n", + "Assume Max is a jompus.", + "Max is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a jompus.\n\n", + "Max is not a shumpus and Max is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a brimpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a grimpus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a grimpus.", + "Rex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a grimpus.\n\n", + "Rex is not a brimpus and Rex is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a grimpus or a tumpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a tumpus and Wren is not a grimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a lorpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a lorpus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a lorpus.", + "Rex is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a lorpus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a zumpus.\n\n", + "Rex is not a lorpus and Rex is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a vumpus is a lorpus. Stella is not a lorpus.", + "query": "Prove: Stella is not a vumpus and Stella is not a sterpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a sterpus.", + "Stella is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a sterpus.\n\n", + "Stella is not a vumpus and Stella is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is a shumpus or a tumpus is a rompus. Everything that is a zumpus or a wumpus is a yumpus. Everything that is a shumpus or a tumpus is a yumpus. Fae is not a brimpus. Fae is not a yumpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a tumpus and Fae is not a shumpus." + ] + } + }, + "example23": { + "in_context_example0": { + "question": "Everything that is a grimpus or a jompus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a jompus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a jompus and Wren is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a vumpus or a lorpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a lorpus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a lorpus.", + "Fae is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a lorpus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a lorpus and Fae is not a vumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a gorpus or a yumpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a yumpus and Rex is not a gorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a jompus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a jompus and Fae is not an impus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is an impus or a jompus.", + "Everything that is an impus or a jompus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is an impus.", + "Fae is an impus or a jompus.", + "Everything that is an impus or a jompus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not an impus.\n\n", + "Fae is not a jompus and Fae is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a jompus or an impus is a brimpus. Polly is not a brimpus.", + "query": "Prove: Polly is not an impus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a jompus or an impus.", + "Everything that is a jompus or an impus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or an impus.", + "Everything that is a jompus or an impus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a jompus.\n\n", + "Polly is not an impus and Polly is not a jompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a brimpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a brimpus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a brimpus.", + "Stella is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a brimpus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a vumpus.\n\n", + "Stella is not a brimpus and Stella is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a wumpus or an impus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not an impus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not an impus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a wumpus.\n\n", + "Wren is not an impus and Wren is not a wumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a zumpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a zumpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a zumpus.", + "Sally is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a zumpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a brimpus.\n\n", + "Sally is not a zumpus and Sally is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a grimpus is a dumpus. Everything that is an impus or a grimpus is a numpus. Everything that is a brimpus or a jompus is a numpus. Alex is not a shumpus. Alex is not a numpus.", + "query": "Prove: Alex is not a grimpus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not an impus.\n\n", + "Alex is not a grimpus and Alex is not an impus." + ] + } + }, + "example24": { + "in_context_example0": { + "question": "Everything that is a lempus or a wumpus is a gorpus. Max is not a gorpus.", + "query": "Prove: Max is not a wumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a wumpus.", + "Max is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a wumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a lempus.\n\n", + "Max is not a wumpus and Max is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a wumpus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a wumpus and Alex is not a dumpus.", + "chain_of_thought": [ + "Assume Alex is a wumpus.", + "Alex is a dumpus or a wumpus.", + "Everything that is a dumpus or a wumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a wumpus.\n\n", + "Assume Alex is a dumpus.", + "Alex is a dumpus or a wumpus.", + "Everything that is a dumpus or a wumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a dumpus.\n\n", + "Alex is not a wumpus and Alex is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a jompus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a jompus and Sam is not a zumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a zumpus.", + "Sam is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a zumpus.\n\n", + "Sam is not a jompus and Sam is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a numpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a numpus and Sally is not a lorpus.", + "chain_of_thought": [ + "Assume Sally is a numpus.", + "Sally is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a numpus.\n\n", + "Assume Sally is a lorpus.", + "Sally is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a lorpus.\n\n", + "Sally is not a numpus and Sally is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a sterpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a sterpus and Polly is not a rompus.", + "chain_of_thought": [ + "Assume Polly is a sterpus.", + "Polly is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a sterpus.\n\n", + "Assume Polly is a rompus.", + "Polly is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a rompus.\n\n", + "Polly is not a sterpus and Polly is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a sterpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a shumpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a shumpus.", + "Sam is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a shumpus.\n\n", + "Sam is not a sterpus and Sam is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a tumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a tumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a tumpus.", + "Sam is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a tumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a tumpus and Sam is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a rompus or a grimpus is a yumpus. Stella is not a yumpus.", + "query": "Prove: Stella is not a grimpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a grimpus and Stella is not a rompus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a vumpus is a brimpus. Everything that is a dumpus or a rompus is a lempus. Everything that is a dumpus or a rompus is a brimpus. Alex is not a brimpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a rompus and Alex is not a dumpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a dumpus.", + "Alex is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a dumpus.\n\n", + "Alex is not a rompus and Alex is not a dumpus." + ] + } + }, + "example25": { + "in_context_example0": { + "question": "Everything that is a rompus or a lorpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a rompus or a lorpus.", + "Everything that is a rompus or a lorpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a lorpus.", + "Everything that is a rompus or a lorpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a rompus.\n\n", + "Wren is not a lorpus and Wren is not a rompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a jompus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not a jompus and Max is not a dumpus.", + "chain_of_thought": [ + "Assume Max is a jompus.", + "Max is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a jompus.\n\n", + "Assume Max is a dumpus.", + "Max is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a dumpus.\n\n", + "Max is not a jompus and Max is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a brimpus is a jompus. Wren is not a jompus.", + "query": "Prove: Wren is not a brimpus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is a brimpus.", + "Wren is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a brimpus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a wumpus.\n\n", + "Wren is not a brimpus and Wren is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a yumpus is a rompus. Alex is not a rompus.", + "query": "Prove: Alex is not a yumpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a yumpus.", + "Alex is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a yumpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a tumpus.\n\n", + "Alex is not a yumpus and Alex is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lorpus or a wumpus is a zumpus. Max is not a zumpus.", + "query": "Prove: Max is not a wumpus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a wumpus.", + "Max is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a zumpus.", + "Max is a zumpus.", + "This contradicts with Max is not a zumpus.", + "Max is not a wumpus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a zumpus.", + "Max is a zumpus.", + "This contradicts with Max is not a zumpus.", + "Max is not a lorpus.\n\n", + "Max is not a wumpus and Max is not a lorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a grimpus or a sterpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a grimpus or a sterpus.", + "Everything that is a grimpus or a sterpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a sterpus.", + "Everything that is a grimpus or a sterpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a sterpus and Stella is not a grimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a sterpus or a gorpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a gorpus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is a gorpus.", + "Sally is a sterpus or a gorpus.", + "Everything that is a sterpus or a gorpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a gorpus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or a gorpus.", + "Everything that is a sterpus or a gorpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a sterpus.\n\n", + "Sally is not a gorpus and Sally is not a sterpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a jompus is a grimpus. Alex is not a grimpus.", + "query": "Prove: Alex is not a jompus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a gorpus.\n\n", + "Alex is not a jompus and Alex is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a jompus or a zumpus is a grimpus. Everything that is a yumpus or a lorpus is an impus. Everything that is a jompus or a zumpus is an impus. Fae is not an impus. Fae is not a sterpus.", + "query": "Prove: Fae is not a zumpus and Fae is not a jompus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a jompus or a zumpus.", + "Everything that is a jompus or a zumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a jompus.", + "Fae is a jompus or a zumpus.", + "Everything that is a jompus or a zumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a jompus.\n\n", + "Fae is not a zumpus and Fae is not a jompus." + ] + } + }, + "example26": { + "in_context_example0": { + "question": "Everything that is a tumpus or a lempus is a jompus. Sam is not a jompus.", + "query": "Prove: Sam is not a lempus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a tumpus.\n\n", + "Sam is not a lempus and Sam is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a lempus is a jompus. Polly is not a jompus.", + "query": "Prove: Polly is not a lempus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is an impus or a lempus.", + "Everything that is an impus or a lempus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a lempus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a lempus.", + "Everything that is an impus or a lempus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not an impus.\n\n", + "Polly is not a lempus and Polly is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a vumpus or a zumpus is a gorpus. Rex is not a gorpus.", + "query": "Prove: Rex is not a zumpus and Rex is not a vumpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a vumpus.", + "Rex is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not a vumpus.\n\n", + "Rex is not a zumpus and Rex is not a vumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a gorpus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a gorpus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a gorpus and Wren is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a brimpus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a brimpus and Alex is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a numpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a numpus and Rex is not an impus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is an impus or a numpus.", + "Everything that is an impus or a numpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a numpus.\n\n", + "Assume Rex is an impus.", + "Rex is an impus or a numpus.", + "Everything that is an impus or a numpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not an impus.\n\n", + "Rex is not a numpus and Rex is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a gorpus is a lempus. Fae is not a lempus.", + "query": "Prove: Fae is not a gorpus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a vumpus.\n\n", + "Fae is not a gorpus and Fae is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a sterpus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a dumpus or a sterpus.", + "Everything that is a dumpus or a sterpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a sterpus.", + "Everything that is a dumpus or a sterpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a dumpus.\n\n", + "Sam is not a sterpus and Sam is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a jompus or a brimpus is a rompus. Everything that is a dumpus or an impus is a rompus. Everything that is a jompus or a brimpus is a tumpus. Alex is not a rompus. Alex is not a numpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a jompus.\n\n", + "Alex is not a brimpus and Alex is not a jompus." + ] + } + }, + "example27": { + "in_context_example0": { + "question": "Everything that is a numpus or a shumpus is an impus. Wren is not an impus.", + "query": "Prove: Wren is not a shumpus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a numpus.\n\n", + "Wren is not a shumpus and Wren is not a numpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lempus or a tumpus is a sterpus. Max is not a sterpus.", + "query": "Prove: Max is not a tumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a lempus.\n\n", + "Max is not a tumpus and Max is not a lempus." + ] + }, + "in_context_example2": { + "question": "Everything that is a jompus or a vumpus is a brimpus. Stella is not a brimpus.", + "query": "Prove: Stella is not a vumpus and Stella is not a jompus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a jompus or a vumpus.", + "Everything that is a jompus or a vumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a jompus.", + "Stella is a jompus or a vumpus.", + "Everything that is a jompus or a vumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a jompus.\n\n", + "Stella is not a vumpus and Stella is not a jompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a dumpus or a jompus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a dumpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a dumpus.", + "Stella is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a dumpus.\n\n", + "Stella is not a jompus and Stella is not a dumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a numpus or a yumpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a yumpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a yumpus.", + "Sam is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a yumpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a numpus.\n\n", + "Sam is not a yumpus and Sam is not a numpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lorpus or a rompus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a rompus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a rompus.", + "Wren is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a rompus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a rompus and Wren is not a lorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a wumpus or a sterpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a sterpus and Sam is not a wumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lorpus or a brimpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a brimpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a brimpus and Sam is not a lorpus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or an impus is a vumpus. Everything that is a wumpus or a tumpus is a brimpus. Everything that is a zumpus or an impus is a brimpus. Rex is not a brimpus. Rex is not a sterpus.", + "query": "Prove: Rex is not an impus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is an impus.", + "Rex is a zumpus or an impus.", + "Everything that is a zumpus or an impus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not an impus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or an impus.", + "Everything that is a zumpus or an impus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a zumpus.\n\n", + "Rex is not an impus and Rex is not a zumpus." + ] + } + }, + "example28": { + "in_context_example0": { + "question": "Everything that is a sterpus or a yumpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a sterpus or a yumpus.", + "Everything that is a sterpus or a yumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a yumpus.", + "Everything that is a sterpus or a yumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a yumpus and Fae is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or an impus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not an impus and Sally is not a rompus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a rompus or an impus.", + "Everything that is a rompus or an impus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not an impus.\n\n", + "Assume Sally is a rompus.", + "Sally is a rompus or an impus.", + "Everything that is a rompus or an impus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a rompus.\n\n", + "Sally is not an impus and Sally is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a brimpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a brimpus and Sally is not a lempus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a lempus.", + "Sally is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a lempus.\n\n", + "Sally is not a brimpus and Sally is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a lorpus is a grimpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a lorpus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a lorpus.", + "Fae is a gorpus or a lorpus.", + "Everything that is a gorpus or a lorpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a lorpus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a lorpus.", + "Everything that is a gorpus or a lorpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a gorpus.\n\n", + "Fae is not a lorpus and Fae is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a brimpus or a gorpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a gorpus and Polly is not a brimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a zumpus is a numpus. Sam is not a numpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a lempus.\n\n", + "Sam is not a zumpus and Sam is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a grimpus is a numpus. Max is not a numpus.", + "query": "Prove: Max is not a grimpus and Max is not a zumpus.", + "chain_of_thought": [ + "Assume Max is a grimpus.", + "Max is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a grimpus.\n\n", + "Assume Max is a zumpus.", + "Max is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a zumpus.\n\n", + "Max is not a grimpus and Max is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a zumpus is a lempus. Max is not a lempus.", + "query": "Prove: Max is not a zumpus and Max is not a yumpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a zumpus.\n\n", + "Assume Max is a yumpus.", + "Max is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a yumpus.\n\n", + "Max is not a zumpus and Max is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or a wumpus is a dumpus. Everything that is a zumpus or a wumpus is a jompus. Everything that is a yumpus or a grimpus is a dumpus. Polly is not a tumpus. Polly is not a dumpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a zumpus or a wumpus.", + "Everything that is a zumpus or a wumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a wumpus.", + "Everything that is a zumpus or a wumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a wumpus and Polly is not a zumpus." + ] + } + }, + "example29": { + "in_context_example0": { + "question": "Everything that is a tumpus or a sterpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a sterpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a sterpus.", + "Wren is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a sterpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a tumpus.\n\n", + "Wren is not a sterpus and Wren is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a dumpus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a dumpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a dumpus.", + "Alex is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a dumpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a jompus.\n\n", + "Alex is not a dumpus and Alex is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a yumpus is an impus. Fae is not an impus.", + "query": "Prove: Fae is not a yumpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a grimpus or a yumpus.", + "Everything that is a grimpus or a yumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a yumpus.", + "Everything that is a grimpus or a yumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a grimpus.\n\n", + "Fae is not a yumpus and Fae is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a wumpus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a wumpus and Sam is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a numpus or a grimpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a numpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a numpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a numpus.\n\n", + "Rex is not a grimpus and Rex is not a numpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a vumpus is a wumpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a vumpus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a vumpus.", + "Alex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a vumpus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a shumpus.\n\n", + "Alex is not a vumpus and Alex is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a dumpus or a tumpus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a tumpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a tumpus.", + "Sam is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a tumpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a dumpus.\n\n", + "Sam is not a tumpus and Sam is not a dumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a lempus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a lempus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a lempus.", + "Stella is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a lempus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a yumpus.\n\n", + "Stella is not a lempus and Stella is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a shumpus or a numpus is a lorpus. Everything that is a gorpus or a brimpus is a lorpus. Everything that is a gorpus or a brimpus is a grimpus. Rex is not a lorpus. Rex is not a dumpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a gorpus or a brimpus.", + "Everything that is a gorpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a brimpus.", + "Everything that is a gorpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a brimpus and Rex is not a gorpus." + ] + } + }, + "example30": { + "in_context_example0": { + "question": "Everything that is a brimpus or a tumpus is a grimpus. Stella is not a grimpus.", + "query": "Prove: Stella is not a tumpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a tumpus and Stella is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a wumpus is a yumpus. Alex is not a yumpus.", + "query": "Prove: Alex is not a wumpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a wumpus.", + "Alex is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a yumpus.", + "Alex is a yumpus.", + "This contradicts with Alex is not a yumpus.", + "Alex is not a wumpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a yumpus.", + "Alex is a yumpus.", + "This contradicts with Alex is not a yumpus.", + "Alex is not a jompus.\n\n", + "Alex is not a wumpus and Alex is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a yumpus is a jompus. Alex is not a jompus.", + "query": "Prove: Alex is not a yumpus and Alex is not a lempus.", + "chain_of_thought": [ + "Assume Alex is a yumpus.", + "Alex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a yumpus.\n\n", + "Assume Alex is a lempus.", + "Alex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a lempus.\n\n", + "Alex is not a yumpus and Alex is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a shumpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a shumpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a shumpus.", + "Fae is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a shumpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a grimpus.\n\n", + "Fae is not a shumpus and Fae is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a numpus or an impus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not an impus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a numpus or an impus.", + "Everything that is a numpus or an impus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or an impus.", + "Everything that is a numpus or an impus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a numpus.\n\n", + "Wren is not an impus and Wren is not a numpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a wumpus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a wumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a wumpus and Fae is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a tumpus or an impus is a vumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not an impus and Fae is not a tumpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a tumpus.", + "Fae is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a tumpus.\n\n", + "Fae is not an impus and Fae is not a tumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a zumpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a zumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a lempus.\n\n", + "Polly is not a zumpus and Polly is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a zumpus is a wumpus. Everything that is a sterpus or a shumpus is a brimpus. Everything that is a lorpus or a zumpus is a brimpus. Wren is not a brimpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a zumpus and Wren is not a lorpus." + ] + } + }, + "example31": { + "in_context_example0": { + "question": "Everything that is a lorpus or a jompus is an impus. Max is not an impus.", + "query": "Prove: Max is not a jompus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a jompus.", + "Max is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a jompus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a lorpus.\n\n", + "Max is not a jompus and Max is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a grimpus is a brimpus. Polly is not a brimpus.", + "query": "Prove: Polly is not a grimpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a grimpus.", + "Polly is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a grimpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a brimpus.", + "Polly is a brimpus.", + "This contradicts with Polly is not a brimpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a grimpus and Polly is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is an impus or a tumpus is a shumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a tumpus and Rex is not an impus.", + "chain_of_thought": [ + "Assume Rex is a tumpus.", + "Rex is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a tumpus.\n\n", + "Assume Rex is an impus.", + "Rex is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not an impus.\n\n", + "Rex is not a tumpus and Rex is not an impus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a zumpus is a wumpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a zumpus and Alex is not a yumpus.", + "chain_of_thought": [ + "Assume Alex is a zumpus.", + "Alex is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a zumpus.\n\n", + "Assume Alex is a yumpus.", + "Alex is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a yumpus.\n\n", + "Alex is not a zumpus and Alex is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a vumpus is a shumpus. Stella is not a shumpus.", + "query": "Prove: Stella is not a vumpus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a vumpus and Stella is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a zumpus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a brimpus.\n\n", + "Sam is not a zumpus and Sam is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a numpus or a gorpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a gorpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a gorpus.", + "Sam is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a gorpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a numpus.\n\n", + "Sam is not a gorpus and Sam is not a numpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a wumpus is a grimpus. Stella is not a grimpus.", + "query": "Prove: Stella is not a wumpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a wumpus.", + "Stella is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a wumpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a wumpus and Stella is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a lempus or a vumpus is a lorpus. Everything that is a zumpus or a numpus is a lorpus. Everything that is a zumpus or a numpus is a dumpus. Polly is not a lorpus. Polly is not a rompus.", + "query": "Prove: Polly is not a numpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a numpus.", + "Polly is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a numpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a numpus and Polly is not a zumpus." + ] + } + }, + "example32": { + "in_context_example0": { + "question": "Everything that is a brimpus or a vumpus is a dumpus. Stella is not a dumpus.", + "query": "Prove: Stella is not a vumpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a dumpus.", + "Stella is a dumpus.", + "This contradicts with Stella is not a dumpus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a dumpus.", + "Stella is a dumpus.", + "This contradicts with Stella is not a dumpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a vumpus and Stella is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a vumpus or a brimpus is a yumpus. Alex is not a yumpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a vumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a yumpus.", + "Alex is a yumpus.", + "This contradicts with Alex is not a yumpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a vumpus.", + "Alex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a yumpus.", + "Alex is a yumpus.", + "This contradicts with Alex is not a yumpus.", + "Alex is not a vumpus.\n\n", + "Alex is not a brimpus and Alex is not a vumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a vumpus or a jompus is a grimpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a jompus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a jompus and Fae is not a vumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a wumpus or a dumpus is a jompus. Max is not a jompus.", + "query": "Prove: Max is not a dumpus and Max is not a wumpus.", + "chain_of_thought": [ + "Assume Max is a dumpus.", + "Max is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a dumpus.\n\n", + "Assume Max is a wumpus.", + "Max is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a wumpus.\n\n", + "Max is not a dumpus and Max is not a wumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a lorpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a lorpus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a grimpus.\n\n", + "Sally is not a lorpus and Sally is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a jompus or a numpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a numpus and Rex is not a jompus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a jompus.", + "Rex is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a jompus.\n\n", + "Rex is not a numpus and Rex is not a jompus." + ] + }, + "in_context_example6": { + "question": "Everything that is a sterpus or a zumpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a zumpus and Max is not a sterpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a sterpus or a zumpus.", + "Everything that is a sterpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a sterpus.", + "Max is a sterpus or a zumpus.", + "Everything that is a sterpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a sterpus.\n\n", + "Max is not a zumpus and Max is not a sterpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a jompus or a shumpus is a wumpus. Sam is not a wumpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a jompus.\n\n", + "Sam is not a shumpus and Sam is not a jompus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a gorpus is a lempus. Everything that is a dumpus or a shumpus is a lempus. Everything that is a lorpus or a gorpus is a grimpus. Alex is not a lempus. Alex is not a numpus.", + "query": "Prove: Alex is not a gorpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a lorpus.\n\n", + "Alex is not a gorpus and Alex is not a lorpus." + ] + } + }, + "example33": { + "in_context_example0": { + "question": "Everything that is a tumpus or a grimpus is a wumpus. Wren is not a wumpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a tumpus or a grimpus.", + "Everything that is a tumpus or a grimpus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a grimpus.", + "Everything that is a tumpus or a grimpus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a tumpus.\n\n", + "Wren is not a grimpus and Wren is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a lorpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a dumpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a dumpus.", + "Wren is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a dumpus.\n\n", + "Wren is not a lorpus and Wren is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a grimpus is a shumpus. Stella is not a shumpus.", + "query": "Prove: Stella is not a grimpus and Stella is not a numpus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a numpus.", + "Stella is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a numpus.\n\n", + "Stella is not a grimpus and Stella is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a zumpus is a numpus. Rex is not a numpus.", + "query": "Prove: Rex is not a zumpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a zumpus and Rex is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a rompus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a rompus and Alex is not a wumpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a wumpus.", + "Alex is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a wumpus.\n\n", + "Alex is not a rompus and Alex is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a gorpus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a gorpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a gorpus.", + "Sally is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a gorpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not an impus.\n\n", + "Sally is not a gorpus and Sally is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or an impus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not an impus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is an impus.", + "Max is a vumpus or an impus.", + "Everything that is a vumpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not an impus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or an impus.", + "Everything that is a vumpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a vumpus.\n\n", + "Max is not an impus and Max is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a lempus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a lempus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a grimpus.\n\n", + "Sally is not a lempus and Sally is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a numpus is a jompus. Everything that is a zumpus or a vumpus is a lempus. Everything that is a zumpus or a vumpus is a jompus. Max is not a jompus. Max is not a gorpus.", + "query": "Prove: Max is not a vumpus and Max is not a zumpus.", + "chain_of_thought": [ + "Assume Max is a vumpus.", + "Max is a zumpus or a vumpus.", + "Everything that is a zumpus or a vumpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a vumpus.\n\n", + "Assume Max is a zumpus.", + "Max is a zumpus or a vumpus.", + "Everything that is a zumpus or a vumpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a zumpus.\n\n", + "Max is not a vumpus and Max is not a zumpus." + ] + } + }, + "example34": { + "in_context_example0": { + "question": "Everything that is an impus or a wumpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a wumpus and Wren is not an impus.", + "chain_of_thought": [ + "Assume Wren is a wumpus.", + "Wren is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a wumpus.\n\n", + "Assume Wren is an impus.", + "Wren is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not an impus.\n\n", + "Wren is not a wumpus and Wren is not an impus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a shumpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a shumpus and Sally is not a jompus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is a jompus.", + "Sally is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a jompus.\n\n", + "Sally is not a shumpus and Sally is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a sterpus or a dumpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a dumpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a dumpus.", + "Wren is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a dumpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a sterpus.\n\n", + "Wren is not a dumpus and Wren is not a sterpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a jompus is a dumpus. Wren is not a dumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a gorpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a gorpus.", + "Wren is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a gorpus.\n\n", + "Wren is not a jompus and Wren is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a yumpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a lempus.\n\n", + "Rex is not a yumpus and Rex is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a rompus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a rompus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a sterpus or a rompus.", + "Everything that is a sterpus or a rompus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a rompus.", + "Everything that is a sterpus or a rompus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a rompus and Sam is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a tumpus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a tumpus and Alex is not a lempus.", + "chain_of_thought": [ + "Assume Alex is a tumpus.", + "Alex is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a tumpus.\n\n", + "Assume Alex is a lempus.", + "Alex is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a lempus.\n\n", + "Alex is not a tumpus and Alex is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a vumpus is a lempus. Stella is not a lempus.", + "query": "Prove: Stella is not a vumpus and Stella is not a sterpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a sterpus.", + "Stella is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a sterpus.\n\n", + "Stella is not a vumpus and Stella is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or a vumpus is a numpus. Everything that is a gorpus or a yumpus is a dumpus. Everything that is a grimpus or a vumpus is a dumpus. Sally is not a lorpus. Sally is not a dumpus.", + "query": "Prove: Sally is not a vumpus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a dumpus.", + "Sally is a dumpus.", + "This contradicts with Sally is not a dumpus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a dumpus.", + "Sally is a dumpus.", + "This contradicts with Sally is not a dumpus.", + "Sally is not a grimpus.\n\n", + "Sally is not a vumpus and Sally is not a grimpus." + ] + } + }, + "example35": { + "in_context_example0": { + "question": "Everything that is a shumpus or a zumpus is a sterpus. Stella is not a sterpus.", + "query": "Prove: Stella is not a zumpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a zumpus.", + "Stella is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a zumpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a zumpus and Stella is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or an impus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not an impus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a brimpus.\n\n", + "Sam is not an impus and Sam is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a rompus is a numpus. Wren is not a numpus.", + "query": "Prove: Wren is not a rompus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a rompus.", + "Wren is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a rompus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a rompus and Wren is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lempus or a lorpus is a grimpus. Wren is not a grimpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a lempus or a lorpus.", + "Everything that is a lempus or a lorpus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a lorpus.", + "Everything that is a lempus or a lorpus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a lempus.\n\n", + "Wren is not a lorpus and Wren is not a lempus." + ] + }, + "in_context_example4": { + "question": "Everything that is a zumpus or a grimpus is a dumpus. Fae is not a dumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a zumpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a zumpus.", + "Fae is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a zumpus.\n\n", + "Fae is not a grimpus and Fae is not a zumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a gorpus or a zumpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a zumpus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a gorpus.\n\n", + "Max is not a zumpus and Max is not a gorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a shumpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a shumpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a shumpus.", + "Everything that is a jompus or a shumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a jompus.\n\n", + "Alex is not a shumpus and Alex is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a shumpus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a shumpus and Stella is not a dumpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a dumpus or a shumpus.", + "Everything that is a dumpus or a shumpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a dumpus.", + "Stella is a dumpus or a shumpus.", + "Everything that is a dumpus or a shumpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a dumpus.\n\n", + "Stella is not a shumpus and Stella is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a lorpus is an impus. Everything that is a sterpus or a vumpus is a tumpus. Everything that is a yumpus or a lorpus is a tumpus. Rex is not a jompus. Rex is not a tumpus.", + "query": "Prove: Rex is not a lorpus and Rex is not a yumpus.", + "chain_of_thought": [ + "Assume Rex is a lorpus.", + "Rex is a yumpus or a lorpus.", + "Everything that is a yumpus or a lorpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a lorpus.\n\n", + "Assume Rex is a yumpus.", + "Rex is a yumpus or a lorpus.", + "Everything that is a yumpus or a lorpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a yumpus.\n\n", + "Rex is not a lorpus and Rex is not a yumpus." + ] + } + }, + "example36": { + "in_context_example0": { + "question": "Everything that is a lorpus or a shumpus is a vumpus. Alex is not a vumpus.", + "query": "Prove: Alex is not a shumpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a lorpus.\n\n", + "Alex is not a shumpus and Alex is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a dumpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a dumpus and Fae is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or a jompus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a jompus and Wren is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a zumpus or a numpus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a numpus and Max is not a zumpus.", + "chain_of_thought": [ + "Assume Max is a numpus.", + "Max is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a numpus.\n\n", + "Assume Max is a zumpus.", + "Max is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a zumpus.\n\n", + "Max is not a numpus and Max is not a zumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a dumpus or an impus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not an impus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a dumpus or an impus.", + "Everything that is a dumpus or an impus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or an impus.", + "Everything that is a dumpus or an impus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a dumpus.\n\n", + "Sam is not an impus and Sam is not a dumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a gorpus or a shumpus is a vumpus. Sam is not a vumpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a shumpus and Sam is not a gorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a tumpus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a jompus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a jompus.", + "Fae is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a jompus.\n\n", + "Fae is not a tumpus and Fae is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a jompus or a brimpus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a brimpus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is a brimpus.", + "Polly is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a brimpus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a jompus.\n\n", + "Polly is not a brimpus and Polly is not a jompus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a rompus is an impus. Everything that is a jompus or a shumpus is a dumpus. Everything that is a sterpus or a rompus is a dumpus. Fae is not a lorpus. Fae is not a dumpus.", + "query": "Prove: Fae is not a rompus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a rompus.", + "Fae is a sterpus or a rompus.", + "Everything that is a sterpus or a rompus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a rompus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a rompus.", + "Everything that is a sterpus or a rompus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a rompus and Fae is not a sterpus." + ] + } + }, + "example37": { + "in_context_example0": { + "question": "Everything that is a numpus or a shumpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a numpus.\n\n", + "Sam is not a shumpus and Sam is not a numpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lempus or a wumpus is a sterpus. Sally is not a sterpus.", + "query": "Prove: Sally is not a wumpus and Sally is not a lempus.", + "chain_of_thought": [ + "Assume Sally is a wumpus.", + "Sally is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a wumpus.\n\n", + "Assume Sally is a lempus.", + "Sally is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a lempus.\n\n", + "Sally is not a wumpus and Sally is not a lempus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a brimpus is a lorpus. Alex is not a lorpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a grimpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a grimpus.", + "Alex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a grimpus.\n\n", + "Alex is not a brimpus and Alex is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a gorpus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a gorpus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a gorpus and Wren is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a brimpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a brimpus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a brimpus.", + "Fae is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a brimpus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a brimpus and Fae is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a yumpus or a brimpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a brimpus and Polly is not a yumpus.", + "chain_of_thought": [ + "Assume Polly is a brimpus.", + "Polly is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a brimpus.\n\n", + "Assume Polly is a yumpus.", + "Polly is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a yumpus.\n\n", + "Polly is not a brimpus and Polly is not a yumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a numpus is a lempus. Polly is not a lempus.", + "query": "Prove: Polly is not a numpus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is a numpus.", + "Polly is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a numpus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or a numpus.", + "Everything that is a jompus or a numpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a jompus.\n\n", + "Polly is not a numpus and Polly is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a tumpus is a numpus. Fae is not a numpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a tumpus and Fae is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a brimpus is a zumpus. Everything that is a sterpus or a brimpus is a rompus. Everything that is a lorpus or an impus is a rompus. Max is not a yumpus. Max is not a rompus.", + "query": "Prove: Max is not a brimpus and Max is not a sterpus.", + "chain_of_thought": [ + "Assume Max is a brimpus.", + "Max is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a brimpus.\n\n", + "Assume Max is a sterpus.", + "Max is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a sterpus.\n\n", + "Max is not a brimpus and Max is not a sterpus." + ] + } + }, + "example38": { + "in_context_example0": { + "question": "Everything that is a lorpus or a vumpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a vumpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a vumpus.", + "Alex is a lorpus or a vumpus.", + "Everything that is a lorpus or a vumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a vumpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a vumpus.", + "Everything that is a lorpus or a vumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a lorpus.\n\n", + "Alex is not a vumpus and Alex is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a lempus is a dumpus. Rex is not a dumpus.", + "query": "Prove: Rex is not a lempus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a tumpus.\n\n", + "Rex is not a lempus and Rex is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a vumpus or a lorpus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a vumpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a vumpus.", + "Wren is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a vumpus.\n\n", + "Wren is not a lorpus and Wren is not a vumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or a yumpus is a numpus. Sally is not a numpus.", + "query": "Prove: Sally is not a yumpus and Sally is not a rompus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is a rompus or a yumpus.", + "Everything that is a rompus or a yumpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is a rompus.", + "Sally is a rompus or a yumpus.", + "Everything that is a rompus or a yumpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a rompus.\n\n", + "Sally is not a yumpus and Sally is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a vumpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a lempus.\n\n", + "Polly is not a vumpus and Polly is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a numpus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a numpus and Rex is not a dumpus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a dumpus.", + "Rex is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a dumpus.\n\n", + "Rex is not a numpus and Rex is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a gorpus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a gorpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a gorpus and Wren is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a lempus is a grimpus. Alex is not a grimpus.", + "query": "Prove: Alex is not a lempus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a sterpus.\n\n", + "Alex is not a lempus and Alex is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a rompus is a sterpus. Everything that is a tumpus or a rompus is a lorpus. Everything that is a gorpus or a brimpus is a sterpus. Alex is not a numpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a rompus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a rompus.", + "Everything that is a tumpus or a rompus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a rompus and Alex is not a tumpus." + ] + } + }, + "example39": { + "in_context_example0": { + "question": "Everything that is an impus or a wumpus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a wumpus and Rex is not an impus.", + "chain_of_thought": [ + "Assume Rex is a wumpus.", + "Rex is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a wumpus.\n\n", + "Assume Rex is an impus.", + "Rex is an impus or a wumpus.", + "Everything that is an impus or a wumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not an impus.\n\n", + "Rex is not a wumpus and Rex is not an impus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a rompus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a rompus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is a rompus.", + "Wren is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a rompus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a wumpus.\n\n", + "Wren is not a rompus and Wren is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a vumpus or a lorpus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a lorpus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a lorpus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a vumpus.\n\n", + "Max is not a lorpus and Max is not a vumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a wumpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a wumpus and Rex is not a jompus.", + "chain_of_thought": [ + "Assume Rex is a wumpus.", + "Rex is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a wumpus.\n\n", + "Assume Rex is a jompus.", + "Rex is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a jompus.\n\n", + "Rex is not a wumpus and Rex is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a dumpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a dumpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not an impus.\n\n", + "Sam is not a dumpus and Sam is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or an impus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not an impus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a numpus or an impus.", + "Everything that is a numpus or an impus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or an impus.", + "Everything that is a numpus or an impus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a numpus.\n\n", + "Polly is not an impus and Polly is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a sterpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a sterpus and Stella is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a numpus is an impus. Stella is not an impus.", + "query": "Prove: Stella is not a numpus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a yumpus.\n\n", + "Stella is not a numpus and Stella is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a sterpus is a shumpus. Everything that is a tumpus or a sterpus is a wumpus. Everything that is an impus or a zumpus is a shumpus. Polly is not a numpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a sterpus and Polly is not a tumpus.", + "chain_of_thought": [ + "Assume Polly is a sterpus.", + "Polly is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a sterpus.\n\n", + "Assume Polly is a tumpus.", + "Polly is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a tumpus.\n\n", + "Polly is not a sterpus and Polly is not a tumpus." + ] + } + }, + "example40": { + "in_context_example0": { + "question": "Everything that is a numpus or a lempus is a rompus. Sally is not a rompus.", + "query": "Prove: Sally is not a lempus and Sally is not a numpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a rompus.", + "Sally is a rompus.", + "This contradicts with Sally is not a rompus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a numpus.", + "Sally is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a rompus.", + "Sally is a rompus.", + "This contradicts with Sally is not a rompus.", + "Sally is not a numpus.\n\n", + "Sally is not a lempus and Sally is not a numpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a lempus is a shumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a lempus and Rex is not an impus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is an impus or a lempus.", + "Everything that is an impus or a lempus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is an impus.", + "Rex is an impus or a lempus.", + "Everything that is an impus or a lempus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not an impus.\n\n", + "Rex is not a lempus and Rex is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a jompus or a tumpus is a vumpus. Sam is not a vumpus.", + "query": "Prove: Sam is not a tumpus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a tumpus.", + "Sam is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a tumpus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a jompus.\n\n", + "Sam is not a tumpus and Sam is not a jompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a sterpus or an impus is a jompus. Wren is not a jompus.", + "query": "Prove: Wren is not an impus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not an impus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a sterpus.\n\n", + "Wren is not an impus and Wren is not a sterpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a lempus is a vumpus. Max is not a vumpus.", + "query": "Prove: Max is not a lempus and Max is not a sterpus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a lempus.\n\n", + "Assume Max is a sterpus.", + "Max is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a sterpus.\n\n", + "Max is not a lempus and Max is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a gorpus or a jompus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a gorpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a gorpus.", + "Stella is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a gorpus.\n\n", + "Stella is not a jompus and Stella is not a gorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a vumpus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a zumpus or a vumpus.", + "Everything that is a zumpus or a vumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a vumpus.", + "Everything that is a zumpus or a vumpus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a vumpus and Polly is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a tumpus or a shumpus is a numpus. Rex is not a numpus.", + "query": "Prove: Rex is not a shumpus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a shumpus.", + "Rex is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a shumpus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a numpus.", + "Rex is a numpus.", + "This contradicts with Rex is not a numpus.", + "Rex is not a tumpus.\n\n", + "Rex is not a shumpus and Rex is not a tumpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a wumpus is a rompus. Everything that is a jompus or a lorpus is a shumpus. Everything that is a jompus or a lorpus is a rompus. Max is not a gorpus. Max is not a rompus.", + "query": "Prove: Max is not a lorpus and Max is not a jompus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a lorpus.\n\n", + "Assume Max is a jompus.", + "Max is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a jompus.\n\n", + "Max is not a lorpus and Max is not a jompus." + ] + } + }, + "example41": { + "in_context_example0": { + "question": "Everything that is a lempus or a dumpus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a dumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a dumpus.", + "Max is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a dumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a lempus.\n\n", + "Max is not a dumpus and Max is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or an impus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not an impus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a brimpus.\n\n", + "Wren is not an impus and Wren is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a lorpus is a yumpus. Polly is not a yumpus.", + "query": "Prove: Polly is not a lorpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a lorpus.", + "Polly is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a lorpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a shumpus.\n\n", + "Polly is not a lorpus and Polly is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a tumpus is a yumpus. Stella is not a yumpus.", + "query": "Prove: Stella is not a tumpus and Stella is not a numpus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a numpus.", + "Stella is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a numpus.\n\n", + "Stella is not a tumpus and Stella is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a rompus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a rompus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a rompus and Sam is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a rompus or a grimpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a grimpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a grimpus and Stella is not a rompus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a rompus is a wumpus. Sally is not a wumpus.", + "query": "Prove: Sally is not a rompus and Sally is not a zumpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a zumpus.", + "Sally is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a zumpus.\n\n", + "Sally is not a rompus and Sally is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a brimpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a brimpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a dumpus or a brimpus.", + "Everything that is a dumpus or a brimpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a brimpus.", + "Everything that is a dumpus or a brimpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a dumpus.\n\n", + "Sam is not a brimpus and Sam is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a yumpus is a zumpus. Everything that is a brimpus or a yumpus is a tumpus. Everything that is a shumpus or an impus is a tumpus. Polly is not a vumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a yumpus and Polly is not a brimpus." + ] + } + }, + "example42": { + "in_context_example0": { + "question": "Everything that is a vumpus or a sterpus is a brimpus. Sally is not a brimpus.", + "query": "Prove: Sally is not a sterpus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a sterpus.", + "Sally is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a sterpus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a vumpus.\n\n", + "Sally is not a sterpus and Sally is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a dumpus is a vumpus. Max is not a vumpus.", + "query": "Prove: Max is not a dumpus and Max is not a jompus.", + "chain_of_thought": [ + "Assume Max is a dumpus.", + "Max is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a dumpus.\n\n", + "Assume Max is a jompus.", + "Max is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a jompus.\n\n", + "Max is not a dumpus and Max is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is an impus or a yumpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a yumpus and Wren is not an impus.", + "chain_of_thought": [ + "Assume Wren is a yumpus.", + "Wren is an impus or a yumpus.", + "Everything that is an impus or a yumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a yumpus.\n\n", + "Assume Wren is an impus.", + "Wren is an impus or a yumpus.", + "Everything that is an impus or a yumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not an impus.\n\n", + "Wren is not a yumpus and Wren is not an impus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a numpus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a numpus and Stella is not a lorpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a lorpus.", + "Stella is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a lorpus.\n\n", + "Stella is not a numpus and Stella is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a brimpus is a sterpus. Sally is not a sterpus.", + "query": "Prove: Sally is not a brimpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a brimpus and Sally is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a grimpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a grimpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a grimpus.", + "Sam is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a grimpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not an impus.\n\n", + "Sam is not a grimpus and Sam is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is an impus or a jompus is a numpus. Polly is not a numpus.", + "query": "Prove: Polly is not a jompus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is an impus or a jompus.", + "Everything that is an impus or a jompus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a jompus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a jompus.", + "Everything that is an impus or a jompus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not an impus.\n\n", + "Polly is not a jompus and Polly is not an impus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a sterpus is a jompus. Sam is not a jompus.", + "query": "Prove: Sam is not a sterpus and Sam is not a zumpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a zumpus.", + "Sam is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a zumpus.\n\n", + "Sam is not a sterpus and Sam is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a grimpus is a gorpus. Everything that is a dumpus or a wumpus is a tumpus. Everything that is a vumpus or a grimpus is a tumpus. Polly is not a tumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a grimpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a grimpus.", + "Polly is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a grimpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a grimpus and Polly is not a vumpus." + ] + } + }, + "example43": { + "in_context_example0": { + "question": "Everything that is a brimpus or a zumpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a zumpus and Max is not a brimpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a brimpus.", + "Max is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a brimpus.\n\n", + "Max is not a zumpus and Max is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a rompus is a sterpus. Sally is not a sterpus.", + "query": "Prove: Sally is not a rompus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a dumpus.\n\n", + "Sally is not a rompus and Sally is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a numpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a numpus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a wumpus or a numpus.", + "Everything that is a wumpus or a numpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or a numpus.", + "Everything that is a wumpus or a numpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a wumpus.\n\n", + "Wren is not a numpus and Wren is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a wumpus or a lorpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a lorpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a wumpus.\n\n", + "Sally is not a lorpus and Sally is not a wumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a yumpus or a gorpus is a numpus. Max is not a numpus.", + "query": "Prove: Max is not a gorpus and Max is not a yumpus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a gorpus.\n\n", + "Assume Max is a yumpus.", + "Max is a yumpus or a gorpus.", + "Everything that is a yumpus or a gorpus is a numpus.", + "Max is a numpus.", + "This contradicts with Max is not a numpus.", + "Max is not a yumpus.\n\n", + "Max is not a gorpus and Max is not a yumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a yumpus or a wumpus is a shumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a yumpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a yumpus or a wumpus.", + "Everything that is a yumpus or a wumpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a yumpus.", + "Polly is a yumpus or a wumpus.", + "Everything that is a yumpus or a wumpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a yumpus.\n\n", + "Polly is not a wumpus and Polly is not a yumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a sterpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a sterpus and Fae is not a jompus.", + "chain_of_thought": [ + "Assume Fae is a sterpus.", + "Fae is a jompus or a sterpus.", + "Everything that is a jompus or a sterpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a sterpus.\n\n", + "Assume Fae is a jompus.", + "Fae is a jompus or a sterpus.", + "Everything that is a jompus or a sterpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a jompus.\n\n", + "Fae is not a sterpus and Fae is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a jompus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a jompus and Sam is not a shumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a shumpus or a jompus.", + "Everything that is a shumpus or a jompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a shumpus.", + "Sam is a shumpus or a jompus.", + "Everything that is a shumpus or a jompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a shumpus.\n\n", + "Sam is not a jompus and Sam is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a wumpus is a grimpus. Everything that is a vumpus or a rompus is a grimpus. Everything that is a gorpus or a wumpus is a brimpus. Sam is not a dumpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a wumpus and Sam is not a gorpus." + ] + } + }, + "example44": { + "in_context_example0": { + "question": "Everything that is a vumpus or a yumpus is a grimpus. Polly is not a grimpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a yumpus and Polly is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a grimpus or a vumpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a vumpus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a grimpus.\n\n", + "Sally is not a vumpus and Sally is not a grimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or an impus is a wumpus. Sally is not a wumpus.", + "query": "Prove: Sally is not an impus and Sally is not a tumpus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not an impus.\n\n", + "Assume Sally is a tumpus.", + "Sally is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a tumpus.\n\n", + "Sally is not an impus and Sally is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a lempus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a lempus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a grimpus.\n\n", + "Sally is not a lempus and Sally is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a dumpus or a jompus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a jompus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a dumpus.\n\n", + "Sam is not a jompus and Sam is not a dumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a jompus is a vumpus. Rex is not a vumpus.", + "query": "Prove: Rex is not a jompus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a lempus.\n\n", + "Rex is not a jompus and Rex is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a tumpus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is a zumpus or a tumpus.", + "Everything that is a zumpus or a tumpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a tumpus.", + "Everything that is a zumpus or a tumpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a tumpus and Wren is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a tumpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a tumpus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a grimpus.\n\n", + "Sally is not a tumpus and Sally is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or a lorpus is a yumpus. Everything that is a rompus or a lempus is a yumpus. Everything that is a rompus or a lempus is a sterpus. Sally is not a vumpus. Sally is not a yumpus.", + "query": "Prove: Sally is not a lempus and Sally is not a rompus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a rompus.", + "Sally is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a rompus.\n\n", + "Sally is not a lempus and Sally is not a rompus." + ] + } + }, + "example45": { + "in_context_example0": { + "question": "Everything that is a shumpus or a lempus is a zumpus. Alex is not a zumpus.", + "query": "Prove: Alex is not a lempus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a shumpus.\n\n", + "Alex is not a lempus and Alex is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a jompus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a jompus and Fae is not an impus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is an impus or a jompus.", + "Everything that is an impus or a jompus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is an impus.", + "Fae is an impus or a jompus.", + "Everything that is an impus or a jompus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not an impus.\n\n", + "Fae is not a jompus and Fae is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or an impus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not an impus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a numpus or an impus.", + "Everything that is a numpus or an impus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or an impus.", + "Everything that is a numpus or an impus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a numpus.\n\n", + "Polly is not an impus and Polly is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a jompus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a jompus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a tumpus.\n\n", + "Rex is not a jompus and Rex is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a brimpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a brimpus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a brimpus.", + "Fae is a gorpus or a brimpus.", + "Everything that is a gorpus or a brimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a brimpus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a brimpus.", + "Everything that is a gorpus or a brimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a gorpus.\n\n", + "Fae is not a brimpus and Fae is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a numpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a numpus and Sam is not a vumpus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a vumpus.", + "Sam is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a vumpus.\n\n", + "Sam is not a numpus and Sam is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lorpus or a grimpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a grimpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a lorpus.\n\n", + "Alex is not a grimpus and Alex is not a lorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a rompus or a gorpus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a gorpus and Rex is not a rompus.", + "chain_of_thought": [ + "Assume Rex is a gorpus.", + "Rex is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a gorpus.\n\n", + "Assume Rex is a rompus.", + "Rex is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a rompus.\n\n", + "Rex is not a gorpus and Rex is not a rompus." + ] + }, + "test_example": { + "question": "Everything that is a numpus or a gorpus is a grimpus. Everything that is a numpus or a gorpus is a sterpus. Everything that is a dumpus or a yumpus is a sterpus. Max is not a sterpus. Max is not a shumpus.", + "query": "Prove: Max is not a gorpus and Max is not a numpus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a gorpus.\n\n", + "Assume Max is a numpus.", + "Max is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a numpus.\n\n", + "Max is not a gorpus and Max is not a numpus." + ] + } + }, + "example46": { + "in_context_example0": { + "question": "Everything that is a shumpus or a brimpus is a tumpus. Max is not a tumpus.", + "query": "Prove: Max is not a brimpus and Max is not a shumpus.", + "chain_of_thought": [ + "Assume Max is a brimpus.", + "Max is a shumpus or a brimpus.", + "Everything that is a shumpus or a brimpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a brimpus.\n\n", + "Assume Max is a shumpus.", + "Max is a shumpus or a brimpus.", + "Everything that is a shumpus or a brimpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a shumpus.\n\n", + "Max is not a brimpus and Max is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a shumpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a shumpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a shumpus.", + "Rex is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a shumpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a wumpus.\n\n", + "Rex is not a shumpus and Rex is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a sterpus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a zumpus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a zumpus.", + "Stella is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a zumpus.\n\n", + "Stella is not a sterpus and Stella is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a rompus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a rompus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a rompus.", + "Stella is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a rompus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a rompus and Stella is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a lorpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a lorpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a lorpus and Sally is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a yumpus or a rompus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a rompus and Max is not a yumpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a yumpus or a rompus.", + "Everything that is a yumpus or a rompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a rompus.\n\n", + "Assume Max is a yumpus.", + "Max is a yumpus or a rompus.", + "Everything that is a yumpus or a rompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a yumpus.\n\n", + "Max is not a rompus and Max is not a yumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a brimpus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a brimpus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is a brimpus.", + "Max is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a brimpus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a vumpus.\n\n", + "Max is not a brimpus and Max is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a vumpus or a rompus is a numpus. Sally is not a numpus.", + "query": "Prove: Sally is not a rompus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a vumpus or a rompus.", + "Everything that is a vumpus or a rompus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a rompus.", + "Everything that is a vumpus or a rompus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a vumpus.\n\n", + "Sally is not a rompus and Sally is not a vumpus." + ] + }, + "test_example": { + "question": "Everything that is a wumpus or a tumpus is a grimpus. Everything that is a lempus or a dumpus is a grimpus. Everything that is a wumpus or a tumpus is a numpus. Fae is not a gorpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a wumpus or a tumpus.", + "Everything that is a wumpus or a tumpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a tumpus.", + "Everything that is a wumpus or a tumpus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a tumpus and Fae is not a wumpus." + ] + } + }, + "example47": { + "in_context_example0": { + "question": "Everything that is a shumpus or a jompus is a numpus. Wren is not a numpus.", + "query": "Prove: Wren is not a jompus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a shumpus or a jompus.", + "Everything that is a shumpus or a jompus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a jompus.", + "Everything that is a shumpus or a jompus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a jompus and Wren is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a numpus or a shumpus is a grimpus. Sally is not a grimpus.", + "query": "Prove: Sally is not a shumpus and Sally is not a numpus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is a numpus.", + "Sally is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a numpus.\n\n", + "Sally is not a shumpus and Sally is not a numpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a shumpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a shumpus and Rex is not a rompus.", + "chain_of_thought": [ + "Assume Rex is a shumpus.", + "Rex is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a shumpus.\n\n", + "Assume Rex is a rompus.", + "Rex is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a rompus.\n\n", + "Rex is not a shumpus and Rex is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a lorpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a lorpus and Fae is not an impus.", + "chain_of_thought": [ + "Assume Fae is a lorpus.", + "Fae is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a lorpus.\n\n", + "Assume Fae is an impus.", + "Fae is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not an impus.\n\n", + "Fae is not a lorpus and Fae is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a rompus is a sterpus. Max is not a sterpus.", + "query": "Prove: Max is not a rompus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a rompus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a gorpus.\n\n", + "Max is not a rompus and Max is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a zumpus is a jompus. Polly is not a jompus.", + "query": "Prove: Polly is not a zumpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a shumpus.\n\n", + "Polly is not a zumpus and Polly is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a gorpus or a lempus is a dumpus. Wren is not a dumpus.", + "query": "Prove: Wren is not a lempus and Wren is not a gorpus.", + "chain_of_thought": [ + "Assume Wren is a lempus.", + "Wren is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a lempus.\n\n", + "Assume Wren is a gorpus.", + "Wren is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a gorpus.\n\n", + "Wren is not a lempus and Wren is not a gorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a zumpus is a lorpus. Wren is not a lorpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a lorpus.", + "Wren is a lorpus.", + "This contradicts with Wren is not a lorpus.", + "Wren is not a lempus.\n\n", + "Wren is not a zumpus and Wren is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a vumpus is a lorpus. Everything that is a tumpus or a vumpus is a shumpus. Everything that is a gorpus or a grimpus is a lorpus. Sally is not a sterpus. Sally is not a lorpus.", + "query": "Prove: Sally is not a vumpus and Sally is not a tumpus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is a tumpus.", + "Sally is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a tumpus.\n\n", + "Sally is not a vumpus and Sally is not a tumpus." + ] + } + }, + "example48": { + "in_context_example0": { + "question": "Everything that is a vumpus or a lorpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a lorpus and Sam is not a vumpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a vumpus.", + "Sam is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a vumpus.\n\n", + "Sam is not a lorpus and Sam is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a lempus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a lempus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a lempus and Sam is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a zumpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a zumpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a numpus or a zumpus.", + "Everything that is a numpus or a zumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a zumpus.", + "Everything that is a numpus or a zumpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a numpus.\n\n", + "Fae is not a zumpus and Fae is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a rompus is a jompus. Max is not a jompus.", + "query": "Prove: Max is not a rompus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a rompus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a lorpus.\n\n", + "Max is not a rompus and Max is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a shumpus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a shumpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a rompus.\n\n", + "Wren is not a shumpus and Wren is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a lempus is a grimpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a lempus and Fae is not an impus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is an impus or a lempus.", + "Everything that is an impus or a lempus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is an impus.", + "Fae is an impus or a lempus.", + "Everything that is an impus or a lempus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not an impus.\n\n", + "Fae is not a lempus and Fae is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or an impus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not an impus and Stella is not a jompus.", + "chain_of_thought": [ + "Assume Stella is an impus.", + "Stella is a jompus or an impus.", + "Everything that is a jompus or an impus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not an impus.\n\n", + "Assume Stella is a jompus.", + "Stella is a jompus or an impus.", + "Everything that is a jompus or an impus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a jompus.\n\n", + "Stella is not an impus and Stella is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lorpus or a rompus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a rompus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a rompus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a rompus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a lorpus.\n\n", + "Max is not a rompus and Max is not a lorpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a lorpus is a jompus. Everything that is a grimpus or a gorpus is a shumpus. Everything that is a grimpus or a gorpus is a jompus. Max is not an impus. Max is not a jompus.", + "query": "Prove: Max is not a gorpus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a gorpus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a grimpus.\n\n", + "Max is not a gorpus and Max is not a grimpus." + ] + } + }, + "example49": { + "in_context_example0": { + "question": "Everything that is a grimpus or a gorpus is a shumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a grimpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a grimpus.", + "Polly is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a grimpus.\n\n", + "Polly is not a gorpus and Polly is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a tumpus is an impus. Polly is not an impus.", + "query": "Prove: Polly is not a tumpus and Polly is not a dumpus.", + "chain_of_thought": [ + "Assume Polly is a tumpus.", + "Polly is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a tumpus.\n\n", + "Assume Polly is a dumpus.", + "Polly is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is an impus.", + "Polly is an impus.", + "This contradicts with Polly is not an impus.", + "Polly is not a dumpus.\n\n", + "Polly is not a tumpus and Polly is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a brimpus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a brimpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a brimpus and Sam is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a brimpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a numpus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a numpus.", + "Rex is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a numpus.\n\n", + "Rex is not a brimpus and Rex is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a yumpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a yumpus and Sally is not a tumpus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is a tumpus.", + "Sally is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a tumpus.\n\n", + "Sally is not a yumpus and Sally is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a gorpus or a shumpus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a shumpus and Sam is not a gorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a dumpus or a numpus is a sterpus. Max is not a sterpus.", + "query": "Prove: Max is not a numpus and Max is not a dumpus.", + "chain_of_thought": [ + "Assume Max is a numpus.", + "Max is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a numpus.\n\n", + "Assume Max is a dumpus.", + "Max is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a dumpus.\n\n", + "Max is not a numpus and Max is not a dumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a gorpus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a gorpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a gorpus.", + "Max is a lempus or a gorpus.", + "Everything that is a lempus or a gorpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a gorpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a gorpus.", + "Everything that is a lempus or a gorpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a lempus.\n\n", + "Max is not a gorpus and Max is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a numpus is a zumpus. Everything that is a tumpus or a numpus is a gorpus. Everything that is a grimpus or a rompus is a zumpus. Fae is not a brimpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a numpus and Fae is not a tumpus.", + "chain_of_thought": [ + "Assume Fae is a numpus.", + "Fae is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a numpus.\n\n", + "Assume Fae is a tumpus.", + "Fae is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a tumpus.\n\n", + "Fae is not a numpus and Fae is not a tumpus." + ] + } + }, + "example50": { + "in_context_example0": { + "question": "Everything that is a lorpus or a zumpus is a rompus. Fae is not a rompus.", + "query": "Prove: Fae is not a zumpus and Fae is not a lorpus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a lorpus.", + "Fae is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a lorpus.\n\n", + "Fae is not a zumpus and Fae is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a zumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a rompus or a zumpus.", + "Everything that is a rompus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a zumpus.", + "Everything that is a rompus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a rompus.\n\n", + "Sam is not a zumpus and Sam is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is an impus or a numpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a numpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is an impus or a numpus.", + "Everything that is an impus or a numpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a numpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a numpus.", + "Everything that is an impus or a numpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not an impus.\n\n", + "Sam is not a numpus and Sam is not an impus." + ] + }, + "in_context_example3": { + "question": "Everything that is a dumpus or a rompus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a rompus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a rompus.", + "Everything that is a dumpus or a rompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a dumpus.\n\n", + "Sally is not a rompus and Sally is not a dumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a dumpus or an impus is a numpus. Polly is not a numpus.", + "query": "Prove: Polly is not an impus and Polly is not a dumpus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a dumpus or an impus.", + "Everything that is a dumpus or an impus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a dumpus.", + "Polly is a dumpus or an impus.", + "Everything that is a dumpus or an impus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a dumpus.\n\n", + "Polly is not an impus and Polly is not a dumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a numpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a numpus and Fae is not a dumpus.", + "chain_of_thought": [ + "Assume Fae is a numpus.", + "Fae is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a numpus.\n\n", + "Assume Fae is a dumpus.", + "Fae is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a dumpus.\n\n", + "Fae is not a numpus and Fae is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a numpus or a gorpus is a tumpus. Stella is not a tumpus.", + "query": "Prove: Stella is not a gorpus and Stella is not a numpus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is a numpus.", + "Stella is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a numpus.\n\n", + "Stella is not a gorpus and Stella is not a numpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a lempus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a lempus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a lempus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a lempus.", + "Everything that is a zumpus or a lempus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a lempus and Polly is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or a lorpus is an impus. Everything that is a zumpus or a lorpus is a rompus. Everything that is a grimpus or a shumpus is an impus. Stella is not a dumpus. Stella is not an impus.", + "query": "Prove: Stella is not a lorpus and Stella is not a zumpus.", + "chain_of_thought": [ + "Assume Stella is a lorpus.", + "Stella is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a lorpus.\n\n", + "Assume Stella is a zumpus.", + "Stella is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a zumpus.\n\n", + "Stella is not a lorpus and Stella is not a zumpus." + ] + } + }, + "example51": { + "in_context_example0": { + "question": "Everything that is a lempus or a yumpus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a lempus.\n\n", + "Polly is not a yumpus and Polly is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a yumpus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a yumpus and Stella is not a tumpus.", + "chain_of_thought": [ + "Assume Stella is a yumpus.", + "Stella is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a yumpus.\n\n", + "Assume Stella is a tumpus.", + "Stella is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a tumpus.\n\n", + "Stella is not a yumpus and Stella is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a shumpus is a grimpus. Wren is not a grimpus.", + "query": "Prove: Wren is not a shumpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a shumpus and Wren is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a zumpus or a dumpus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a dumpus and Alex is not a zumpus.", + "chain_of_thought": [ + "Assume Alex is a dumpus.", + "Alex is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a dumpus.\n\n", + "Assume Alex is a zumpus.", + "Alex is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a zumpus.\n\n", + "Alex is not a dumpus and Alex is not a zumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a dumpus or a lempus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a lempus and Fae is not a dumpus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a dumpus.", + "Fae is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a dumpus.\n\n", + "Fae is not a lempus and Fae is not a dumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a brimpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a brimpus and Sally is not a numpus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a numpus.", + "Sally is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a numpus.\n\n", + "Sally is not a brimpus and Sally is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a sterpus or a lorpus is a tumpus. Wren is not a tumpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not a sterpus.\n\n", + "Wren is not a lorpus and Wren is not a sterpus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a rompus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a rompus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is an impus or a rompus.", + "Everything that is an impus or a rompus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a rompus.", + "Everything that is an impus or a rompus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not an impus.\n\n", + "Alex is not a rompus and Alex is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a wumpus or a sterpus is a zumpus. Everything that is a yumpus or a dumpus is a grimpus. Everything that is a yumpus or a dumpus is a zumpus. Polly is not a zumpus. Polly is not a jompus.", + "query": "Prove: Polly is not a dumpus and Polly is not a yumpus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a yumpus.", + "Polly is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a yumpus.\n\n", + "Polly is not a dumpus and Polly is not a yumpus." + ] + } + }, + "example52": { + "in_context_example0": { + "question": "Everything that is a wumpus or an impus is a gorpus. Rex is not a gorpus.", + "query": "Prove: Rex is not an impus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is an impus.", + "Rex is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not an impus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not a wumpus.\n\n", + "Rex is not an impus and Rex is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a wumpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a jompus.\n\n", + "Sam is not a wumpus and Sam is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a tumpus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a tumpus and Wren is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a dumpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a dumpus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or a dumpus.", + "Everything that is a jompus or a dumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a jompus.\n\n", + "Polly is not a dumpus and Polly is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a vumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a vumpus.", + "Everything that is a gorpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a vumpus and Sam is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a brimpus is a tumpus. Max is not a tumpus.", + "query": "Prove: Max is not a brimpus and Max is not a numpus.", + "chain_of_thought": [ + "Assume Max is a brimpus.", + "Max is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a brimpus.\n\n", + "Assume Max is a numpus.", + "Max is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a numpus.\n\n", + "Max is not a brimpus and Max is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a grimpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a yumpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a yumpus.", + "Fae is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a yumpus.\n\n", + "Fae is not a grimpus and Fae is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a zumpus or a gorpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a zumpus or a gorpus.", + "Everything that is a zumpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a gorpus.", + "Everything that is a zumpus or a gorpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a gorpus and Polly is not a zumpus." + ] + }, + "test_example": { + "question": "Everything that is a lempus or a brimpus is an impus. Everything that is a shumpus or a jompus is an impus. Everything that is a lempus or a brimpus is a wumpus. Rex is not a zumpus. Rex is not an impus.", + "query": "Prove: Rex is not a brimpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a lempus.\n\n", + "Rex is not a brimpus and Rex is not a lempus." + ] + } + }, + "example53": { + "in_context_example0": { + "question": "Everything that is a sterpus or a tumpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a tumpus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a sterpus or a tumpus.", + "Everything that is a sterpus or a tumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or a tumpus.", + "Everything that is a sterpus or a tumpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a sterpus.\n\n", + "Sally is not a tumpus and Sally is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a gorpus or a sterpus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a sterpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a sterpus.", + "Rex is a gorpus or a sterpus.", + "Everything that is a gorpus or a sterpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a sterpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a sterpus.", + "Everything that is a gorpus or a sterpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a sterpus and Rex is not a gorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a jompus is a yumpus. Sally is not a yumpus.", + "query": "Prove: Sally is not a jompus and Sally is not a numpus.", + "chain_of_thought": [ + "Assume Sally is a jompus.", + "Sally is a numpus or a jompus.", + "Everything that is a numpus or a jompus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a jompus.\n\n", + "Assume Sally is a numpus.", + "Sally is a numpus or a jompus.", + "Everything that is a numpus or a jompus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a numpus.\n\n", + "Sally is not a jompus and Sally is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a zumpus or a jompus is a grimpus. Wren is not a grimpus.", + "query": "Prove: Wren is not a jompus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a jompus and Wren is not a zumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lempus or a vumpus is a yumpus. Max is not a yumpus.", + "query": "Prove: Max is not a vumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a vumpus.", + "Max is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a vumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a lempus.\n\n", + "Max is not a vumpus and Max is not a lempus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a dumpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a dumpus and Rex is not an impus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is an impus.", + "Rex is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not an impus.\n\n", + "Rex is not a dumpus and Rex is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a grimpus is an impus. Stella is not an impus.", + "query": "Prove: Stella is not a grimpus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a grimpus.", + "Everything that is a vumpus or a grimpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a vumpus.\n\n", + "Stella is not a grimpus and Stella is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a vumpus is an impus. Stella is not an impus.", + "query": "Prove: Stella is not a vumpus and Stella is not a wumpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a wumpus.", + "Stella is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a wumpus.\n\n", + "Stella is not a vumpus and Stella is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a shumpus or a zumpus is a lempus. Everything that is a gorpus or a lorpus is a lempus. Everything that is a gorpus or a lorpus is an impus. Wren is not a lempus. Wren is not a numpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a gorpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a gorpus or a lorpus.", + "Everything that is a gorpus or a lorpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a gorpus.", + "Wren is a gorpus or a lorpus.", + "Everything that is a gorpus or a lorpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a gorpus.\n\n", + "Wren is not a lorpus and Wren is not a gorpus." + ] + } + }, + "example54": { + "in_context_example0": { + "question": "Everything that is a zumpus or a numpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a numpus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a numpus.", + "Everything that is a zumpus or a numpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a zumpus.\n\n", + "Rex is not a numpus and Rex is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a grimpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a grimpus and Sam is not a shumpus.", + "chain_of_thought": [ + "Assume Sam is a grimpus.", + "Sam is a shumpus or a grimpus.", + "Everything that is a shumpus or a grimpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a grimpus.\n\n", + "Assume Sam is a shumpus.", + "Sam is a shumpus or a grimpus.", + "Everything that is a shumpus or a grimpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a shumpus.\n\n", + "Sam is not a grimpus and Sam is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a wumpus is a lorpus. Stella is not a lorpus.", + "query": "Prove: Stella is not a wumpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a wumpus.", + "Stella is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a wumpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a rompus.\n\n", + "Stella is not a wumpus and Stella is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a brimpus or a zumpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a zumpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a zumpus.", + "Stella is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a zumpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a zumpus and Stella is not a brimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is an impus or a lempus is a gorpus. Polly is not a gorpus.", + "query": "Prove: Polly is not a lempus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is an impus or a lempus.", + "Everything that is an impus or a lempus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a lempus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a lempus.", + "Everything that is an impus or a lempus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not an impus.\n\n", + "Polly is not a lempus and Polly is not an impus." + ] + }, + "in_context_example5": { + "question": "Everything that is a wumpus or a gorpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a gorpus and Alex is not a wumpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a wumpus.", + "Alex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a wumpus.\n\n", + "Alex is not a gorpus and Alex is not a wumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a wumpus is a grimpus. Sally is not a grimpus.", + "query": "Prove: Sally is not a wumpus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a wumpus.", + "Sally is a vumpus or a wumpus.", + "Everything that is a vumpus or a wumpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a wumpus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a wumpus.", + "Everything that is a vumpus or a wumpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a vumpus.\n\n", + "Sally is not a wumpus and Sally is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a lorpus is a grimpus. Sally is not a grimpus.", + "query": "Prove: Sally is not a lorpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not an impus.\n\n", + "Sally is not a lorpus and Sally is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a shumpus or a tumpus is a jompus. Everything that is a shumpus or a tumpus is a gorpus. Everything that is a brimpus or a dumpus is a gorpus. Wren is not a gorpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a tumpus and Wren is not a shumpus." + ] + } + }, + "example55": { + "in_context_example0": { + "question": "Everything that is a sterpus or a wumpus is a grimpus. Stella is not a grimpus.", + "query": "Prove: Stella is not a wumpus and Stella is not a sterpus.", + "chain_of_thought": [ + "Assume Stella is a wumpus.", + "Stella is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a wumpus.\n\n", + "Assume Stella is a sterpus.", + "Stella is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a sterpus.\n\n", + "Stella is not a wumpus and Stella is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a grimpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a rompus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a rompus.", + "Fae is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a rompus.\n\n", + "Fae is not a grimpus and Fae is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a jompus or a lempus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a lempus and Fae is not a jompus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a jompus.", + "Fae is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a jompus.\n\n", + "Fae is not a lempus and Fae is not a jompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a jompus is a grimpus. Fae is not a grimpus.", + "query": "Prove: Fae is not a jompus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a grimpus.", + "Fae is a grimpus.", + "This contradicts with Fae is not a grimpus.", + "Fae is not a gorpus.\n\n", + "Fae is not a jompus and Fae is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a shumpus is a yumpus. Fae is not a yumpus.", + "query": "Prove: Fae is not a shumpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a shumpus.", + "Fae is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a shumpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a grimpus.\n\n", + "Fae is not a shumpus and Fae is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a grimpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a grimpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a grimpus.", + "Sam is a dumpus or a grimpus.", + "Everything that is a dumpus or a grimpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a grimpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a grimpus.", + "Everything that is a dumpus or a grimpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a dumpus.\n\n", + "Sam is not a grimpus and Sam is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a numpus or a gorpus is a shumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or a gorpus.", + "Everything that is a numpus or a gorpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a numpus.\n\n", + "Polly is not a gorpus and Polly is not a numpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a jompus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a jompus and Polly is not a gorpus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a jompus.\n\n", + "Assume Polly is a gorpus.", + "Polly is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a gorpus.\n\n", + "Polly is not a jompus and Polly is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a brimpus is a zumpus. Everything that is a vumpus or a brimpus is a jompus. Everything that is a gorpus or a grimpus is a jompus. Polly is not a sterpus. Polly is not a jompus.", + "query": "Prove: Polly is not a brimpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a brimpus.", + "Polly is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a brimpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a vumpus.\n\n", + "Polly is not a brimpus and Polly is not a vumpus." + ] + } + }, + "example56": { + "in_context_example0": { + "question": "Everything that is a gorpus or a jompus is a lempus. Fae is not a lempus.", + "query": "Prove: Fae is not a jompus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a lempus.", + "Fae is a lempus.", + "This contradicts with Fae is not a lempus.", + "Fae is not a gorpus.\n\n", + "Fae is not a jompus and Fae is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a sterpus or a tumpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a tumpus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a sterpus or a tumpus.", + "Everything that is a sterpus or a tumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or a tumpus.", + "Everything that is a sterpus or a tumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a sterpus.\n\n", + "Sally is not a tumpus and Sally is not a sterpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a brimpus is a grimpus. Sally is not a grimpus.", + "query": "Prove: Sally is not a brimpus and Sally is not a rompus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a rompus or a brimpus.", + "Everything that is a rompus or a brimpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a rompus.", + "Sally is a rompus or a brimpus.", + "Everything that is a rompus or a brimpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a rompus.\n\n", + "Sally is not a brimpus and Sally is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a sterpus or an impus is a yumpus. Fae is not a yumpus.", + "query": "Prove: Fae is not an impus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not an impus and Fae is not a sterpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a numpus is a brimpus. Sally is not a brimpus.", + "query": "Prove: Sally is not a numpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a numpus.", + "Sally is a wumpus or a numpus.", + "Everything that is a wumpus or a numpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a numpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a numpus.", + "Everything that is a wumpus or a numpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a numpus and Sally is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a vumpus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a vumpus.", + "Everything that is a numpus or a vumpus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a numpus.\n\n", + "Sam is not a vumpus and Sam is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a sterpus or a vumpus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a vumpus and Sam is not a sterpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a lorpus is a wumpus. Sam is not a wumpus.", + "query": "Prove: Sam is not a lorpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a dumpus.\n\n", + "Sam is not a lorpus and Sam is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a lorpus is a tumpus. Everything that is a vumpus or a lorpus is a dumpus. Everything that is a lempus or a zumpus is a dumpus. Max is not a dumpus. Max is not a yumpus.", + "query": "Prove: Max is not a lorpus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a lorpus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or a lorpus.", + "Everything that is a vumpus or a lorpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a vumpus.\n\n", + "Max is not a lorpus and Max is not a vumpus." + ] + } + }, + "example57": { + "in_context_example0": { + "question": "Everything that is a lempus or a numpus is an impus. Max is not an impus.", + "query": "Prove: Max is not a numpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a numpus.", + "Max is a lempus or a numpus.", + "Everything that is a lempus or a numpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a numpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a numpus.", + "Everything that is a lempus or a numpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a lempus.\n\n", + "Max is not a numpus and Max is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a wumpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a wumpus.", + "Everything that is a shumpus or a wumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a shumpus.\n\n", + "Polly is not a wumpus and Polly is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a zumpus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a zumpus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a tumpus.\n\n", + "Rex is not a zumpus and Rex is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a brimpus or a zumpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a zumpus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a brimpus.\n\n", + "Rex is not a zumpus and Rex is not a brimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a lorpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a lorpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a lorpus and Sally is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a grimpus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a numpus.\n\n", + "Fae is not a grimpus and Fae is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lorpus or a lempus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a lempus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a lorpus.\n\n", + "Rex is not a lempus and Rex is not a lorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a vumpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a vumpus and Polly is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or an impus is a grimpus. Everything that is a numpus or a zumpus is a vumpus. Everything that is a gorpus or an impus is a vumpus. Max is not a sterpus. Max is not a vumpus.", + "query": "Prove: Max is not an impus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is an impus.", + "Max is a gorpus or an impus.", + "Everything that is a gorpus or an impus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not an impus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or an impus.", + "Everything that is a gorpus or an impus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a gorpus.\n\n", + "Max is not an impus and Max is not a gorpus." + ] + } + }, + "example58": { + "in_context_example0": { + "question": "Everything that is a lorpus or a lempus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a lempus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a lempus and Sam is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a grimpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a grimpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a grimpus.", + "Polly is a shumpus or a grimpus.", + "Everything that is a shumpus or a grimpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a grimpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a grimpus.", + "Everything that is a shumpus or a grimpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a shumpus.\n\n", + "Polly is not a grimpus and Polly is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a wumpus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a wumpus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a wumpus.", + "Rex is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a wumpus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a lorpus.\n\n", + "Rex is not a wumpus and Rex is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a vumpus or a jompus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a jompus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a jompus and Fae is not a vumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a vumpus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a vumpus.", + "Everything that is a wumpus or a vumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a vumpus and Polly is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a jompus is a yumpus. Rex is not a yumpus.", + "query": "Prove: Rex is not a jompus and Rex is not a vumpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a vumpus.", + "Rex is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a vumpus.\n\n", + "Rex is not a jompus and Rex is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a gorpus or a wumpus is a jompus. Sam is not a jompus.", + "query": "Prove: Sam is not a wumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a gorpus.\n\n", + "Sam is not a wumpus and Sam is not a gorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a tumpus is a yumpus. Rex is not a yumpus.", + "query": "Prove: Rex is not a tumpus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a tumpus.", + "Rex is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a tumpus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a brimpus.\n\n", + "Rex is not a tumpus and Rex is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a numpus or a tumpus is a lorpus. Everything that is a numpus or a tumpus is a brimpus. Everything that is a lempus or a jompus is a lorpus. Sam is not a lorpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a tumpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a tumpus.", + "Sam is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a tumpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a numpus.\n\n", + "Sam is not a tumpus and Sam is not a numpus." + ] + } + }, + "example59": { + "in_context_example0": { + "question": "Everything that is a gorpus or a jompus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a gorpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a gorpus.", + "Stella is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a gorpus.\n\n", + "Stella is not a jompus and Stella is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a dumpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a shumpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a shumpus or a dumpus.", + "Everything that is a shumpus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a shumpus.", + "Sam is a shumpus or a dumpus.", + "Everything that is a shumpus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a shumpus.\n\n", + "Sam is not a dumpus and Sam is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a shumpus is a tumpus. Stella is not a tumpus.", + "query": "Prove: Stella is not a shumpus and Stella is not a zumpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a zumpus.", + "Stella is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a zumpus.\n\n", + "Stella is not a shumpus and Stella is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a lorpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a lorpus and Wren is not an impus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is an impus.", + "Wren is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not an impus.\n\n", + "Wren is not a lorpus and Wren is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or an impus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not an impus and Rex is not a rompus.", + "chain_of_thought": [ + "Assume Rex is an impus.", + "Rex is a rompus or an impus.", + "Everything that is a rompus or an impus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not an impus.\n\n", + "Assume Rex is a rompus.", + "Rex is a rompus or an impus.", + "Everything that is a rompus or an impus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a rompus.\n\n", + "Rex is not an impus and Rex is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a dumpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a dumpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a dumpus.", + "Sally is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a dumpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a brimpus.\n\n", + "Sally is not a dumpus and Sally is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a vumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a brimpus.\n\n", + "Sam is not a vumpus and Sam is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a tumpus or a shumpus is a brimpus. Stella is not a brimpus.", + "query": "Prove: Stella is not a shumpus and Stella is not a tumpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a tumpus.", + "Stella is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a tumpus.\n\n", + "Stella is not a shumpus and Stella is not a tumpus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a jompus is a zumpus. Everything that is a wumpus or an impus is a numpus. Everything that is a wumpus or an impus is a zumpus. Sally is not a dumpus. Sally is not a zumpus.", + "query": "Prove: Sally is not an impus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not an impus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a wumpus.\n\n", + "Sally is not an impus and Sally is not a wumpus." + ] + } + }, + "example60": { + "in_context_example0": { + "question": "Everything that is a wumpus or a lempus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a lempus and Alex is not a wumpus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a wumpus.", + "Alex is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a wumpus.\n\n", + "Alex is not a lempus and Alex is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a dumpus is an impus. Max is not an impus.", + "query": "Prove: Max is not a dumpus and Max is not a yumpus.", + "chain_of_thought": [ + "Assume Max is a dumpus.", + "Max is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a dumpus.\n\n", + "Assume Max is a yumpus.", + "Max is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a yumpus.\n\n", + "Max is not a dumpus and Max is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a wumpus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a wumpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a wumpus.", + "Wren is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a wumpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a rompus.\n\n", + "Wren is not a wumpus and Wren is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a jompus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a jompus and Sally is not a lorpus.", + "chain_of_thought": [ + "Assume Sally is a jompus.", + "Sally is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a jompus.\n\n", + "Assume Sally is a lorpus.", + "Sally is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a lorpus.\n\n", + "Sally is not a jompus and Sally is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a yumpus or a vumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a yumpus or a vumpus.", + "Everything that is a yumpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a vumpus.", + "Everything that is a yumpus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a vumpus and Sam is not a yumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a jompus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a lempus.\n\n", + "Wren is not a jompus and Wren is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a tumpus or a zumpus is a lorpus. Max is not a lorpus.", + "query": "Prove: Max is not a zumpus and Max is not a tumpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a tumpus.", + "Max is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a tumpus.\n\n", + "Max is not a zumpus and Max is not a tumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a grimpus is a sterpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a grimpus and Fae is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a numpus is a sterpus. Everything that is a lempus or a jompus is a sterpus. Everything that is a gorpus or a numpus is a tumpus. Wren is not a grimpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a numpus and Wren is not a gorpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a gorpus or a numpus.", + "Everything that is a gorpus or a numpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a gorpus.", + "Wren is a gorpus or a numpus.", + "Everything that is a gorpus or a numpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a gorpus.\n\n", + "Wren is not a numpus and Wren is not a gorpus." + ] + } + }, + "example61": { + "in_context_example0": { + "question": "Everything that is a vumpus or an impus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not an impus and Rex is not a vumpus.", + "chain_of_thought": [ + "Assume Rex is an impus.", + "Rex is a vumpus or an impus.", + "Everything that is a vumpus or an impus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not an impus.\n\n", + "Assume Rex is a vumpus.", + "Rex is a vumpus or an impus.", + "Everything that is a vumpus or an impus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a vumpus.\n\n", + "Rex is not an impus and Rex is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a zumpus or a sterpus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a sterpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a sterpus.", + "Wren is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a sterpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a sterpus and Wren is not a zumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a shumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a shumpus and Sam is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a grimpus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a grimpus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not an impus.\n\n", + "Alex is not a grimpus and Alex is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a vumpus or a numpus is an impus. Max is not an impus.", + "query": "Prove: Max is not a numpus and Max is not a vumpus.", + "chain_of_thought": [ + "Assume Max is a numpus.", + "Max is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a numpus.\n\n", + "Assume Max is a vumpus.", + "Max is a vumpus or a numpus.", + "Everything that is a vumpus or a numpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a vumpus.\n\n", + "Max is not a numpus and Max is not a vumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a grimpus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a grimpus and Rex is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a rompus or a lempus is a shumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a lempus and Polly is not a rompus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a lempus.\n\n", + "Assume Polly is a rompus.", + "Polly is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a rompus.\n\n", + "Polly is not a lempus and Polly is not a rompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a rompus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a rompus and Wren is not a shumpus.", + "chain_of_thought": [ + "Assume Wren is a rompus.", + "Wren is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a rompus.\n\n", + "Assume Wren is a shumpus.", + "Wren is a shumpus or a rompus.", + "Everything that is a shumpus or a rompus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a shumpus.\n\n", + "Wren is not a rompus and Wren is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a shumpus is a rompus. Everything that is a brimpus or a tumpus is a numpus. Everything that is an impus or a shumpus is a numpus. Sam is not a numpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a shumpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not an impus.\n\n", + "Sam is not a shumpus and Sam is not an impus." + ] + } + }, + "example62": { + "in_context_example0": { + "question": "Everything that is a grimpus or a lempus is a yumpus. Max is not a yumpus.", + "query": "Prove: Max is not a lempus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a lempus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a grimpus.\n\n", + "Max is not a lempus and Max is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a grimpus is a shumpus. Wren is not a shumpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Wren is a shumpus.", + "This contradicts with Wren is not a shumpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a grimpus and Wren is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a lempus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a lempus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a lempus.", + "Stella is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a lempus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a lempus.", + "Everything that is a rompus or a lempus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a lempus and Stella is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or a jompus is a brimpus. Max is not a brimpus.", + "query": "Prove: Max is not a jompus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a jompus.", + "Max is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a jompus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a jompus.", + "Everything that is a rompus or a jompus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a rompus.\n\n", + "Max is not a jompus and Max is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a shumpus or a numpus is a yumpus. Stella is not a yumpus.", + "query": "Prove: Stella is not a numpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a numpus and Stella is not a shumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a wumpus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a wumpus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a wumpus.", + "Rex is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a wumpus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a brimpus.\n\n", + "Rex is not a wumpus and Rex is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is an impus or a jompus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a jompus and Alex is not an impus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is an impus or a jompus.", + "Everything that is an impus or a jompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is an impus.", + "Alex is an impus or a jompus.", + "Everything that is an impus or a jompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not an impus.\n\n", + "Alex is not a jompus and Alex is not an impus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a vumpus is a lempus. Stella is not a lempus.", + "query": "Prove: Stella is not a vumpus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not an impus.\n\n", + "Stella is not a vumpus and Stella is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a shumpus is a rompus. Everything that is a brimpus or a jompus is a rompus. Everything that is a brimpus or a jompus is a numpus. Sam is not a vumpus. Sam is not a rompus.", + "query": "Prove: Sam is not a jompus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a brimpus.\n\n", + "Sam is not a jompus and Sam is not a brimpus." + ] + } + }, + "example63": { + "in_context_example0": { + "question": "Everything that is a wumpus or a yumpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a yumpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a yumpus and Sally is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a grimpus or a lorpus is an impus. Fae is not an impus.", + "query": "Prove: Fae is not a lorpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a lorpus.", + "Fae is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a lorpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a grimpus.\n\n", + "Fae is not a lorpus and Fae is not a grimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a sterpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a sterpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a sterpus.", + "Alex is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a sterpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a sterpus and Alex is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a vumpus or a wumpus is a numpus. Fae is not a numpus.", + "query": "Prove: Fae is not a wumpus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a vumpus or a wumpus.", + "Everything that is a vumpus or a wumpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a wumpus.", + "Everything that is a vumpus or a wumpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a wumpus and Fae is not a vumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a lempus is a gorpus. Polly is not a gorpus.", + "query": "Prove: Polly is not a lempus and Polly is not a sterpus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a lempus.\n\n", + "Assume Polly is a sterpus.", + "Polly is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a sterpus.\n\n", + "Polly is not a lempus and Polly is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a tumpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a tumpus and Rex is not a numpus.", + "chain_of_thought": [ + "Assume Rex is a tumpus.", + "Rex is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a tumpus.\n\n", + "Assume Rex is a numpus.", + "Rex is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a numpus.\n\n", + "Rex is not a tumpus and Rex is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a brimpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a shumpus or a brimpus.", + "Everything that is a shumpus or a brimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a brimpus.", + "Everything that is a shumpus or a brimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a shumpus.\n\n", + "Alex is not a brimpus and Alex is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a lempus is a yumpus. Max is not a yumpus.", + "query": "Prove: Max is not a lempus and Max is not a wumpus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a lempus.\n\n", + "Assume Max is a wumpus.", + "Max is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a wumpus.\n\n", + "Max is not a lempus and Max is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a grimpus is a gorpus. Everything that is a zumpus or a dumpus is a gorpus. Everything that is a yumpus or a grimpus is a vumpus. Sally is not a wumpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a grimpus and Sally is not a yumpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a yumpus.", + "Sally is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a yumpus.\n\n", + "Sally is not a grimpus and Sally is not a yumpus." + ] + } + }, + "example64": { + "in_context_example0": { + "question": "Everything that is a gorpus or a jompus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a jompus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a jompus.", + "Everything that is a gorpus or a jompus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a gorpus.\n\n", + "Alex is not a jompus and Alex is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a vumpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a vumpus and Rex is not a rompus.", + "chain_of_thought": [ + "Assume Rex is a vumpus.", + "Rex is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a vumpus.\n\n", + "Assume Rex is a rompus.", + "Rex is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a rompus.\n\n", + "Rex is not a vumpus and Rex is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a zumpus or a wumpus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a zumpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a zumpus or a wumpus.", + "Everything that is a zumpus or a wumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a zumpus.", + "Polly is a zumpus or a wumpus.", + "Everything that is a zumpus or a wumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a zumpus.\n\n", + "Polly is not a wumpus and Polly is not a zumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a jompus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a jompus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a jompus and Wren is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or an impus is a yumpus. Polly is not a yumpus.", + "query": "Prove: Polly is not an impus and Polly is not a grimpus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a grimpus.", + "Polly is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a grimpus.\n\n", + "Polly is not an impus and Polly is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a dumpus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a dumpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a lempus.\n\n", + "Rex is not a dumpus and Rex is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a wumpus or an impus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not an impus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not an impus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or an impus.", + "Everything that is a wumpus or an impus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a wumpus.\n\n", + "Sally is not an impus and Sally is not a wumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a jompus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a jompus and Stella is not a dumpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a dumpus.", + "Stella is a dumpus or a jompus.", + "Everything that is a dumpus or a jompus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a dumpus.\n\n", + "Stella is not a jompus and Stella is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a numpus is a dumpus. Everything that is a yumpus or a numpus is a gorpus. Everything that is a lempus or a tumpus is a dumpus. Max is not a dumpus. Max is not a lorpus.", + "query": "Prove: Max is not a numpus and Max is not a yumpus.", + "chain_of_thought": [ + "Assume Max is a numpus.", + "Max is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a numpus.\n\n", + "Assume Max is a yumpus.", + "Max is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a yumpus.\n\n", + "Max is not a numpus and Max is not a yumpus." + ] + } + }, + "example65": { + "in_context_example0": { + "question": "Everything that is a gorpus or a shumpus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a shumpus and Polly is not a gorpus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a gorpus.", + "Polly is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a gorpus.\n\n", + "Polly is not a shumpus and Polly is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a gorpus or a rompus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a rompus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a rompus and Sam is not a gorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a numpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a numpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a tumpus.\n\n", + "Sam is not a numpus and Sam is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a vumpus or a yumpus is a jompus. Polly is not a jompus.", + "query": "Prove: Polly is not a yumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a vumpus.\n\n", + "Polly is not a yumpus and Polly is not a vumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a grimpus is a rompus. Fae is not a rompus.", + "query": "Prove: Fae is not a grimpus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a sterpus.\n\n", + "Fae is not a grimpus and Fae is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a tumpus or a sterpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a sterpus and Polly is not a tumpus.", + "chain_of_thought": [ + "Assume Polly is a sterpus.", + "Polly is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a sterpus.\n\n", + "Assume Polly is a tumpus.", + "Polly is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a tumpus.\n\n", + "Polly is not a sterpus and Polly is not a tumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a zumpus is a dumpus. Polly is not a dumpus.", + "query": "Prove: Polly is not a zumpus and Polly is not a shumpus.", + "chain_of_thought": [ + "Assume Polly is a zumpus.", + "Polly is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a zumpus.\n\n", + "Assume Polly is a shumpus.", + "Polly is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a dumpus.", + "Polly is a dumpus.", + "This contradicts with Polly is not a dumpus.", + "Polly is not a shumpus.\n\n", + "Polly is not a zumpus and Polly is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a tumpus is a lorpus. Stella is not a lorpus.", + "query": "Prove: Stella is not a tumpus and Stella is not a lempus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a lempus.", + "Stella is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a lorpus.", + "Stella is a lorpus.", + "This contradicts with Stella is not a lorpus.", + "Stella is not a lempus.\n\n", + "Stella is not a tumpus and Stella is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a grimpus is a shumpus. Everything that is a wumpus or a gorpus is a shumpus. Everything that is a yumpus or a grimpus is a tumpus. Polly is not a zumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a grimpus and Polly is not a yumpus.", + "chain_of_thought": [ + "Assume Polly is a grimpus.", + "Polly is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a grimpus.\n\n", + "Assume Polly is a yumpus.", + "Polly is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a yumpus.\n\n", + "Polly is not a grimpus and Polly is not a yumpus." + ] + } + }, + "example66": { + "in_context_example0": { + "question": "Everything that is a wumpus or a gorpus is a vumpus. Rex is not a vumpus.", + "query": "Prove: Rex is not a gorpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a gorpus.", + "Rex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a gorpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a wumpus.\n\n", + "Rex is not a gorpus and Rex is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a grimpus or a shumpus is an impus. Alex is not an impus.", + "query": "Prove: Alex is not a shumpus and Alex is not a grimpus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a grimpus.", + "Alex is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a grimpus.\n\n", + "Alex is not a shumpus and Alex is not a grimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a numpus is a zumpus. Stella is not a zumpus.", + "query": "Prove: Stella is not a numpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a zumpus.", + "Stella is a zumpus.", + "This contradicts with Stella is not a zumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a numpus and Stella is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a dumpus is a jompus. Stella is not a jompus.", + "query": "Prove: Stella is not a dumpus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a dumpus.", + "Stella is a grimpus or a dumpus.", + "Everything that is a grimpus or a dumpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a dumpus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a dumpus.", + "Everything that is a grimpus or a dumpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a grimpus.\n\n", + "Stella is not a dumpus and Stella is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a numpus is a wumpus. Sam is not a wumpus.", + "query": "Prove: Sam is not a numpus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a sterpus or a numpus.", + "Everything that is a sterpus or a numpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a numpus.", + "Everything that is a sterpus or a numpus is a wumpus.", + "Sam is a wumpus.", + "This contradicts with Sam is not a wumpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a numpus and Sam is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a tumpus is a yumpus. Polly is not a yumpus.", + "query": "Prove: Polly is not a tumpus and Polly is not a dumpus.", + "chain_of_thought": [ + "Assume Polly is a tumpus.", + "Polly is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a tumpus.\n\n", + "Assume Polly is a dumpus.", + "Polly is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a yumpus.", + "Polly is a yumpus.", + "This contradicts with Polly is not a yumpus.", + "Polly is not a dumpus.\n\n", + "Polly is not a tumpus and Polly is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a gorpus is an impus. Alex is not an impus.", + "query": "Prove: Alex is not a gorpus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a gorpus.", + "Everything that is a brimpus or a gorpus is an impus.", + "Alex is an impus.", + "This contradicts with Alex is not an impus.", + "Alex is not a brimpus.\n\n", + "Alex is not a gorpus and Alex is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a brimpus is a vumpus. Alex is not a vumpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a yumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a yumpus.", + "Alex is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a yumpus.\n\n", + "Alex is not a brimpus and Alex is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a brimpus is a shumpus. Everything that is a yumpus or a brimpus is a sterpus. Everything that is a wumpus or a lempus is a shumpus. Stella is not a shumpus. Stella is not a rompus.", + "query": "Prove: Stella is not a brimpus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a brimpus.", + "Stella is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a brimpus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a yumpus.\n\n", + "Stella is not a brimpus and Stella is not a yumpus." + ] + } + }, + "example67": { + "in_context_example0": { + "question": "Everything that is a rompus or a yumpus is a numpus. Sally is not a numpus.", + "query": "Prove: Sally is not a yumpus and Sally is not a rompus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is a rompus or a yumpus.", + "Everything that is a rompus or a yumpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is a rompus.", + "Sally is a rompus or a yumpus.", + "Everything that is a rompus or a yumpus is a numpus.", + "Sally is a numpus.", + "This contradicts with Sally is not a numpus.", + "Sally is not a rompus.\n\n", + "Sally is not a yumpus and Sally is not a rompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a numpus or a grimpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a numpus.\n\n", + "Wren is not a grimpus and Wren is not a numpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a tumpus is a grimpus. Max is not a grimpus.", + "query": "Prove: Max is not a tumpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a tumpus.", + "Everything that is a lempus or a tumpus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a lempus.\n\n", + "Max is not a tumpus and Max is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a rompus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a rompus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a jompus.\n\n", + "Alex is not a rompus and Alex is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a lempus is a yumpus. Sally is not a yumpus.", + "query": "Prove: Sally is not a lempus and Sally is not a gorpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a gorpus.", + "Sally is a gorpus or a lempus.", + "Everything that is a gorpus or a lempus is a yumpus.", + "Sally is a yumpus.", + "This contradicts with Sally is not a yumpus.", + "Sally is not a gorpus.\n\n", + "Sally is not a lempus and Sally is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a dumpus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a dumpus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a dumpus.", + "Alex is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a dumpus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a sterpus.\n\n", + "Alex is not a dumpus and Alex is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a sterpus or a yumpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a yumpus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a yumpus.", + "Sam is a sterpus or a yumpus.", + "Everything that is a sterpus or a yumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a yumpus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a yumpus.", + "Everything that is a sterpus or a yumpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a yumpus and Sam is not a sterpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a numpus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a numpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a sterpus or a numpus.", + "Everything that is a sterpus or a numpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a numpus.", + "Everything that is a sterpus or a numpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a sterpus.\n\n", + "Wren is not a numpus and Wren is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or a shumpus is a rompus. Everything that is a zumpus or a shumpus is an impus. Everything that is a lorpus or a jompus is a rompus. Sam is not a rompus. Sam is not a grimpus.", + "query": "Prove: Sam is not a shumpus and Sam is not a zumpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a zumpus.", + "Sam is a zumpus or a shumpus.", + "Everything that is a zumpus or a shumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a zumpus.\n\n", + "Sam is not a shumpus and Sam is not a zumpus." + ] + } + }, + "example68": { + "in_context_example0": { + "question": "Everything that is a zumpus or a rompus is a lempus. Sally is not a lempus.", + "query": "Prove: Sally is not a rompus and Sally is not a zumpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a zumpus.", + "Sally is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a lempus.", + "Sally is a lempus.", + "This contradicts with Sally is not a lempus.", + "Sally is not a zumpus.\n\n", + "Sally is not a rompus and Sally is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a grimpus or an impus is a vumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not an impus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is an impus.", + "Fae is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not an impus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or an impus.", + "Everything that is a grimpus or an impus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a grimpus.\n\n", + "Fae is not an impus and Fae is not a grimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a yumpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a yumpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a yumpus.", + "Wren is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a yumpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a yumpus.", + "Everything that is a tumpus or a yumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a tumpus.\n\n", + "Wren is not a yumpus and Wren is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a wumpus is a rompus. Polly is not a rompus.", + "query": "Prove: Polly is not a wumpus and Polly is not a lorpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a lorpus.", + "Polly is a lorpus or a wumpus.", + "Everything that is a lorpus or a wumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a lorpus.\n\n", + "Polly is not a wumpus and Polly is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a wumpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a sterpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a sterpus.", + "Polly is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a sterpus.\n\n", + "Polly is not a wumpus and Polly is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a gorpus is a brimpus. Sally is not a brimpus.", + "query": "Prove: Sally is not a gorpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a gorpus.", + "Sally is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a gorpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not an impus.\n\n", + "Sally is not a gorpus and Sally is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lorpus or a shumpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a shumpus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a shumpus and Wren is not a lorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a numpus is a lorpus. Sally is not a lorpus.", + "query": "Prove: Sally is not a numpus and Sally is not a grimpus.", + "chain_of_thought": [ + "Assume Sally is a numpus.", + "Sally is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a numpus.\n\n", + "Assume Sally is a grimpus.", + "Sally is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a grimpus.\n\n", + "Sally is not a numpus and Sally is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a zumpus is a tumpus. Everything that is a vumpus or a zumpus is a yumpus. Everything that is a lempus or a gorpus is a tumpus. Sally is not an impus. Sally is not a tumpus.", + "query": "Prove: Sally is not a zumpus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a zumpus.", + "Sally is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a zumpus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a vumpus.\n\n", + "Sally is not a zumpus and Sally is not a vumpus." + ] + } + }, + "example69": { + "in_context_example0": { + "question": "Everything that is a grimpus or a sterpus is a tumpus. Max is not a tumpus.", + "query": "Prove: Max is not a sterpus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is a grimpus or a sterpus.", + "Everything that is a grimpus or a sterpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a sterpus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a sterpus.", + "Everything that is a grimpus or a sterpus is a tumpus.", + "Max is a tumpus.", + "This contradicts with Max is not a tumpus.", + "Max is not a grimpus.\n\n", + "Max is not a sterpus and Max is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lempus or a shumpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a shumpus and Sally is not a lempus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is a lempus or a shumpus.", + "Everything that is a lempus or a shumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is a lempus.", + "Sally is a lempus or a shumpus.", + "Everything that is a lempus or a shumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a lempus.\n\n", + "Sally is not a shumpus and Sally is not a lempus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a yumpus is a dumpus. Rex is not a dumpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a dumpus.", + "Rex is a dumpus.", + "This contradicts with Rex is not a dumpus.", + "Rex is not a brimpus.\n\n", + "Rex is not a yumpus and Rex is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a wumpus or a jompus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a jompus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a wumpus or a jompus.", + "Everything that is a wumpus or a jompus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a jompus.", + "Everything that is a wumpus or a jompus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a jompus and Sam is not a wumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a yumpus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a yumpus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a yumpus.", + "Alex is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a yumpus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a yumpus.", + "Everything that is a gorpus or a yumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a gorpus.\n\n", + "Alex is not a yumpus and Alex is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a sterpus is a lempus. Max is not a lempus.", + "query": "Prove: Max is not a sterpus and Max is not a numpus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is a numpus or a sterpus.", + "Everything that is a numpus or a sterpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a sterpus.\n\n", + "Assume Max is a numpus.", + "Max is a numpus or a sterpus.", + "Everything that is a numpus or a sterpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a numpus.\n\n", + "Max is not a sterpus and Max is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lorpus or a zumpus is a gorpus. Stella is not a gorpus.", + "query": "Prove: Stella is not a zumpus and Stella is not a lorpus.", + "chain_of_thought": [ + "Assume Stella is a zumpus.", + "Stella is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a zumpus.\n\n", + "Assume Stella is a lorpus.", + "Stella is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a lorpus.\n\n", + "Stella is not a zumpus and Stella is not a lorpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a tumpus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a tumpus and Alex is not a grimpus.", + "chain_of_thought": [ + "Assume Alex is a tumpus.", + "Alex is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a tumpus.\n\n", + "Assume Alex is a grimpus.", + "Alex is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a grimpus.\n\n", + "Alex is not a tumpus and Alex is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is a numpus or a dumpus is a shumpus. Everything that is an impus or a wumpus is a shumpus. Everything that is a numpus or a dumpus is a jompus. Polly is not a brimpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a dumpus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a numpus or a dumpus.", + "Everything that is a numpus or a dumpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or a dumpus.", + "Everything that is a numpus or a dumpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a numpus.\n\n", + "Polly is not a dumpus and Polly is not a numpus." + ] + } + }, + "example70": { + "in_context_example0": { + "question": "Everything that is a lorpus or a sterpus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a sterpus and Sam is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a brimpus or a numpus is a sterpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a numpus and Rex is not a brimpus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a brimpus or a numpus.", + "Everything that is a brimpus or a numpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a brimpus.", + "Rex is a brimpus or a numpus.", + "Everything that is a brimpus or a numpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a brimpus.\n\n", + "Rex is not a numpus and Rex is not a brimpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a sterpus or a grimpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a grimpus and Fae is not a sterpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a grimpus is a shumpus. Fae is not a shumpus.", + "query": "Prove: Fae is not a grimpus and Fae is not a yumpus.", + "chain_of_thought": [ + "Assume Fae is a grimpus.", + "Fae is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a grimpus.\n\n", + "Assume Fae is a yumpus.", + "Fae is a yumpus or a grimpus.", + "Everything that is a yumpus or a grimpus is a shumpus.", + "Fae is a shumpus.", + "This contradicts with Fae is not a shumpus.", + "Fae is not a yumpus.\n\n", + "Fae is not a grimpus and Fae is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a tumpus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a grimpus.\n\n", + "Fae is not a tumpus and Fae is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a tumpus or a vumpus is a jompus. Stella is not a jompus.", + "query": "Prove: Stella is not a vumpus and Stella is not a tumpus.", + "chain_of_thought": [ + "Assume Stella is a vumpus.", + "Stella is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a vumpus.\n\n", + "Assume Stella is a tumpus.", + "Stella is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a tumpus.\n\n", + "Stella is not a vumpus and Stella is not a tumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a sterpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a sterpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a sterpus.", + "Sam is a yumpus or a sterpus.", + "Everything that is a yumpus or a sterpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a sterpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a sterpus.", + "Everything that is a yumpus or a sterpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a sterpus and Sam is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a numpus or a grimpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a grimpus and Max is not a numpus.", + "chain_of_thought": [ + "Assume Max is a grimpus.", + "Max is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a grimpus.\n\n", + "Assume Max is a numpus.", + "Max is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a numpus.\n\n", + "Max is not a grimpus and Max is not a numpus." + ] + }, + "test_example": { + "question": "Everything that is a vumpus or a yumpus is a sterpus. Everything that is a lempus or a lorpus is a numpus. Everything that is a vumpus or a yumpus is a numpus. Polly is not a numpus. Polly is not a brimpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a yumpus and Polly is not a vumpus." + ] + } + }, + "example71": { + "in_context_example0": { + "question": "Everything that is a numpus or a jompus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a jompus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a numpus or a jompus.", + "Everything that is a numpus or a jompus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or a jompus.", + "Everything that is a numpus or a jompus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a numpus.\n\n", + "Wren is not a jompus and Wren is not a numpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a numpus is a sterpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a numpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a numpus.", + "Fae is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a numpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a numpus.", + "Everything that is a shumpus or a numpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a numpus and Fae is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a lempus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a lempus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a tumpus.\n\n", + "Rex is not a lempus and Rex is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lempus or a rompus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a rompus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a rompus.", + "Polly is a lempus or a rompus.", + "Everything that is a lempus or a rompus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a rompus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a rompus.", + "Everything that is a lempus or a rompus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a lempus.\n\n", + "Polly is not a rompus and Polly is not a lempus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a zumpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a zumpus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is a zumpus.", + "Sally is a sterpus or a zumpus.", + "Everything that is a sterpus or a zumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a zumpus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or a zumpus.", + "Everything that is a sterpus or a zumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a sterpus.\n\n", + "Sally is not a zumpus and Sally is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a zumpus or a grimpus is a jompus. Stella is not a jompus.", + "query": "Prove: Stella is not a grimpus and Stella is not a zumpus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a zumpus.", + "Stella is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a jompus.", + "Stella is a jompus.", + "This contradicts with Stella is not a jompus.", + "Stella is not a zumpus.\n\n", + "Stella is not a grimpus and Stella is not a zumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a vumpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a vumpus and Polly is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a yumpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a dumpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a dumpus.", + "Fae is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a dumpus.\n\n", + "Fae is not a yumpus and Fae is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a wumpus or a lorpus is a yumpus. Everything that is a jompus or a lempus is a yumpus. Everything that is a jompus or a lempus is a rompus. Fae is not a shumpus. Fae is not a yumpus.", + "query": "Prove: Fae is not a lempus and Fae is not a jompus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a jompus.", + "Fae is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a yumpus.", + "Fae is a yumpus.", + "This contradicts with Fae is not a yumpus.", + "Fae is not a jompus.\n\n", + "Fae is not a lempus and Fae is not a jompus." + ] + } + }, + "example72": { + "in_context_example0": { + "question": "Everything that is a jompus or a yumpus is a tumpus. Alex is not a tumpus.", + "query": "Prove: Alex is not a yumpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a yumpus.", + "Alex is a jompus or a yumpus.", + "Everything that is a jompus or a yumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a yumpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a yumpus.", + "Everything that is a jompus or a yumpus is a tumpus.", + "Alex is a tumpus.", + "This contradicts with Alex is not a tumpus.", + "Alex is not a jompus.\n\n", + "Alex is not a yumpus and Alex is not a jompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a tumpus is a vumpus. Polly is not a vumpus.", + "query": "Prove: Polly is not a tumpus and Polly is not a rompus.", + "chain_of_thought": [ + "Assume Polly is a tumpus.", + "Polly is a rompus or a tumpus.", + "Everything that is a rompus or a tumpus is a vumpus.", + "Polly is a vumpus.", + "This contradicts with Polly is not a vumpus.", + "Polly is not a tumpus.\n\n", + "Assume Polly is a rompus.", + "Polly is a rompus or a tumpus.", + "Everything that is a rompus or a tumpus is a vumpus.", + "Polly is a vumpus.", + "This contradicts with Polly is not a vumpus.", + "Polly is not a rompus.\n\n", + "Polly is not a tumpus and Polly is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a dumpus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a dumpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a dumpus.", + "Stella is a shumpus or a dumpus.", + "Everything that is a shumpus or a dumpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a dumpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a dumpus.", + "Everything that is a shumpus or a dumpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a shumpus.\n\n", + "Stella is not a dumpus and Stella is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or a gorpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a gorpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a gorpus and Stella is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a zumpus or a sterpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a sterpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a sterpus.", + "Wren is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a sterpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a sterpus.", + "Everything that is a zumpus or a sterpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a zumpus.\n\n", + "Wren is not a sterpus and Wren is not a zumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a rompus is a gorpus. Alex is not a gorpus.", + "query": "Prove: Alex is not a rompus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a brimpus or a rompus.", + "Everything that is a brimpus or a rompus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a rompus.", + "Everything that is a brimpus or a rompus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a brimpus.\n\n", + "Alex is not a rompus and Alex is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a lorpus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a lorpus and Stella is not a lempus.", + "chain_of_thought": [ + "Assume Stella is a lorpus.", + "Stella is a lempus or a lorpus.", + "Everything that is a lempus or a lorpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a lorpus.\n\n", + "Assume Stella is a lempus.", + "Stella is a lempus or a lorpus.", + "Everything that is a lempus or a lorpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a lempus.\n\n", + "Stella is not a lorpus and Stella is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a tumpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a tumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a tumpus.", + "Sam is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a tumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a tumpus.", + "Everything that is a yumpus or a tumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a yumpus.\n\n", + "Sam is not a tumpus and Sam is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a vumpus is a grimpus. Everything that is a wumpus or a lorpus is a grimpus. Everything that is a wumpus or a lorpus is a dumpus. Rex is not a brimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a lorpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a lorpus.", + "Rex is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a lorpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a wumpus.\n\n", + "Rex is not a lorpus and Rex is not a wumpus." + ] + } + }, + "example73": { + "in_context_example0": { + "question": "Everything that is a gorpus or an impus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not an impus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is an impus.", + "Max is a gorpus or an impus.", + "Everything that is a gorpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not an impus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or an impus.", + "Everything that is a gorpus or an impus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a gorpus.\n\n", + "Max is not an impus and Max is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a vumpus or a shumpus is a gorpus. Stella is not a gorpus.", + "query": "Prove: Stella is not a shumpus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a shumpus.", + "Stella is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a shumpus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a vumpus.\n\n", + "Stella is not a shumpus and Stella is not a vumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a lempus is a rompus. Alex is not a rompus.", + "query": "Prove: Alex is not a lempus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a shumpus.\n\n", + "Alex is not a lempus and Alex is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a brimpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a brimpus and Alex is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a jompus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a jompus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a wumpus or a jompus.", + "Everything that is a wumpus or a jompus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a jompus.", + "Everything that is a wumpus or a jompus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a jompus and Sam is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lorpus or a lempus is a numpus. Sam is not a numpus.", + "query": "Prove: Sam is not a lempus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a lempus and Sam is not a lorpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a tumpus is a lorpus. Alex is not a lorpus.", + "query": "Prove: Alex is not a tumpus and Alex is not a zumpus.", + "chain_of_thought": [ + "Assume Alex is a tumpus.", + "Alex is a zumpus or a tumpus.", + "Everything that is a zumpus or a tumpus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a tumpus.\n\n", + "Assume Alex is a zumpus.", + "Alex is a zumpus or a tumpus.", + "Everything that is a zumpus or a tumpus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a zumpus.\n\n", + "Alex is not a tumpus and Alex is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a vumpus is a gorpus. Wren is not a gorpus.", + "query": "Prove: Wren is not a vumpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a vumpus.", + "Wren is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a vumpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a vumpus.", + "Everything that is a sterpus or a vumpus is a gorpus.", + "Wren is a gorpus.", + "This contradicts with Wren is not a gorpus.", + "Wren is not a sterpus.\n\n", + "Wren is not a vumpus and Wren is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a gorpus is a jompus. Everything that is an impus or a gorpus is a lorpus. Everything that is a yumpus or a shumpus is a lorpus. Sam is not a lorpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a gorpus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a gorpus.", + "Sam is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a gorpus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a gorpus.", + "Everything that is an impus or a gorpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not an impus.\n\n", + "Sam is not a gorpus and Sam is not an impus." + ] + } + }, + "example74": { + "in_context_example0": { + "question": "Everything that is a rompus or a tumpus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a tumpus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a rompus or a tumpus.", + "Everything that is a rompus or a tumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a tumpus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a tumpus.", + "Everything that is a rompus or a tumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a rompus.\n\n", + "Max is not a tumpus and Max is not a rompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a vumpus is a dumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a rompus.\n\n", + "Sam is not a vumpus and Sam is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a yumpus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a yumpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a yumpus.", + "Stella is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a yumpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a brimpus.\n\n", + "Stella is not a yumpus and Stella is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a zumpus is a shumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a zumpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a zumpus and Rex is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a brimpus is a jompus. Sam is not a jompus.", + "query": "Prove: Sam is not a brimpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a brimpus.", + "Everything that is a wumpus or a brimpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a wumpus.\n\n", + "Sam is not a brimpus and Sam is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a tumpus or a lorpus is an impus. Wren is not an impus.", + "query": "Prove: Wren is not a lorpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a tumpus.\n\n", + "Wren is not a lorpus and Wren is not a tumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a jompus is a wumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a jompus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a jompus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a brimpus.\n\n", + "Polly is not a jompus and Polly is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a grimpus or a lempus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a lempus and Sam is not a grimpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a grimpus.", + "Sam is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a grimpus.\n\n", + "Sam is not a lempus and Sam is not a grimpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a jompus is a sterpus. Everything that is an impus or a lempus is a sterpus. Everything that is a tumpus or a jompus is a vumpus. Wren is not a dumpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a jompus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a jompus.", + "Everything that is a tumpus or a jompus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a tumpus.\n\n", + "Wren is not a jompus and Wren is not a tumpus." + ] + } + }, + "example75": { + "in_context_example0": { + "question": "Everything that is a rompus or a grimpus is a lorpus. Max is not a lorpus.", + "query": "Prove: Max is not a grimpus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a grimpus.", + "Max is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a grimpus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a lorpus.", + "Max is a lorpus.", + "This contradicts with Max is not a lorpus.", + "Max is not a rompus.\n\n", + "Max is not a grimpus and Max is not a rompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a wumpus or a shumpus is an impus. Sam is not an impus.", + "query": "Prove: Sam is not a shumpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a wumpus.\n\n", + "Sam is not a shumpus and Sam is not a wumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a shumpus is an impus. Fae is not an impus.", + "query": "Prove: Fae is not a shumpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a shumpus.", + "Fae is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a shumpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a numpus.\n\n", + "Fae is not a shumpus and Fae is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a lorpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a lorpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a tumpus.\n\n", + "Sam is not a lorpus and Sam is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a numpus is a wumpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a numpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a numpus.", + "Alex is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a numpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a numpus.", + "Everything that is a tumpus or a numpus is a wumpus.", + "Alex is a wumpus.", + "This contradicts with Alex is not a wumpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a numpus and Alex is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a lorpus is a rompus. Max is not a rompus.", + "query": "Prove: Max is not a lorpus and Max is not a dumpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a lorpus.\n\n", + "Assume Max is a dumpus.", + "Max is a dumpus or a lorpus.", + "Everything that is a dumpus or a lorpus is a rompus.", + "Max is a rompus.", + "This contradicts with Max is not a rompus.", + "Max is not a dumpus.\n\n", + "Max is not a lorpus and Max is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a zumpus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a zumpus.", + "Everything that is a lempus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a lempus.\n\n", + "Wren is not a zumpus and Wren is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a lempus is a brimpus. Wren is not a brimpus.", + "query": "Prove: Wren is not a lempus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a lempus.", + "Wren is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a lempus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a brimpus.", + "Wren is a brimpus.", + "This contradicts with Wren is not a brimpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a lempus and Wren is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a dumpus is a sterpus. Everything that is a brimpus or a wumpus is a sterpus. Everything that is a yumpus or a dumpus is an impus. Rex is not a numpus. Rex is not a sterpus.", + "query": "Prove: Rex is not a dumpus and Rex is not a yumpus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is a yumpus.", + "Rex is a yumpus or a dumpus.", + "Everything that is a yumpus or a dumpus is a sterpus.", + "Rex is a sterpus.", + "This contradicts with Rex is not a sterpus.", + "Rex is not a yumpus.\n\n", + "Rex is not a dumpus and Rex is not a yumpus." + ] + } + }, + "example76": { + "in_context_example0": { + "question": "Everything that is a wumpus or a zumpus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a zumpus.", + "Everything that is a wumpus or a zumpus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a zumpus and Sam is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lempus or a wumpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a wumpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a wumpus.", + "Sam is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a wumpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a lempus.\n\n", + "Sam is not a wumpus and Sam is not a lempus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a brimpus is a sterpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a brimpus and Fae is not a lorpus.", + "chain_of_thought": [ + "Assume Fae is a brimpus.", + "Fae is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a brimpus.\n\n", + "Assume Fae is a lorpus.", + "Fae is a lorpus or a brimpus.", + "Everything that is a lorpus or a brimpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a lorpus.\n\n", + "Fae is not a brimpus and Fae is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a tumpus or a lempus is a vumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not a lempus and Fae is not a tumpus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a tumpus.", + "Fae is a tumpus or a lempus.", + "Everything that is a tumpus or a lempus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a tumpus.\n\n", + "Fae is not a lempus and Fae is not a tumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or a sterpus is a jompus. Wren is not a jompus.", + "query": "Prove: Wren is not a sterpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a sterpus.", + "Wren is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a sterpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a sterpus.", + "Everything that is a tumpus or a sterpus is a jompus.", + "Wren is a jompus.", + "This contradicts with Wren is not a jompus.", + "Wren is not a tumpus.\n\n", + "Wren is not a sterpus and Wren is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a wumpus or a dumpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a dumpus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a dumpus.", + "Everything that is a wumpus or a dumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a wumpus.\n\n", + "Sam is not a dumpus and Sam is not a wumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or an impus is a tumpus. Wren is not a tumpus.", + "query": "Prove: Wren is not an impus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or an impus.", + "Everything that is a brimpus or an impus is a tumpus.", + "Wren is a tumpus.", + "This contradicts with Wren is not a tumpus.", + "Wren is not a brimpus.\n\n", + "Wren is not an impus and Wren is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a yumpus is an impus. Sam is not an impus.", + "query": "Prove: Sam is not a yumpus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a yumpus.", + "Sam is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a yumpus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a yumpus.", + "Everything that is a brimpus or a yumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a brimpus.\n\n", + "Sam is not a yumpus and Sam is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a zumpus is a brimpus. Everything that is a vumpus or a lempus is a brimpus. Everything that is a gorpus or a zumpus is a shumpus. Max is not a brimpus. Max is not a rompus.", + "query": "Prove: Max is not a zumpus and Max is not a gorpus.", + "chain_of_thought": [ + "Assume Max is a zumpus.", + "Max is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a zumpus.\n\n", + "Assume Max is a gorpus.", + "Max is a gorpus or a zumpus.", + "Everything that is a gorpus or a zumpus is a brimpus.", + "Max is a brimpus.", + "This contradicts with Max is not a brimpus.", + "Max is not a gorpus.\n\n", + "Max is not a zumpus and Max is not a gorpus." + ] + } + }, + "example77": { + "in_context_example0": { + "question": "Everything that is a tumpus or a wumpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a wumpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a wumpus.", + "Alex is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a wumpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a wumpus and Alex is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a zumpus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a rompus or a zumpus.", + "Everything that is a rompus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a zumpus.", + "Everything that is a rompus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a rompus.\n\n", + "Wren is not a zumpus and Wren is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a gorpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a gorpus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a gorpus.", + "Rex is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a gorpus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a lorpus.\n\n", + "Rex is not a gorpus and Rex is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a shumpus is a rompus. Alex is not a rompus.", + "query": "Prove: Alex is not a shumpus and Alex is not a numpus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a numpus.", + "Alex is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a numpus.\n\n", + "Alex is not a shumpus and Alex is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a jompus is a shumpus. Stella is not a shumpus.", + "query": "Prove: Stella is not a jompus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a jompus.", + "Everything that is a grimpus or a jompus is a shumpus.", + "Stella is a shumpus.", + "This contradicts with Stella is not a shumpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a jompus and Stella is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a numpus is a brimpus. Sam is not a brimpus.", + "query": "Prove: Sam is not a numpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a brimpus.", + "Sam is a brimpus.", + "This contradicts with Sam is not a brimpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a brimpus.", + "Sam is a brimpus.", + "This contradicts with Sam is not a brimpus.", + "Sam is not a lempus.\n\n", + "Sam is not a numpus and Sam is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a tumpus or a gorpus is a brimpus. Fae is not a brimpus.", + "query": "Prove: Fae is not a gorpus and Fae is not a tumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a tumpus or a gorpus.", + "Everything that is a tumpus or a gorpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a tumpus.", + "Fae is a tumpus or a gorpus.", + "Everything that is a tumpus or a gorpus is a brimpus.", + "Fae is a brimpus.", + "This contradicts with Fae is not a brimpus.", + "Fae is not a tumpus.\n\n", + "Fae is not a gorpus and Fae is not a tumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a rompus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a rompus and Sally is not a gorpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a gorpus.", + "Sally is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a gorpus.\n\n", + "Sally is not a rompus and Sally is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a shumpus is a sterpus. Everything that is a jompus or a rompus is a sterpus. Everything that is a lorpus or a shumpus is a tumpus. Max is not a sterpus. Max is not a dumpus.", + "query": "Prove: Max is not a shumpus and Max is not a lorpus.", + "chain_of_thought": [ + "Assume Max is a shumpus.", + "Max is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a shumpus.\n\n", + "Assume Max is a lorpus.", + "Max is a lorpus or a shumpus.", + "Everything that is a lorpus or a shumpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a lorpus.\n\n", + "Max is not a shumpus and Max is not a lorpus." + ] + } + }, + "example78": { + "in_context_example0": { + "question": "Everything that is a lempus or a rompus is an impus. Fae is not an impus.", + "query": "Prove: Fae is not a rompus and Fae is not a lempus.", + "chain_of_thought": [ + "Assume Fae is a rompus.", + "Fae is a lempus or a rompus.", + "Everything that is a lempus or a rompus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a rompus.\n\n", + "Assume Fae is a lempus.", + "Fae is a lempus or a rompus.", + "Everything that is a lempus or a rompus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a lempus.\n\n", + "Fae is not a rompus and Fae is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a brimpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a brimpus and Fae is not a tumpus.", + "chain_of_thought": [ + "Assume Fae is a brimpus.", + "Fae is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a brimpus.\n\n", + "Assume Fae is a tumpus.", + "Fae is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a tumpus.\n\n", + "Fae is not a brimpus and Fae is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or an impus is a gorpus. Stella is not a gorpus.", + "query": "Prove: Stella is not an impus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is an impus.", + "Stella is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not an impus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a gorpus.", + "Stella is a gorpus.", + "This contradicts with Stella is not a gorpus.", + "Stella is not a yumpus.\n\n", + "Stella is not an impus and Stella is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a dumpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a gorpus.\n\n", + "Fae is not a dumpus and Fae is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a numpus is a grimpus. Sam is not a grimpus.", + "query": "Prove: Sam is not a numpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a numpus.", + "Sam is a rompus or a numpus.", + "Everything that is a rompus or a numpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a numpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a numpus.", + "Everything that is a rompus or a numpus is a grimpus.", + "Sam is a grimpus.", + "This contradicts with Sam is not a grimpus.", + "Sam is not a rompus.\n\n", + "Sam is not a numpus and Sam is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a sterpus is a jompus. Max is not a jompus.", + "query": "Prove: Max is not a sterpus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is a lempus or a sterpus.", + "Everything that is a lempus or a sterpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a sterpus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a sterpus.", + "Everything that is a lempus or a sterpus is a jompus.", + "Max is a jompus.", + "This contradicts with Max is not a jompus.", + "Max is not a lempus.\n\n", + "Max is not a sterpus and Max is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a numpus or a tumpus is a rompus. Polly is not a rompus.", + "query": "Prove: Polly is not a tumpus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is a tumpus.", + "Polly is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a tumpus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or a tumpus.", + "Everything that is a numpus or a tumpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a numpus.\n\n", + "Polly is not a tumpus and Polly is not a numpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a jompus or a gorpus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a gorpus and Stella is not a jompus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is a jompus or a gorpus.", + "Everything that is a jompus or a gorpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is a jompus.", + "Stella is a jompus or a gorpus.", + "Everything that is a jompus or a gorpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a jompus.\n\n", + "Stella is not a gorpus and Stella is not a jompus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or a rompus is a sterpus. Everything that is a zumpus or a rompus is a lorpus. Everything that is a wumpus or a shumpus is a lorpus. Alex is not a lorpus. Alex is not a grimpus.", + "query": "Prove: Alex is not a rompus and Alex is not a zumpus.", + "chain_of_thought": [ + "Assume Alex is a rompus.", + "Alex is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a rompus.\n\n", + "Assume Alex is a zumpus.", + "Alex is a zumpus or a rompus.", + "Everything that is a zumpus or a rompus is a lorpus.", + "Alex is a lorpus.", + "This contradicts with Alex is not a lorpus.", + "Alex is not a zumpus.\n\n", + "Alex is not a rompus and Alex is not a zumpus." + ] + } + }, + "example79": { + "in_context_example0": { + "question": "Everything that is a grimpus or a shumpus is a dumpus. Max is not a dumpus.", + "query": "Prove: Max is not a shumpus and Max is not a grimpus.", + "chain_of_thought": [ + "Assume Max is a shumpus.", + "Max is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a shumpus.\n\n", + "Assume Max is a grimpus.", + "Max is a grimpus or a shumpus.", + "Everything that is a grimpus or a shumpus is a dumpus.", + "Max is a dumpus.", + "This contradicts with Max is not a dumpus.", + "Max is not a grimpus.\n\n", + "Max is not a shumpus and Max is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a vumpus is a zumpus. Sally is not a zumpus.", + "query": "Prove: Sally is not a vumpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a vumpus.", + "Sally is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a vumpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not an impus.\n\n", + "Sally is not a vumpus and Sally is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a vumpus is a rompus. Sam is not a rompus.", + "query": "Prove: Sam is not a vumpus and Sam is not a grimpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a grimpus.", + "Sam is a grimpus or a vumpus.", + "Everything that is a grimpus or a vumpus is a rompus.", + "Sam is a rompus.", + "This contradicts with Sam is not a rompus.", + "Sam is not a grimpus.\n\n", + "Sam is not a vumpus and Sam is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a gorpus is a numpus. Polly is not a numpus.", + "query": "Prove: Polly is not a gorpus and Polly is not a grimpus.", + "chain_of_thought": [ + "Assume Polly is a gorpus.", + "Polly is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a gorpus.\n\n", + "Assume Polly is a grimpus.", + "Polly is a grimpus or a gorpus.", + "Everything that is a grimpus or a gorpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a grimpus.\n\n", + "Polly is not a gorpus and Polly is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a yumpus is a vumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a yumpus and Fae is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a lorpus is a zumpus. Alex is not a zumpus.", + "query": "Prove: Alex is not a lorpus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a lorpus.", + "Alex is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a lorpus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a sterpus.\n\n", + "Alex is not a lorpus and Alex is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a zumpus or a grimpus is a lorpus. Sally is not a lorpus.", + "query": "Prove: Sally is not a grimpus and Sally is not a zumpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a zumpus.", + "Sally is a zumpus or a grimpus.", + "Everything that is a zumpus or a grimpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a zumpus.\n\n", + "Sally is not a grimpus and Sally is not a zumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a vumpus or a yumpus is a gorpus. Polly is not a gorpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a yumpus.", + "Everything that is a vumpus or a yumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a vumpus.\n\n", + "Polly is not a yumpus and Polly is not a vumpus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a lempus is a jompus. Everything that is a shumpus or a sterpus is a zumpus. Everything that is a lorpus or a lempus is a zumpus. Rex is not a grimpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a lempus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a lorpus.\n\n", + "Rex is not a lempus and Rex is not a lorpus." + ] + } + }, + "example80": { + "in_context_example0": { + "question": "Everything that is a lempus or a yumpus is a dumpus. Fae is not a dumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a lempus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a lempus.", + "Fae is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a dumpus.", + "Fae is a dumpus.", + "This contradicts with Fae is not a dumpus.", + "Fae is not a lempus.\n\n", + "Fae is not a yumpus and Fae is not a lempus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or a grimpus is a brimpus. Alex is not a brimpus.", + "query": "Prove: Alex is not a grimpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a jompus.\n\n", + "Alex is not a grimpus and Alex is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a lempus is a wumpus. Sally is not a wumpus.", + "query": "Prove: Sally is not a lempus and Sally is not a lorpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a lorpus.", + "Sally is a lorpus or a lempus.", + "Everything that is a lorpus or a lempus is a wumpus.", + "Sally is a wumpus.", + "This contradicts with Sally is not a wumpus.", + "Sally is not a lorpus.\n\n", + "Sally is not a lempus and Sally is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a jompus is a tumpus. Sally is not a tumpus.", + "query": "Prove: Sally is not a jompus and Sally is not a yumpus.", + "chain_of_thought": [ + "Assume Sally is a jompus.", + "Sally is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a jompus.\n\n", + "Assume Sally is a yumpus.", + "Sally is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a yumpus.\n\n", + "Sally is not a jompus and Sally is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a grimpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a grimpus and Sally is not a wumpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a wumpus.", + "Sally is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a wumpus.\n\n", + "Sally is not a grimpus and Sally is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a jompus or a lorpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a lorpus and Sally is not a jompus.", + "chain_of_thought": [ + "Assume Sally is a lorpus.", + "Sally is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a lorpus.\n\n", + "Assume Sally is a jompus.", + "Sally is a jompus or a lorpus.", + "Everything that is a jompus or a lorpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a jompus.\n\n", + "Sally is not a lorpus and Sally is not a jompus." + ] + }, + "in_context_example6": { + "question": "Everything that is a dumpus or a gorpus is a rompus. Alex is not a rompus.", + "query": "Prove: Alex is not a gorpus and Alex is not a dumpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a dumpus or a gorpus.", + "Everything that is a dumpus or a gorpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a dumpus.", + "Alex is a dumpus or a gorpus.", + "Everything that is a dumpus or a gorpus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a dumpus.\n\n", + "Alex is not a gorpus and Alex is not a dumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a yumpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a yumpus and Rex is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a tumpus or a lorpus is a gorpus. Everything that is a rompus or a shumpus is a gorpus. Everything that is a tumpus or a lorpus is a wumpus. Max is not a gorpus. Max is not a zumpus.", + "query": "Prove: Max is not a lorpus and Max is not a tumpus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a lorpus.\n\n", + "Assume Max is a tumpus.", + "Max is a tumpus or a lorpus.", + "Everything that is a tumpus or a lorpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a tumpus.\n\n", + "Max is not a lorpus and Max is not a tumpus." + ] + } + }, + "example81": { + "in_context_example0": { + "question": "Everything that is a grimpus or a numpus is a lempus. Rex is not a lempus.", + "query": "Prove: Rex is not a numpus and Rex is not a grimpus.", + "chain_of_thought": [ + "Assume Rex is a numpus.", + "Rex is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a numpus.\n\n", + "Assume Rex is a grimpus.", + "Rex is a grimpus or a numpus.", + "Everything that is a grimpus or a numpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a grimpus.\n\n", + "Rex is not a numpus and Rex is not a grimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a brimpus is a gorpus. Sally is not a gorpus.", + "query": "Prove: Sally is not a brimpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is an impus or a brimpus.", + "Everything that is an impus or a brimpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a brimpus.", + "Everything that is an impus or a brimpus is a gorpus.", + "Sally is a gorpus.", + "This contradicts with Sally is not a gorpus.", + "Sally is not an impus.\n\n", + "Sally is not a brimpus and Sally is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a numpus is a shumpus. Sally is not a shumpus.", + "query": "Prove: Sally is not a numpus and Sally is not a lorpus.", + "chain_of_thought": [ + "Assume Sally is a numpus.", + "Sally is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a numpus.\n\n", + "Assume Sally is a lorpus.", + "Sally is a lorpus or a numpus.", + "Everything that is a lorpus or a numpus is a shumpus.", + "Sally is a shumpus.", + "This contradicts with Sally is not a shumpus.", + "Sally is not a lorpus.\n\n", + "Sally is not a numpus and Sally is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a zumpus or a jompus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a jompus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a jompus.", + "Rex is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a jompus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a jompus.", + "Everything that is a zumpus or a jompus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a zumpus.\n\n", + "Rex is not a jompus and Rex is not a zumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a vumpus or a lempus is a brimpus. Sally is not a brimpus.", + "query": "Prove: Sally is not a lempus and Sally is not a vumpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a vumpus or a lempus.", + "Everything that is a vumpus or a lempus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a vumpus.", + "Sally is a vumpus or a lempus.", + "Everything that is a vumpus or a lempus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a vumpus.\n\n", + "Sally is not a lempus and Sally is not a vumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a sterpus is a shumpus. Max is not a shumpus.", + "query": "Prove: Max is not a sterpus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a sterpus.", + "Max is an impus or a sterpus.", + "Everything that is an impus or a sterpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not a sterpus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a sterpus.", + "Everything that is an impus or a sterpus is a shumpus.", + "Max is a shumpus.", + "This contradicts with Max is not a shumpus.", + "Max is not an impus.\n\n", + "Max is not a sterpus and Max is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a dumpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a vumpus or a dumpus.", + "Everything that is a vumpus or a dumpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a dumpus.", + "Everything that is a vumpus or a dumpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a dumpus and Fae is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a gorpus or a rompus is a vumpus. Sam is not a vumpus.", + "query": "Prove: Sam is not a rompus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a rompus and Sam is not a gorpus." + ] + }, + "test_example": { + "question": "Everything that is a wumpus or a gorpus is an impus. Everything that is a wumpus or a gorpus is a numpus. Everything that is a grimpus or a rompus is a numpus. Fae is not a numpus. Fae is not a vumpus.", + "query": "Prove: Fae is not a gorpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a gorpus and Fae is not a wumpus." + ] + } + }, + "example82": { + "in_context_example0": { + "question": "Everything that is a tumpus or a brimpus is a grimpus. Sally is not a grimpus.", + "query": "Prove: Sally is not a brimpus and Sally is not a tumpus.", + "chain_of_thought": [ + "Assume Sally is a brimpus.", + "Sally is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a brimpus.\n\n", + "Assume Sally is a tumpus.", + "Sally is a tumpus or a brimpus.", + "Everything that is a tumpus or a brimpus is a grimpus.", + "Sally is a grimpus.", + "This contradicts with Sally is not a grimpus.", + "Sally is not a tumpus.\n\n", + "Sally is not a brimpus and Sally is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a numpus or a shumpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a shumpus and Sam is not a numpus.", + "chain_of_thought": [ + "Assume Sam is a shumpus.", + "Sam is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a shumpus.\n\n", + "Assume Sam is a numpus.", + "Sam is a numpus or a shumpus.", + "Everything that is a numpus or a shumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a numpus.\n\n", + "Sam is not a shumpus and Sam is not a numpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a numpus is a vumpus. Alex is not a vumpus.", + "query": "Prove: Alex is not a numpus and Alex is not a lempus.", + "chain_of_thought": [ + "Assume Alex is a numpus.", + "Alex is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a numpus.\n\n", + "Assume Alex is a lempus.", + "Alex is a lempus or a numpus.", + "Everything that is a lempus or a numpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a lempus.\n\n", + "Alex is not a numpus and Alex is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a zumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a zumpus.", + "Everything that is a yumpus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a zumpus and Sam is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a brimpus or a tumpus is a vumpus. Wren is not a vumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not a brimpus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is a brimpus.", + "Wren is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a vumpus.", + "Wren is a vumpus.", + "This contradicts with Wren is not a vumpus.", + "Wren is not a brimpus.\n\n", + "Wren is not a tumpus and Wren is not a brimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a jompus is a yumpus. Sam is not a yumpus.", + "query": "Prove: Sam is not a jompus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a jompus.", + "Everything that is a sterpus or a jompus is a yumpus.", + "Sam is a yumpus.", + "This contradicts with Sam is not a yumpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a jompus and Sam is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a zumpus is a sterpus. Wren is not a sterpus.", + "query": "Prove: Wren is not a zumpus and Wren is not a grimpus.", + "chain_of_thought": [ + "Assume Wren is a zumpus.", + "Wren is a grimpus or a zumpus.", + "Everything that is a grimpus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a zumpus.\n\n", + "Assume Wren is a grimpus.", + "Wren is a grimpus or a zumpus.", + "Everything that is a grimpus or a zumpus is a sterpus.", + "Wren is a sterpus.", + "This contradicts with Wren is not a sterpus.", + "Wren is not a grimpus.\n\n", + "Wren is not a zumpus and Wren is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a zumpus is a lempus. Rex is not a lempus.", + "query": "Prove: Rex is not a zumpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a zumpus.", + "Rex is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a zumpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a shumpus.\n\n", + "Rex is not a zumpus and Rex is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a sterpus or a wumpus is a gorpus. Everything that is a sterpus or a wumpus is a grimpus. Everything that is a tumpus or a numpus is a gorpus. Fae is not a lorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a wumpus and Fae is not a sterpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a sterpus.", + "Fae is a sterpus or a wumpus.", + "Everything that is a sterpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a sterpus.\n\n", + "Fae is not a wumpus and Fae is not a sterpus." + ] + } + }, + "example83": { + "in_context_example0": { + "question": "Everything that is a sterpus or a lorpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a lorpus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a lorpus.", + "Alex is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a lorpus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a sterpus.\n\n", + "Alex is not a lorpus and Alex is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a jompus or an impus is a dumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not an impus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a jompus or an impus.", + "Everything that is a jompus or an impus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or an impus.", + "Everything that is a jompus or an impus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a jompus.\n\n", + "Sam is not an impus and Sam is not a jompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lorpus or a jompus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a jompus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a jompus.", + "Alex is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a jompus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a jompus.", + "Everything that is a lorpus or a jompus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a lorpus.\n\n", + "Alex is not a jompus and Alex is not a lorpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a numpus or a brimpus is a dumpus. Alex is not a dumpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a numpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a numpus.", + "Alex is a numpus or a brimpus.", + "Everything that is a numpus or a brimpus is a dumpus.", + "Alex is a dumpus.", + "This contradicts with Alex is not a dumpus.", + "Alex is not a numpus.\n\n", + "Alex is not a brimpus and Alex is not a numpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a brimpus is a lorpus. Rex is not a lorpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a lorpus.", + "Rex is a lorpus.", + "This contradicts with Rex is not a lorpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a brimpus and Rex is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a dumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a sterpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a sterpus.", + "Sam is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a sterpus.\n\n", + "Sam is not a dumpus and Sam is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is an impus or a tumpus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a tumpus and Wren is not an impus.", + "chain_of_thought": [ + "Assume Wren is a tumpus.", + "Wren is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a tumpus.\n\n", + "Assume Wren is an impus.", + "Wren is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not an impus.\n\n", + "Wren is not a tumpus and Wren is not an impus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a numpus is a tumpus. Stella is not a tumpus.", + "query": "Prove: Stella is not a numpus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a yumpus.\n\n", + "Stella is not a numpus and Stella is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a jompus or a rompus is a shumpus. Everything that is a jompus or a rompus is a wumpus. Everything that is a lempus or a grimpus is a wumpus. Polly is not a vumpus. Polly is not a wumpus.", + "query": "Prove: Polly is not a rompus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is a rompus.", + "Polly is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a rompus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a wumpus.", + "Polly is a wumpus.", + "This contradicts with Polly is not a wumpus.", + "Polly is not a jompus.\n\n", + "Polly is not a rompus and Polly is not a jompus." + ] + } + }, + "example84": { + "in_context_example0": { + "question": "Everything that is a sterpus or a lempus is a rompus. Stella is not a rompus.", + "query": "Prove: Stella is not a lempus and Stella is not a sterpus.", + "chain_of_thought": [ + "Assume Stella is a lempus.", + "Stella is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a lempus.\n\n", + "Assume Stella is a sterpus.", + "Stella is a sterpus or a lempus.", + "Everything that is a sterpus or a lempus is a rompus.", + "Stella is a rompus.", + "This contradicts with Stella is not a rompus.", + "Stella is not a sterpus.\n\n", + "Stella is not a lempus and Stella is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a lempus is a numpus. Fae is not a numpus.", + "query": "Prove: Fae is not a lempus and Fae is not an impus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is an impus or a lempus.", + "Everything that is an impus or a lempus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a lempus.\n\n", + "Assume Fae is an impus.", + "Fae is an impus or a lempus.", + "Everything that is an impus or a lempus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not an impus.\n\n", + "Fae is not a lempus and Fae is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or a lempus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a lempus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a lempus.", + "Everything that is a yumpus or a lempus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a lempus and Sam is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or an impus is a brimpus. Sam is not a brimpus.", + "query": "Prove: Sam is not an impus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a lorpus or an impus.", + "Everything that is a lorpus or an impus is a brimpus.", + "Sam is a brimpus.", + "This contradicts with Sam is not a brimpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or an impus.", + "Everything that is a lorpus or an impus is a brimpus.", + "Sam is a brimpus.", + "This contradicts with Sam is not a brimpus.", + "Sam is not a lorpus.\n\n", + "Sam is not an impus and Sam is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a shumpus is a lorpus. Sally is not a lorpus.", + "query": "Prove: Sally is not a shumpus and Sally is not a gorpus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is a gorpus.", + "Sally is a gorpus or a shumpus.", + "Everything that is a gorpus or a shumpus is a lorpus.", + "Sally is a lorpus.", + "This contradicts with Sally is not a lorpus.", + "Sally is not a gorpus.\n\n", + "Sally is not a shumpus and Sally is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a sterpus or a grimpus is a gorpus. Rex is not a gorpus.", + "query": "Prove: Rex is not a grimpus and Rex is not a sterpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a sterpus.", + "Rex is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a gorpus.", + "Rex is a gorpus.", + "This contradicts with Rex is not a gorpus.", + "Rex is not a sterpus.\n\n", + "Rex is not a grimpus and Rex is not a sterpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a numpus or a rompus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a rompus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is a rompus.", + "Wren is a numpus or a rompus.", + "Everything that is a numpus or a rompus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a rompus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or a rompus.", + "Everything that is a numpus or a rompus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a numpus.\n\n", + "Wren is not a rompus and Wren is not a numpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or an impus is a grimpus. Polly is not a grimpus.", + "query": "Prove: Polly is not an impus and Polly is not a yumpus.", + "chain_of_thought": [ + "Assume Polly is an impus.", + "Polly is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not an impus.\n\n", + "Assume Polly is a yumpus.", + "Polly is a yumpus or an impus.", + "Everything that is a yumpus or an impus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a yumpus.\n\n", + "Polly is not an impus and Polly is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is a numpus or a lempus is a dumpus. Everything that is a shumpus or a vumpus is a dumpus. Everything that is a numpus or a lempus is a rompus. Wren is not a brimpus. Wren is not a dumpus.", + "query": "Prove: Wren is not a lempus and Wren is not a numpus.", + "chain_of_thought": [ + "Assume Wren is a lempus.", + "Wren is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a lempus.\n\n", + "Assume Wren is a numpus.", + "Wren is a numpus or a lempus.", + "Everything that is a numpus or a lempus is a dumpus.", + "Wren is a dumpus.", + "This contradicts with Wren is not a dumpus.", + "Wren is not a numpus.\n\n", + "Wren is not a lempus and Wren is not a numpus." + ] + } + }, + "example85": { + "in_context_example0": { + "question": "Everything that is a jompus or a tumpus is a vumpus. Alex is not a vumpus.", + "query": "Prove: Alex is not a tumpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a tumpus.", + "Alex is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a tumpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a tumpus.", + "Everything that is a jompus or a tumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a jompus.\n\n", + "Alex is not a tumpus and Alex is not a jompus." + ] + }, + "in_context_example1": { + "question": "Everything that is a dumpus or a tumpus is a sterpus. Sally is not a sterpus.", + "query": "Prove: Sally is not a tumpus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a sterpus.", + "Sally is a sterpus.", + "This contradicts with Sally is not a sterpus.", + "Sally is not a dumpus.\n\n", + "Sally is not a tumpus and Sally is not a dumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a grimpus or a tumpus is a vumpus. Fae is not a vumpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a tumpus.", + "Everything that is a grimpus or a tumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a grimpus.\n\n", + "Fae is not a tumpus and Fae is not a grimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a vumpus or a sterpus is a brimpus. Alex is not a brimpus.", + "query": "Prove: Alex is not a sterpus and Alex is not a vumpus.", + "chain_of_thought": [ + "Assume Alex is a sterpus.", + "Alex is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a sterpus.\n\n", + "Assume Alex is a vumpus.", + "Alex is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a vumpus.\n\n", + "Alex is not a sterpus and Alex is not a vumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a jompus or a brimpus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a brimpus and Wren is not a jompus.", + "chain_of_thought": [ + "Assume Wren is a brimpus.", + "Wren is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a brimpus.\n\n", + "Assume Wren is a jompus.", + "Wren is a jompus or a brimpus.", + "Everything that is a jompus or a brimpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a jompus.\n\n", + "Wren is not a brimpus and Wren is not a jompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a brimpus is a tumpus. Rex is not a tumpus.", + "query": "Prove: Rex is not a brimpus and Rex is not a vumpus.", + "chain_of_thought": [ + "Assume Rex is a brimpus.", + "Rex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a brimpus.\n\n", + "Assume Rex is a vumpus.", + "Rex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a tumpus.", + "Rex is a tumpus.", + "This contradicts with Rex is not a tumpus.", + "Rex is not a vumpus.\n\n", + "Rex is not a brimpus and Rex is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a lorpus is a vumpus. Sam is not a vumpus.", + "query": "Prove: Sam is not a lorpus and Sam is not a grimpus.", + "chain_of_thought": [ + "Assume Sam is a lorpus.", + "Sam is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a lorpus.\n\n", + "Assume Sam is a grimpus.", + "Sam is a grimpus or a lorpus.", + "Everything that is a grimpus or a lorpus is a vumpus.", + "Sam is a vumpus.", + "This contradicts with Sam is not a vumpus.", + "Sam is not a grimpus.\n\n", + "Sam is not a lorpus and Sam is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a tumpus is a wumpus. Stella is not a wumpus.", + "query": "Prove: Stella is not a tumpus and Stella is not a brimpus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a brimpus.", + "Stella is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a wumpus.", + "Stella is a wumpus.", + "This contradicts with Stella is not a wumpus.", + "Stella is not a brimpus.\n\n", + "Stella is not a tumpus and Stella is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a grimpus is a jompus. Everything that is a yumpus or an impus is a numpus. Everything that is a lorpus or a grimpus is a numpus. Alex is not a numpus. Alex is not a rompus.", + "query": "Prove: Alex is not a grimpus and Alex is not a lorpus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a lorpus.", + "Alex is a lorpus or a grimpus.", + "Everything that is a lorpus or a grimpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a lorpus.\n\n", + "Alex is not a grimpus and Alex is not a lorpus." + ] + } + }, + "example86": { + "in_context_example0": { + "question": "Everything that is an impus or a dumpus is a vumpus. Sally is not a vumpus.", + "query": "Prove: Sally is not a dumpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a dumpus.", + "Sally is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a dumpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a dumpus.", + "Everything that is an impus or a dumpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not an impus.\n\n", + "Sally is not a dumpus and Sally is not an impus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or an impus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not an impus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is an impus.", + "Wren is a rompus or an impus.", + "Everything that is a rompus or an impus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not an impus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or an impus.", + "Everything that is a rompus or an impus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a rompus.\n\n", + "Wren is not an impus and Wren is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a jompus is a zumpus. Sally is not a zumpus.", + "query": "Prove: Sally is not a jompus and Sally is not a lempus.", + "chain_of_thought": [ + "Assume Sally is a jompus.", + "Sally is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a jompus.\n\n", + "Assume Sally is a lempus.", + "Sally is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a lempus.\n\n", + "Sally is not a jompus and Sally is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a lempus is a tumpus. Sally is not a tumpus.", + "query": "Prove: Sally is not a lempus and Sally is not a shumpus.", + "chain_of_thought": [ + "Assume Sally is a lempus.", + "Sally is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a lempus.\n\n", + "Assume Sally is a shumpus.", + "Sally is a shumpus or a lempus.", + "Everything that is a shumpus or a lempus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a shumpus.\n\n", + "Sally is not a lempus and Sally is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a tumpus or an impus is a jompus. Alex is not a jompus.", + "query": "Prove: Alex is not an impus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is an impus.", + "Alex is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not an impus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or an impus.", + "Everything that is a tumpus or an impus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a tumpus.\n\n", + "Alex is not an impus and Alex is not a tumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a lempus or a jompus is a grimpus. Max is not a grimpus.", + "query": "Prove: Max is not a jompus and Max is not a lempus.", + "chain_of_thought": [ + "Assume Max is a jompus.", + "Max is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a jompus.\n\n", + "Assume Max is a lempus.", + "Max is a lempus or a jompus.", + "Everything that is a lempus or a jompus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a lempus.\n\n", + "Max is not a jompus and Max is not a lempus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or a vumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a vumpus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or a vumpus.", + "Everything that is a lempus or a vumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a lempus.\n\n", + "Sam is not a vumpus and Sam is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a sterpus or a gorpus is a jompus. Alex is not a jompus.", + "query": "Prove: Alex is not a gorpus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a sterpus or a gorpus.", + "Everything that is a sterpus or a gorpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or a gorpus.", + "Everything that is a sterpus or a gorpus is a jompus.", + "Alex is a jompus.", + "This contradicts with Alex is not a jompus.", + "Alex is not a sterpus.\n\n", + "Alex is not a gorpus and Alex is not a sterpus." + ] + }, + "test_example": { + "question": "Everything that is a rompus or a shumpus is a vumpus. Everything that is a rompus or a shumpus is a grimpus. Everything that is a wumpus or a tumpus is a vumpus. Max is not a vumpus. Max is not a jompus.", + "query": "Prove: Max is not a shumpus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a shumpus.", + "Max is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a shumpus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a shumpus.", + "Everything that is a rompus or a shumpus is a vumpus.", + "Max is a vumpus.", + "This contradicts with Max is not a vumpus.", + "Max is not a rompus.\n\n", + "Max is not a shumpus and Max is not a rompus." + ] + } + }, + "example87": { + "in_context_example0": { + "question": "Everything that is a dumpus or a yumpus is a rompus. Sally is not a rompus.", + "query": "Prove: Sally is not a yumpus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a yumpus.", + "Sally is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a rompus.", + "Sally is a rompus.", + "This contradicts with Sally is not a rompus.", + "Sally is not a yumpus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a yumpus.", + "Everything that is a dumpus or a yumpus is a rompus.", + "Sally is a rompus.", + "This contradicts with Sally is not a rompus.", + "Sally is not a dumpus.\n\n", + "Sally is not a yumpus and Sally is not a dumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a vumpus is a jompus. Sam is not a jompus.", + "query": "Prove: Sam is not a vumpus and Sam is not a rompus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a rompus.", + "Sam is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a jompus.", + "Sam is a jompus.", + "This contradicts with Sam is not a jompus.", + "Sam is not a rompus.\n\n", + "Sam is not a vumpus and Sam is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a dumpus or a tumpus is a lempus. Stella is not a lempus.", + "query": "Prove: Stella is not a tumpus and Stella is not a dumpus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a dumpus.", + "Stella is a dumpus or a tumpus.", + "Everything that is a dumpus or a tumpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a dumpus.\n\n", + "Stella is not a tumpus and Stella is not a dumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is an impus or a lempus is a yumpus. Max is not a yumpus.", + "query": "Prove: Max is not a lempus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a lempus.", + "Max is an impus or a lempus.", + "Everything that is an impus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a lempus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a lempus.", + "Everything that is an impus or a lempus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not an impus.\n\n", + "Max is not a lempus and Max is not an impus." + ] + }, + "in_context_example4": { + "question": "Everything that is a vumpus or a jompus is a sterpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a jompus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a jompus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a jompus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a jompus.", + "Everything that is a vumpus or a jompus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a jompus and Fae is not a vumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a shumpus is a jompus. Sally is not a jompus.", + "query": "Prove: Sally is not a shumpus and Sally is not an impus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is an impus.", + "Sally is an impus or a shumpus.", + "Everything that is an impus or a shumpus is a jompus.", + "Sally is a jompus.", + "This contradicts with Sally is not a jompus.", + "Sally is not an impus.\n\n", + "Sally is not a shumpus and Sally is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a vumpus or a gorpus is an impus. Sam is not an impus.", + "query": "Prove: Sam is not a gorpus and Sam is not a vumpus.", + "chain_of_thought": [ + "Assume Sam is a gorpus.", + "Sam is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a gorpus.\n\n", + "Assume Sam is a vumpus.", + "Sam is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a vumpus.\n\n", + "Sam is not a gorpus and Sam is not a vumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a tumpus is a lempus. Max is not a lempus.", + "query": "Prove: Max is not a tumpus and Max is not a wumpus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is a wumpus or a tumpus.", + "Everything that is a wumpus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a tumpus.\n\n", + "Assume Max is a wumpus.", + "Max is a wumpus or a tumpus.", + "Everything that is a wumpus or a tumpus is a lempus.", + "Max is a lempus.", + "This contradicts with Max is not a lempus.", + "Max is not a wumpus.\n\n", + "Max is not a tumpus and Max is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a dumpus is an impus. Everything that is a zumpus or a wumpus is a vumpus. Everything that is a brimpus or a dumpus is a vumpus. Fae is not a vumpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a dumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a dumpus.", + "Fae is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a dumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a vumpus.", + "Fae is a vumpus.", + "This contradicts with Fae is not a vumpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a dumpus and Fae is not a brimpus." + ] + } + }, + "example88": { + "in_context_example0": { + "question": "Everything that is a gorpus or a wumpus is a rompus. Fae is not a rompus.", + "query": "Prove: Fae is not a wumpus and Fae is not a gorpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a gorpus.", + "Fae is a gorpus or a wumpus.", + "Everything that is a gorpus or a wumpus is a rompus.", + "Fae is a rompus.", + "This contradicts with Fae is not a rompus.", + "Fae is not a gorpus.\n\n", + "Fae is not a wumpus and Fae is not a gorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a shumpus or a tumpus is a brimpus. Stella is not a brimpus.", + "query": "Prove: Stella is not a tumpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a tumpus.", + "Stella is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a tumpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a tumpus.", + "Everything that is a shumpus or a tumpus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a tumpus and Stella is not a shumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a rompus or a wumpus is an impus. Max is not an impus.", + "query": "Prove: Max is not a wumpus and Max is not a rompus.", + "chain_of_thought": [ + "Assume Max is a wumpus.", + "Max is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a wumpus.\n\n", + "Assume Max is a rompus.", + "Max is a rompus or a wumpus.", + "Everything that is a rompus or a wumpus is an impus.", + "Max is an impus.", + "This contradicts with Max is not an impus.", + "Max is not a rompus.\n\n", + "Max is not a wumpus and Max is not a rompus." + ] + }, + "in_context_example3": { + "question": "Everything that is a grimpus or a rompus is a brimpus. Stella is not a brimpus.", + "query": "Prove: Stella is not a rompus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a rompus.", + "Stella is a grimpus or a rompus.", + "Everything that is a grimpus or a rompus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a rompus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a rompus.", + "Everything that is a grimpus or a rompus is a brimpus.", + "Stella is a brimpus.", + "This contradicts with Stella is not a brimpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a rompus and Stella is not a grimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a jompus or an impus is a rompus. Alex is not a rompus.", + "query": "Prove: Alex is not an impus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is an impus.", + "Alex is a jompus or an impus.", + "Everything that is a jompus or an impus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not an impus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or an impus.", + "Everything that is a jompus or an impus is a rompus.", + "Alex is a rompus.", + "This contradicts with Alex is not a rompus.", + "Alex is not a jompus.\n\n", + "Alex is not an impus and Alex is not a jompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a numpus or a yumpus is a grimpus. Polly is not a grimpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a numpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a numpus.", + "Polly is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a numpus.\n\n", + "Polly is not a yumpus and Polly is not a numpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a rompus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a rompus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a rompus.", + "Stella is a grimpus or a rompus.", + "Everything that is a grimpus or a rompus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a rompus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a rompus.", + "Everything that is a grimpus or a rompus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a rompus and Stella is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a sterpus is a rompus. Polly is not a rompus.", + "query": "Prove: Polly is not a sterpus and Polly is not a dumpus.", + "chain_of_thought": [ + "Assume Polly is a sterpus.", + "Polly is a dumpus or a sterpus.", + "Everything that is a dumpus or a sterpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a sterpus.\n\n", + "Assume Polly is a dumpus.", + "Polly is a dumpus or a sterpus.", + "Everything that is a dumpus or a sterpus is a rompus.", + "Polly is a rompus.", + "This contradicts with Polly is not a rompus.", + "Polly is not a dumpus.\n\n", + "Polly is not a sterpus and Polly is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a numpus or a rompus is a zumpus. Everything that is a numpus or a rompus is a lorpus. Everything that is a dumpus or a yumpus is a zumpus. Sally is not a zumpus. Sally is not a brimpus.", + "query": "Prove: Sally is not a rompus and Sally is not a numpus.", + "chain_of_thought": [ + "Assume Sally is a rompus.", + "Sally is a numpus or a rompus.", + "Everything that is a numpus or a rompus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a rompus.\n\n", + "Assume Sally is a numpus.", + "Sally is a numpus or a rompus.", + "Everything that is a numpus or a rompus is a zumpus.", + "Sally is a zumpus.", + "This contradicts with Sally is not a zumpus.", + "Sally is not a numpus.\n\n", + "Sally is not a rompus and Sally is not a numpus." + ] + } + }, + "example89": { + "in_context_example0": { + "question": "Everything that is a tumpus or a vumpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a vumpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a vumpus.", + "Wren is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a vumpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a tumpus.\n\n", + "Wren is not a vumpus and Wren is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a sterpus or an impus is a brimpus. Sally is not a brimpus.", + "query": "Prove: Sally is not an impus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is an impus.", + "Sally is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not an impus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a brimpus.", + "Sally is a brimpus.", + "This contradicts with Sally is not a brimpus.", + "Sally is not a sterpus.\n\n", + "Sally is not an impus and Sally is not a sterpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a shumpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a shumpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a shumpus.", + "Fae is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a shumpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a shumpus.", + "Everything that is a wumpus or a shumpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a shumpus and Fae is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a lorpus is a vumpus. Stella is not a vumpus.", + "query": "Prove: Stella is not a lorpus and Stella is not a shumpus.", + "chain_of_thought": [ + "Assume Stella is a lorpus.", + "Stella is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a lorpus.\n\n", + "Assume Stella is a shumpus.", + "Stella is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a vumpus.", + "Stella is a vumpus.", + "This contradicts with Stella is not a vumpus.", + "Stella is not a shumpus.\n\n", + "Stella is not a lorpus and Stella is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a zumpus or a dumpus is a vumpus. Rex is not a vumpus.", + "query": "Prove: Rex is not a dumpus and Rex is not a zumpus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is a zumpus.", + "Rex is a zumpus or a dumpus.", + "Everything that is a zumpus or a dumpus is a vumpus.", + "Rex is a vumpus.", + "This contradicts with Rex is not a vumpus.", + "Rex is not a zumpus.\n\n", + "Rex is not a dumpus and Rex is not a zumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a zumpus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a zumpus and Alex is not a dumpus.", + "chain_of_thought": [ + "Assume Alex is a zumpus.", + "Alex is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a zumpus.\n\n", + "Assume Alex is a dumpus.", + "Alex is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a dumpus.\n\n", + "Alex is not a zumpus and Alex is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a lempus or an impus is a numpus. Sam is not a numpus.", + "query": "Prove: Sam is not an impus and Sam is not a lempus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a lempus or an impus.", + "Everything that is a lempus or an impus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not an impus.\n\n", + "Assume Sam is a lempus.", + "Sam is a lempus or an impus.", + "Everything that is a lempus or an impus is a numpus.", + "Sam is a numpus.", + "This contradicts with Sam is not a numpus.", + "Sam is not a lempus.\n\n", + "Sam is not an impus and Sam is not a lempus." + ] + }, + "in_context_example7": { + "question": "Everything that is a jompus or a lempus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not a lempus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a lempus.", + "Alex is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a lempus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a lempus.", + "Everything that is a jompus or a lempus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a jompus.\n\n", + "Alex is not a lempus and Alex is not a jompus." + ] + }, + "test_example": { + "question": "Everything that is a gorpus or a dumpus is an impus. Everything that is a gorpus or a dumpus is a brimpus. Everything that is a zumpus or a lorpus is a brimpus. Rex is not a lempus. Rex is not a brimpus.", + "query": "Prove: Rex is not a dumpus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a dumpus.", + "Rex is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a dumpus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a gorpus.\n\n", + "Rex is not a dumpus and Rex is not a gorpus." + ] + } + }, + "example90": { + "in_context_example0": { + "question": "Everything that is an impus or a grimpus is a lempus. Stella is not a lempus.", + "query": "Prove: Stella is not a grimpus and Stella is not an impus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is an impus.", + "Stella is an impus or a grimpus.", + "Everything that is an impus or a grimpus is a lempus.", + "Stella is a lempus.", + "This contradicts with Stella is not a lempus.", + "Stella is not an impus.\n\n", + "Stella is not a grimpus and Stella is not an impus." + ] + }, + "in_context_example1": { + "question": "Everything that is a gorpus or a rompus is a lempus. Rex is not a lempus.", + "query": "Prove: Rex is not a rompus and Rex is not a gorpus.", + "chain_of_thought": [ + "Assume Rex is a rompus.", + "Rex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a rompus.\n\n", + "Assume Rex is a gorpus.", + "Rex is a gorpus or a rompus.", + "Everything that is a gorpus or a rompus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a gorpus.\n\n", + "Rex is not a rompus and Rex is not a gorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a tumpus or a vumpus is a jompus. Rex is not a jompus.", + "query": "Prove: Rex is not a vumpus and Rex is not a tumpus.", + "chain_of_thought": [ + "Assume Rex is a vumpus.", + "Rex is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a vumpus.\n\n", + "Assume Rex is a tumpus.", + "Rex is a tumpus or a vumpus.", + "Everything that is a tumpus or a vumpus is a jompus.", + "Rex is a jompus.", + "This contradicts with Rex is not a jompus.", + "Rex is not a tumpus.\n\n", + "Rex is not a vumpus and Rex is not a tumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a rompus is a lorpus. Sam is not a lorpus.", + "query": "Prove: Sam is not a rompus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a rompus.", + "Everything that is a jompus or a rompus is a lorpus.", + "Sam is a lorpus.", + "This contradicts with Sam is not a lorpus.", + "Sam is not a jompus.\n\n", + "Sam is not a rompus and Sam is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a grimpus is a tumpus. Sally is not a tumpus.", + "query": "Prove: Sally is not a grimpus and Sally is not a sterpus.", + "chain_of_thought": [ + "Assume Sally is a grimpus.", + "Sally is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a grimpus.\n\n", + "Assume Sally is a sterpus.", + "Sally is a sterpus or a grimpus.", + "Everything that is a sterpus or a grimpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a sterpus.\n\n", + "Sally is not a grimpus and Sally is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a lempus is a zumpus. Rex is not a zumpus.", + "query": "Prove: Rex is not a lempus and Rex is not a dumpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a dumpus.", + "Rex is a dumpus or a lempus.", + "Everything that is a dumpus or a lempus is a zumpus.", + "Rex is a zumpus.", + "This contradicts with Rex is not a zumpus.", + "Rex is not a dumpus.\n\n", + "Rex is not a lempus and Rex is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a numpus is an impus. Stella is not an impus.", + "query": "Prove: Stella is not a numpus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a numpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a numpus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is an impus.", + "Stella is an impus.", + "This contradicts with Stella is not an impus.", + "Stella is not a yumpus.\n\n", + "Stella is not a numpus and Stella is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a yumpus or a jompus is a grimpus. Wren is not a grimpus.", + "query": "Prove: Wren is not a jompus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a jompus.", + "Wren is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a jompus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a grimpus.", + "Wren is a grimpus.", + "This contradicts with Wren is not a grimpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a jompus and Wren is not a yumpus." + ] + }, + "test_example": { + "question": "Everything that is an impus or a grimpus is a sterpus. Everything that is a gorpus or a numpus is a tumpus. Everything that is a gorpus or a numpus is a sterpus. Alex is not a sterpus. Alex is not a wumpus.", + "query": "Prove: Alex is not a numpus and Alex is not a gorpus.", + "chain_of_thought": [ + "Assume Alex is a numpus.", + "Alex is a gorpus or a numpus.", + "Everything that is a gorpus or a numpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a numpus.\n\n", + "Assume Alex is a gorpus.", + "Alex is a gorpus or a numpus.", + "Everything that is a gorpus or a numpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a gorpus.\n\n", + "Alex is not a numpus and Alex is not a gorpus." + ] + } + }, + "example91": { + "in_context_example0": { + "question": "Everything that is a wumpus or a grimpus is an impus. Wren is not an impus.", + "query": "Prove: Wren is not a grimpus and Wren is not a wumpus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a wumpus.", + "Wren is a wumpus or a grimpus.", + "Everything that is a wumpus or a grimpus is an impus.", + "Wren is an impus.", + "This contradicts with Wren is not an impus.", + "Wren is not a wumpus.\n\n", + "Wren is not a grimpus and Wren is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a vumpus or a shumpus is a jompus. Polly is not a jompus.", + "query": "Prove: Polly is not a shumpus and Polly is not a vumpus.", + "chain_of_thought": [ + "Assume Polly is a shumpus.", + "Polly is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a shumpus.\n\n", + "Assume Polly is a vumpus.", + "Polly is a vumpus or a shumpus.", + "Everything that is a vumpus or a shumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a vumpus.\n\n", + "Polly is not a shumpus and Polly is not a vumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a sterpus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a sterpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a sterpus.", + "Rex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a sterpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a sterpus and Rex is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a brimpus or a dumpus is a shumpus. Sam is not a shumpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a brimpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a brimpus.", + "Sam is a brimpus or a dumpus.", + "Everything that is a brimpus or a dumpus is a shumpus.", + "Sam is a shumpus.", + "This contradicts with Sam is not a shumpus.", + "Sam is not a brimpus.\n\n", + "Sam is not a dumpus and Sam is not a brimpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a sterpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a sterpus and Fae is not a wumpus.", + "chain_of_thought": [ + "Assume Fae is a sterpus.", + "Fae is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a sterpus.\n\n", + "Assume Fae is a wumpus.", + "Fae is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a wumpus.\n\n", + "Fae is not a sterpus and Fae is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a yumpus or a shumpus is a gorpus. Alex is not a gorpus.", + "query": "Prove: Alex is not a shumpus and Alex is not a yumpus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a yumpus or a shumpus.", + "Everything that is a yumpus or a shumpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a yumpus.", + "Alex is a yumpus or a shumpus.", + "Everything that is a yumpus or a shumpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a yumpus.\n\n", + "Alex is not a shumpus and Alex is not a yumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a shumpus or a yumpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a yumpus and Fae is not a shumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lempus or a yumpus is a brimpus. Rex is not a brimpus.", + "query": "Prove: Rex is not a yumpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a yumpus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a yumpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a yumpus.", + "Everything that is a lempus or a yumpus is a brimpus.", + "Rex is a brimpus.", + "This contradicts with Rex is not a brimpus.", + "Rex is not a lempus.\n\n", + "Rex is not a yumpus and Rex is not a lempus." + ] + }, + "test_example": { + "question": "Everything that is a dumpus or a numpus is a vumpus. Everything that is a dumpus or a numpus is a lempus. Everything that is a rompus or a wumpus is a vumpus. Sally is not a vumpus. Sally is not a zumpus.", + "query": "Prove: Sally is not a numpus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a numpus.", + "Sally is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a numpus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a numpus.", + "Everything that is a dumpus or a numpus is a vumpus.", + "Sally is a vumpus.", + "This contradicts with Sally is not a vumpus.", + "Sally is not a dumpus.\n\n", + "Sally is not a numpus and Sally is not a dumpus." + ] + } + }, + "example92": { + "in_context_example0": { + "question": "Everything that is a lorpus or a rompus is a numpus. Fae is not a numpus.", + "query": "Prove: Fae is not a rompus and Fae is not a lorpus.", + "chain_of_thought": [ + "Assume Fae is a rompus.", + "Fae is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a rompus.\n\n", + "Assume Fae is a lorpus.", + "Fae is a lorpus or a rompus.", + "Everything that is a lorpus or a rompus is a numpus.", + "Fae is a numpus.", + "This contradicts with Fae is not a numpus.", + "Fae is not a lorpus.\n\n", + "Fae is not a rompus and Fae is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a vumpus is a zumpus. Polly is not a zumpus.", + "query": "Prove: Polly is not a vumpus and Polly is not a rompus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is a rompus.", + "Polly is a rompus or a vumpus.", + "Everything that is a rompus or a vumpus is a zumpus.", + "Polly is a zumpus.", + "This contradicts with Polly is not a zumpus.", + "Polly is not a rompus.\n\n", + "Polly is not a vumpus and Polly is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a lempus is a dumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a lempus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a lempus.", + "Sam is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a lempus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a lempus and Sam is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a vumpus is a grimpus. Max is not a grimpus.", + "query": "Prove: Max is not a vumpus and Max is not a jompus.", + "chain_of_thought": [ + "Assume Max is a vumpus.", + "Max is a jompus or a vumpus.", + "Everything that is a jompus or a vumpus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a vumpus.\n\n", + "Assume Max is a jompus.", + "Max is a jompus or a vumpus.", + "Everything that is a jompus or a vumpus is a grimpus.", + "Max is a grimpus.", + "This contradicts with Max is not a grimpus.", + "Max is not a jompus.\n\n", + "Max is not a vumpus and Max is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a brimpus is a lorpus. Polly is not a lorpus.", + "query": "Prove: Polly is not a brimpus and Polly is not a rompus.", + "chain_of_thought": [ + "Assume Polly is a brimpus.", + "Polly is a rompus or a brimpus.", + "Everything that is a rompus or a brimpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a brimpus.\n\n", + "Assume Polly is a rompus.", + "Polly is a rompus or a brimpus.", + "Everything that is a rompus or a brimpus is a lorpus.", + "Polly is a lorpus.", + "This contradicts with Polly is not a lorpus.", + "Polly is not a rompus.\n\n", + "Polly is not a brimpus and Polly is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or an impus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not an impus and Sam is not a shumpus.", + "chain_of_thought": [ + "Assume Sam is an impus.", + "Sam is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not an impus.\n\n", + "Assume Sam is a shumpus.", + "Sam is a shumpus or an impus.", + "Everything that is a shumpus or an impus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a shumpus.\n\n", + "Sam is not an impus and Sam is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a wumpus or a yumpus is a grimpus. Polly is not a grimpus.", + "query": "Prove: Polly is not a yumpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a yumpus.", + "Polly is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a yumpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a yumpus.", + "Everything that is a wumpus or a yumpus is a grimpus.", + "Polly is a grimpus.", + "This contradicts with Polly is not a grimpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a yumpus and Polly is not a wumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a brimpus or a tumpus is an impus. Sally is not an impus.", + "query": "Prove: Sally is not a tumpus and Sally is not a brimpus.", + "chain_of_thought": [ + "Assume Sally is a tumpus.", + "Sally is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a tumpus.\n\n", + "Assume Sally is a brimpus.", + "Sally is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is an impus.", + "Sally is an impus.", + "This contradicts with Sally is not an impus.", + "Sally is not a brimpus.\n\n", + "Sally is not a tumpus and Sally is not a brimpus." + ] + }, + "test_example": { + "question": "Everything that is a rompus or a zumpus is a yumpus. Everything that is a lempus or a brimpus is a yumpus. Everything that is a lempus or a brimpus is a shumpus. Wren is not a grimpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a brimpus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a brimpus.", + "Wren is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a brimpus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a brimpus.", + "Everything that is a lempus or a brimpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a lempus.\n\n", + "Wren is not a brimpus and Wren is not a lempus." + ] + } + }, + "example93": { + "in_context_example0": { + "question": "Everything that is a vumpus or a tumpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a vumpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a vumpus or a tumpus.", + "Everything that is a vumpus or a tumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a vumpus.", + "Fae is a vumpus or a tumpus.", + "Everything that is a vumpus or a tumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a vumpus.\n\n", + "Fae is not a tumpus and Fae is not a vumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a tumpus or a shumpus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a shumpus and Wren is not a tumpus.", + "chain_of_thought": [ + "Assume Wren is a shumpus.", + "Wren is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a shumpus.\n\n", + "Assume Wren is a tumpus.", + "Wren is a tumpus or a shumpus.", + "Everything that is a tumpus or a shumpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a tumpus.\n\n", + "Wren is not a shumpus and Wren is not a tumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a zumpus is a sterpus. Fae is not a sterpus.", + "query": "Prove: Fae is not a zumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a zumpus.", + "Fae is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a zumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a zumpus.", + "Everything that is a shumpus or a zumpus is a sterpus.", + "Fae is a sterpus.", + "This contradicts with Fae is not a sterpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a zumpus and Fae is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a vumpus or a lempus is a shumpus. Rex is not a shumpus.", + "query": "Prove: Rex is not a lempus and Rex is not a vumpus.", + "chain_of_thought": [ + "Assume Rex is a lempus.", + "Rex is a vumpus or a lempus.", + "Everything that is a vumpus or a lempus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a lempus.\n\n", + "Assume Rex is a vumpus.", + "Rex is a vumpus or a lempus.", + "Everything that is a vumpus or a lempus is a shumpus.", + "Rex is a shumpus.", + "This contradicts with Rex is not a shumpus.", + "Rex is not a vumpus.\n\n", + "Rex is not a lempus and Rex is not a vumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a wumpus or a lorpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a lorpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a lorpus.", + "Rex is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a lorpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a lorpus.", + "Everything that is a wumpus or a lorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a wumpus.\n\n", + "Rex is not a lorpus and Rex is not a wumpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a yumpus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a yumpus.", + "Everything that is a shumpus or a yumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a yumpus and Fae is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a grimpus is a zumpus. Wren is not a zumpus.", + "query": "Prove: Wren is not a grimpus and Wren is not a jompus.", + "chain_of_thought": [ + "Assume Wren is a grimpus.", + "Wren is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a grimpus.\n\n", + "Assume Wren is a jompus.", + "Wren is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a jompus.\n\n", + "Wren is not a grimpus and Wren is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a tumpus is a yumpus. Max is not a yumpus.", + "query": "Prove: Max is not a tumpus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a tumpus.", + "Max is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not a tumpus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a yumpus.", + "Max is a yumpus.", + "This contradicts with Max is not a yumpus.", + "Max is not an impus.\n\n", + "Max is not a tumpus and Max is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a lorpus or a sterpus is a dumpus. Everything that is a vumpus or a gorpus is a lempus. Everything that is a lorpus or a sterpus is a lempus. Rex is not a lempus. Rex is not an impus.", + "query": "Prove: Rex is not a sterpus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a sterpus.", + "Rex is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a sterpus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a lempus.", + "Rex is a lempus.", + "This contradicts with Rex is not a lempus.", + "Rex is not a lorpus.\n\n", + "Rex is not a sterpus and Rex is not a lorpus." + ] + } + }, + "example94": { + "in_context_example0": { + "question": "Everything that is a wumpus or a lempus is a tumpus. Polly is not a tumpus.", + "query": "Prove: Polly is not a lempus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a lempus.", + "Polly is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a lempus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a lempus.", + "Everything that is a wumpus or a lempus is a tumpus.", + "Polly is a tumpus.", + "This contradicts with Polly is not a tumpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a lempus and Polly is not a wumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is an impus or a tumpus is a sterpus. Polly is not a sterpus.", + "query": "Prove: Polly is not a tumpus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a tumpus.", + "Polly is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not a tumpus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a tumpus.", + "Everything that is an impus or a tumpus is a sterpus.", + "Polly is a sterpus.", + "This contradicts with Polly is not a sterpus.", + "Polly is not an impus.\n\n", + "Polly is not a tumpus and Polly is not an impus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a wumpus is a gorpus. Fae is not a gorpus.", + "query": "Prove: Fae is not a wumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a wumpus.", + "Fae is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a wumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a wumpus.", + "Everything that is a brimpus or a wumpus is a gorpus.", + "Fae is a gorpus.", + "This contradicts with Fae is not a gorpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a wumpus and Fae is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a gorpus or a grimpus is a shumpus. Polly is not a shumpus.", + "query": "Prove: Polly is not a grimpus and Polly is not a gorpus.", + "chain_of_thought": [ + "Assume Polly is a grimpus.", + "Polly is a gorpus or a grimpus.", + "Everything that is a gorpus or a grimpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a grimpus.\n\n", + "Assume Polly is a gorpus.", + "Polly is a gorpus or a grimpus.", + "Everything that is a gorpus or a grimpus is a shumpus.", + "Polly is a shumpus.", + "This contradicts with Polly is not a shumpus.", + "Polly is not a gorpus.\n\n", + "Polly is not a grimpus and Polly is not a gorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a gorpus or a dumpus is a zumpus. Sam is not a zumpus.", + "query": "Prove: Sam is not a dumpus and Sam is not a gorpus.", + "chain_of_thought": [ + "Assume Sam is a dumpus.", + "Sam is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a dumpus.\n\n", + "Assume Sam is a gorpus.", + "Sam is a gorpus or a dumpus.", + "Everything that is a gorpus or a dumpus is a zumpus.", + "Sam is a zumpus.", + "This contradicts with Sam is not a zumpus.", + "Sam is not a gorpus.\n\n", + "Sam is not a dumpus and Sam is not a gorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is an impus or a vumpus is a gorpus. Polly is not a gorpus.", + "query": "Prove: Polly is not a vumpus and Polly is not an impus.", + "chain_of_thought": [ + "Assume Polly is a vumpus.", + "Polly is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a vumpus.\n\n", + "Assume Polly is an impus.", + "Polly is an impus or a vumpus.", + "Everything that is an impus or a vumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not an impus.\n\n", + "Polly is not a vumpus and Polly is not an impus." + ] + }, + "in_context_example6": { + "question": "Everything that is a jompus or a wumpus is a gorpus. Polly is not a gorpus.", + "query": "Prove: Polly is not a wumpus and Polly is not a jompus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a jompus.", + "Polly is a jompus or a wumpus.", + "Everything that is a jompus or a wumpus is a gorpus.", + "Polly is a gorpus.", + "This contradicts with Polly is not a gorpus.", + "Polly is not a jompus.\n\n", + "Polly is not a wumpus and Polly is not a jompus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a jompus is a tumpus. Sam is not a tumpus.", + "query": "Prove: Sam is not a jompus and Sam is not an impus.", + "chain_of_thought": [ + "Assume Sam is a jompus.", + "Sam is an impus or a jompus.", + "Everything that is an impus or a jompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not a jompus.\n\n", + "Assume Sam is an impus.", + "Sam is an impus or a jompus.", + "Everything that is an impus or a jompus is a tumpus.", + "Sam is a tumpus.", + "This contradicts with Sam is not a tumpus.", + "Sam is not an impus.\n\n", + "Sam is not a jompus and Sam is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or a yumpus is a jompus. Everything that is a lempus or a dumpus is a jompus. Everything that is a lempus or a dumpus is a numpus. Polly is not a brimpus. Polly is not a jompus.", + "query": "Prove: Polly is not a dumpus and Polly is not a lempus.", + "chain_of_thought": [ + "Assume Polly is a dumpus.", + "Polly is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a dumpus.\n\n", + "Assume Polly is a lempus.", + "Polly is a lempus or a dumpus.", + "Everything that is a lempus or a dumpus is a jompus.", + "Polly is a jompus.", + "This contradicts with Polly is not a jompus.", + "Polly is not a lempus.\n\n", + "Polly is not a dumpus and Polly is not a lempus." + ] + } + }, + "example95": { + "in_context_example0": { + "question": "Everything that is a shumpus or a vumpus is a yumpus. Rex is not a yumpus.", + "query": "Prove: Rex is not a vumpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a vumpus.", + "Rex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a vumpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a vumpus.", + "Everything that is a shumpus or a vumpus is a yumpus.", + "Rex is a yumpus.", + "This contradicts with Rex is not a yumpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a vumpus and Rex is not a shumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a sterpus or a lorpus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a lorpus.", + "Everything that is a sterpus or a lorpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a sterpus.\n\n", + "Wren is not a lorpus and Wren is not a sterpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a brimpus or a tumpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a tumpus and Fae is not a brimpus.", + "chain_of_thought": [ + "Assume Fae is a tumpus.", + "Fae is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a tumpus.\n\n", + "Assume Fae is a brimpus.", + "Fae is a brimpus or a tumpus.", + "Everything that is a brimpus or a tumpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a brimpus.\n\n", + "Fae is not a tumpus and Fae is not a brimpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or an impus is a numpus. Alex is not a numpus.", + "query": "Prove: Alex is not an impus and Alex is not a rompus.", + "chain_of_thought": [ + "Assume Alex is an impus.", + "Alex is a rompus or an impus.", + "Everything that is a rompus or an impus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not an impus.\n\n", + "Assume Alex is a rompus.", + "Alex is a rompus or an impus.", + "Everything that is a rompus or an impus is a numpus.", + "Alex is a numpus.", + "This contradicts with Alex is not a numpus.", + "Alex is not a rompus.\n\n", + "Alex is not an impus and Alex is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a jompus or a yumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a yumpus and Sam is not a jompus.", + "chain_of_thought": [ + "Assume Sam is a yumpus.", + "Sam is a jompus or a yumpus.", + "Everything that is a jompus or a yumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a yumpus.\n\n", + "Assume Sam is a jompus.", + "Sam is a jompus or a yumpus.", + "Everything that is a jompus or a yumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a jompus.\n\n", + "Sam is not a yumpus and Sam is not a jompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a gorpus is a zumpus. Alex is not a zumpus.", + "query": "Prove: Alex is not a gorpus and Alex is not a vumpus.", + "chain_of_thought": [ + "Assume Alex is a gorpus.", + "Alex is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a gorpus.\n\n", + "Assume Alex is a vumpus.", + "Alex is a vumpus or a gorpus.", + "Everything that is a vumpus or a gorpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a vumpus.\n\n", + "Alex is not a gorpus and Alex is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a yumpus or a sterpus is a grimpus. Alex is not a grimpus.", + "query": "Prove: Alex is not a sterpus and Alex is not a yumpus.", + "chain_of_thought": [ + "Assume Alex is a sterpus.", + "Alex is a yumpus or a sterpus.", + "Everything that is a yumpus or a sterpus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a sterpus.\n\n", + "Assume Alex is a yumpus.", + "Alex is a yumpus or a sterpus.", + "Everything that is a yumpus or a sterpus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a yumpus.\n\n", + "Alex is not a sterpus and Alex is not a yumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a rompus is a dumpus. Sam is not a dumpus.", + "query": "Prove: Sam is not a rompus and Sam is not a wumpus.", + "chain_of_thought": [ + "Assume Sam is a rompus.", + "Sam is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a rompus.\n\n", + "Assume Sam is a wumpus.", + "Sam is a wumpus or a rompus.", + "Everything that is a wumpus or a rompus is a dumpus.", + "Sam is a dumpus.", + "This contradicts with Sam is not a dumpus.", + "Sam is not a wumpus.\n\n", + "Sam is not a rompus and Sam is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a brimpus or a jompus is a tumpus. Everything that is a dumpus or a vumpus is a lempus. Everything that is a brimpus or a jompus is a lempus. Polly is not a lempus. Polly is not a rompus.", + "query": "Prove: Polly is not a jompus and Polly is not a brimpus.", + "chain_of_thought": [ + "Assume Polly is a jompus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a jompus.\n\n", + "Assume Polly is a brimpus.", + "Polly is a brimpus or a jompus.", + "Everything that is a brimpus or a jompus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a brimpus.\n\n", + "Polly is not a jompus and Polly is not a brimpus." + ] + } + }, + "example96": { + "in_context_example0": { + "question": "Everything that is a sterpus or a brimpus is a gorpus. Max is not a gorpus.", + "query": "Prove: Max is not a brimpus and Max is not a sterpus.", + "chain_of_thought": [ + "Assume Max is a brimpus.", + "Max is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a brimpus.\n\n", + "Assume Max is a sterpus.", + "Max is a sterpus or a brimpus.", + "Everything that is a sterpus or a brimpus is a gorpus.", + "Max is a gorpus.", + "This contradicts with Max is not a gorpus.", + "Max is not a sterpus.\n\n", + "Max is not a brimpus and Max is not a sterpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a vumpus or a sterpus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a vumpus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a vumpus.", + "Stella is a vumpus or a sterpus.", + "Everything that is a vumpus or a sterpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a vumpus.\n\n", + "Stella is not a sterpus and Stella is not a vumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a lempus or a grimpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a grimpus and Rex is not a lempus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a lempus or a grimpus.", + "Everything that is a lempus or a grimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a lempus.", + "Rex is a lempus or a grimpus.", + "Everything that is a lempus or a grimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a lempus.\n\n", + "Rex is not a grimpus and Rex is not a lempus." + ] + }, + "in_context_example3": { + "question": "Everything that is a rompus or a gorpus is a lempus. Wren is not a lempus.", + "query": "Prove: Wren is not a gorpus and Wren is not a rompus.", + "chain_of_thought": [ + "Assume Wren is a gorpus.", + "Wren is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a gorpus.\n\n", + "Assume Wren is a rompus.", + "Wren is a rompus or a gorpus.", + "Everything that is a rompus or a gorpus is a lempus.", + "Wren is a lempus.", + "This contradicts with Wren is not a lempus.", + "Wren is not a rompus.\n\n", + "Wren is not a gorpus and Wren is not a rompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a sterpus or a dumpus is a rompus. Wren is not a rompus.", + "query": "Prove: Wren is not a dumpus and Wren is not a sterpus.", + "chain_of_thought": [ + "Assume Wren is a dumpus.", + "Wren is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a dumpus.\n\n", + "Assume Wren is a sterpus.", + "Wren is a sterpus or a dumpus.", + "Everything that is a sterpus or a dumpus is a rompus.", + "Wren is a rompus.", + "This contradicts with Wren is not a rompus.", + "Wren is not a sterpus.\n\n", + "Wren is not a dumpus and Wren is not a sterpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a tumpus or a wumpus is a vumpus. Alex is not a vumpus.", + "query": "Prove: Alex is not a wumpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a wumpus.", + "Alex is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a wumpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a wumpus.", + "Everything that is a tumpus or a wumpus is a vumpus.", + "Alex is a vumpus.", + "This contradicts with Alex is not a vumpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a wumpus and Alex is not a tumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a dumpus or a zumpus is a lempus. Sam is not a lempus.", + "query": "Prove: Sam is not a zumpus and Sam is not a dumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a dumpus.", + "Sam is a dumpus or a zumpus.", + "Everything that is a dumpus or a zumpus is a lempus.", + "Sam is a lempus.", + "This contradicts with Sam is not a lempus.", + "Sam is not a dumpus.\n\n", + "Sam is not a zumpus and Sam is not a dumpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a lorpus or a zumpus is a sterpus. Sam is not a sterpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a lorpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a lorpus.", + "Sam is a lorpus or a zumpus.", + "Everything that is a lorpus or a zumpus is a sterpus.", + "Sam is a sterpus.", + "This contradicts with Sam is not a sterpus.", + "Sam is not a lorpus.\n\n", + "Sam is not a zumpus and Sam is not a lorpus." + ] + }, + "test_example": { + "question": "Everything that is a dumpus or a yumpus is a zumpus. Everything that is a lempus or a wumpus is an impus. Everything that is a lempus or a wumpus is a zumpus. Wren is not a jompus. Wren is not a zumpus.", + "query": "Prove: Wren is not a wumpus and Wren is not a lempus.", + "chain_of_thought": [ + "Assume Wren is a wumpus.", + "Wren is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a wumpus.\n\n", + "Assume Wren is a lempus.", + "Wren is a lempus or a wumpus.", + "Everything that is a lempus or a wumpus is a zumpus.", + "Wren is a zumpus.", + "This contradicts with Wren is not a zumpus.", + "Wren is not a lempus.\n\n", + "Wren is not a wumpus and Wren is not a lempus." + ] + } + }, + "example97": { + "in_context_example0": { + "question": "Everything that is a zumpus or a lorpus is a numpus. Wren is not a numpus.", + "query": "Prove: Wren is not a lorpus and Wren is not a zumpus.", + "chain_of_thought": [ + "Assume Wren is a lorpus.", + "Wren is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a lorpus.\n\n", + "Assume Wren is a zumpus.", + "Wren is a zumpus or a lorpus.", + "Everything that is a zumpus or a lorpus is a numpus.", + "Wren is a numpus.", + "This contradicts with Wren is not a numpus.", + "Wren is not a zumpus.\n\n", + "Wren is not a lorpus and Wren is not a zumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a brimpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a brimpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a brimpus.", + "Sam is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a brimpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a brimpus.", + "Everything that is a yumpus or a brimpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a yumpus.\n\n", + "Sam is not a brimpus and Sam is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a shumpus or a lorpus is a tumpus. Fae is not a tumpus.", + "query": "Prove: Fae is not a lorpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a lorpus.", + "Fae is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a lorpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a lorpus.", + "Everything that is a shumpus or a lorpus is a tumpus.", + "Fae is a tumpus.", + "This contradicts with Fae is not a tumpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a lorpus and Fae is not a shumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a shumpus or a sterpus is a grimpus. Rex is not a grimpus.", + "query": "Prove: Rex is not a sterpus and Rex is not a shumpus.", + "chain_of_thought": [ + "Assume Rex is a sterpus.", + "Rex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a sterpus.\n\n", + "Assume Rex is a shumpus.", + "Rex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a grimpus.", + "Rex is a grimpus.", + "This contradicts with Rex is not a grimpus.", + "Rex is not a shumpus.\n\n", + "Rex is not a sterpus and Rex is not a shumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a grimpus or a dumpus is a numpus. Stella is not a numpus.", + "query": "Prove: Stella is not a dumpus and Stella is not a grimpus.", + "chain_of_thought": [ + "Assume Stella is a dumpus.", + "Stella is a grimpus or a dumpus.", + "Everything that is a grimpus or a dumpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a dumpus.\n\n", + "Assume Stella is a grimpus.", + "Stella is a grimpus or a dumpus.", + "Everything that is a grimpus or a dumpus is a numpus.", + "Stella is a numpus.", + "This contradicts with Stella is not a numpus.", + "Stella is not a grimpus.\n\n", + "Stella is not a dumpus and Stella is not a grimpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a brimpus or a zumpus is a grimpus. Alex is not a grimpus.", + "query": "Prove: Alex is not a zumpus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a zumpus.", + "Alex is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a zumpus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a zumpus.", + "Everything that is a brimpus or a zumpus is a grimpus.", + "Alex is a grimpus.", + "This contradicts with Alex is not a grimpus.", + "Alex is not a brimpus.\n\n", + "Alex is not a zumpus and Alex is not a brimpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a brimpus or a vumpus is a shumpus. Alex is not a shumpus.", + "query": "Prove: Alex is not a vumpus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a vumpus.", + "Alex is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a vumpus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a vumpus.", + "Everything that is a brimpus or a vumpus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a brimpus.\n\n", + "Alex is not a vumpus and Alex is not a brimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a dumpus or a shumpus is a tumpus. Sally is not a tumpus.", + "query": "Prove: Sally is not a shumpus and Sally is not a dumpus.", + "chain_of_thought": [ + "Assume Sally is a shumpus.", + "Sally is a dumpus or a shumpus.", + "Everything that is a dumpus or a shumpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a shumpus.\n\n", + "Assume Sally is a dumpus.", + "Sally is a dumpus or a shumpus.", + "Everything that is a dumpus or a shumpus is a tumpus.", + "Sally is a tumpus.", + "This contradicts with Sally is not a tumpus.", + "Sally is not a dumpus.\n\n", + "Sally is not a shumpus and Sally is not a dumpus." + ] + }, + "test_example": { + "question": "Everything that is a zumpus or a dumpus is a shumpus. Everything that is a sterpus or an impus is a brimpus. Everything that is a sterpus or an impus is a shumpus. Alex is not a shumpus. Alex is not a lorpus.", + "query": "Prove: Alex is not an impus and Alex is not a sterpus.", + "chain_of_thought": [ + "Assume Alex is an impus.", + "Alex is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not an impus.\n\n", + "Assume Alex is a sterpus.", + "Alex is a sterpus or an impus.", + "Everything that is a sterpus or an impus is a shumpus.", + "Alex is a shumpus.", + "This contradicts with Alex is not a shumpus.", + "Alex is not a sterpus.\n\n", + "Alex is not an impus and Alex is not a sterpus." + ] + } + }, + "example98": { + "in_context_example0": { + "question": "Everything that is a brimpus or a shumpus is a sterpus. Alex is not a sterpus.", + "query": "Prove: Alex is not a shumpus and Alex is not a brimpus.", + "chain_of_thought": [ + "Assume Alex is a shumpus.", + "Alex is a brimpus or a shumpus.", + "Everything that is a brimpus or a shumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a shumpus.\n\n", + "Assume Alex is a brimpus.", + "Alex is a brimpus or a shumpus.", + "Everything that is a brimpus or a shumpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a brimpus.\n\n", + "Alex is not a shumpus and Alex is not a brimpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a yumpus or a jompus is a grimpus. Stella is not a grimpus.", + "query": "Prove: Stella is not a jompus and Stella is not a yumpus.", + "chain_of_thought": [ + "Assume Stella is a jompus.", + "Stella is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a jompus.\n\n", + "Assume Stella is a yumpus.", + "Stella is a yumpus or a jompus.", + "Everything that is a yumpus or a jompus is a grimpus.", + "Stella is a grimpus.", + "This contradicts with Stella is not a grimpus.", + "Stella is not a yumpus.\n\n", + "Stella is not a jompus and Stella is not a yumpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a numpus or a yumpus is a wumpus. Fae is not a wumpus.", + "query": "Prove: Fae is not a yumpus and Fae is not a numpus.", + "chain_of_thought": [ + "Assume Fae is a yumpus.", + "Fae is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a yumpus.\n\n", + "Assume Fae is a numpus.", + "Fae is a numpus or a yumpus.", + "Everything that is a numpus or a yumpus is a wumpus.", + "Fae is a wumpus.", + "This contradicts with Fae is not a wumpus.", + "Fae is not a numpus.\n\n", + "Fae is not a yumpus and Fae is not a numpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a lorpus or a sterpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a sterpus and Rex is not a lorpus.", + "chain_of_thought": [ + "Assume Rex is a sterpus.", + "Rex is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a sterpus.\n\n", + "Assume Rex is a lorpus.", + "Rex is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a lorpus.\n\n", + "Rex is not a sterpus and Rex is not a lorpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a rompus or a grimpus is a sterpus. Stella is not a sterpus.", + "query": "Prove: Stella is not a grimpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a grimpus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a grimpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a grimpus.", + "Everything that is a rompus or a grimpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a rompus.\n\n", + "Stella is not a grimpus and Stella is not a rompus." + ] + }, + "in_context_example5": { + "question": "Everything that is a dumpus or a vumpus is a wumpus. Max is not a wumpus.", + "query": "Prove: Max is not a vumpus and Max is not a dumpus.", + "chain_of_thought": [ + "Assume Max is a vumpus.", + "Max is a dumpus or a vumpus.", + "Everything that is a dumpus or a vumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a vumpus.\n\n", + "Assume Max is a dumpus.", + "Max is a dumpus or a vumpus.", + "Everything that is a dumpus or a vumpus is a wumpus.", + "Max is a wumpus.", + "This contradicts with Max is not a wumpus.", + "Max is not a dumpus.\n\n", + "Max is not a vumpus and Max is not a dumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a wumpus is a lempus. Polly is not a lempus.", + "query": "Prove: Polly is not a wumpus and Polly is not a grimpus.", + "chain_of_thought": [ + "Assume Polly is a wumpus.", + "Polly is a grimpus or a wumpus.", + "Everything that is a grimpus or a wumpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a wumpus.\n\n", + "Assume Polly is a grimpus.", + "Polly is a grimpus or a wumpus.", + "Everything that is a grimpus or a wumpus is a lempus.", + "Polly is a lempus.", + "This contradicts with Polly is not a lempus.", + "Polly is not a grimpus.\n\n", + "Polly is not a wumpus and Polly is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is a wumpus or a gorpus is a rompus. Rex is not a rompus.", + "query": "Prove: Rex is not a gorpus and Rex is not a wumpus.", + "chain_of_thought": [ + "Assume Rex is a gorpus.", + "Rex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a gorpus.\n\n", + "Assume Rex is a wumpus.", + "Rex is a wumpus or a gorpus.", + "Everything that is a wumpus or a gorpus is a rompus.", + "Rex is a rompus.", + "This contradicts with Rex is not a rompus.", + "Rex is not a wumpus.\n\n", + "Rex is not a gorpus and Rex is not a wumpus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or a brimpus is a sterpus. Everything that is a vumpus or a lorpus is a sterpus. Everything that is a grimpus or a brimpus is a lempus. Alex is not a sterpus. Alex is not a rompus.", + "query": "Prove: Alex is not a brimpus and Alex is not a grimpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a grimpus.", + "Alex is a grimpus or a brimpus.", + "Everything that is a grimpus or a brimpus is a sterpus.", + "Alex is a sterpus.", + "This contradicts with Alex is not a sterpus.", + "Alex is not a grimpus.\n\n", + "Alex is not a brimpus and Alex is not a grimpus." + ] + } + }, + "example99": { + "in_context_example0": { + "question": "Everything that is a tumpus or a zumpus is an impus. Sam is not an impus.", + "query": "Prove: Sam is not a zumpus and Sam is not a tumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a tumpus.", + "Sam is a tumpus or a zumpus.", + "Everything that is a tumpus or a zumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a tumpus.\n\n", + "Sam is not a zumpus and Sam is not a tumpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a lorpus or a gorpus is a sterpus. Stella is not a sterpus.", + "query": "Prove: Stella is not a gorpus and Stella is not a lorpus.", + "chain_of_thought": [ + "Assume Stella is a gorpus.", + "Stella is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a gorpus.\n\n", + "Assume Stella is a lorpus.", + "Stella is a lorpus or a gorpus.", + "Everything that is a lorpus or a gorpus is a sterpus.", + "Stella is a sterpus.", + "This contradicts with Stella is not a sterpus.", + "Stella is not a lorpus.\n\n", + "Stella is not a gorpus and Stella is not a lorpus." + ] + }, + "in_context_example2": { + "question": "Everything that is a wumpus or a sterpus is a numpus. Polly is not a numpus.", + "query": "Prove: Polly is not a sterpus and Polly is not a wumpus.", + "chain_of_thought": [ + "Assume Polly is a sterpus.", + "Polly is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a sterpus.\n\n", + "Assume Polly is a wumpus.", + "Polly is a wumpus or a sterpus.", + "Everything that is a wumpus or a sterpus is a numpus.", + "Polly is a numpus.", + "This contradicts with Polly is not a numpus.", + "Polly is not a wumpus.\n\n", + "Polly is not a sterpus and Polly is not a wumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a jompus or a grimpus is a lempus. Alex is not a lempus.", + "query": "Prove: Alex is not a grimpus and Alex is not a jompus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a jompus.", + "Alex is a jompus or a grimpus.", + "Everything that is a jompus or a grimpus is a lempus.", + "Alex is a lempus.", + "This contradicts with Alex is not a lempus.", + "Alex is not a jompus.\n\n", + "Alex is not a grimpus and Alex is not a jompus." + ] + }, + "in_context_example4": { + "question": "Everything that is a lorpus or a sterpus is a yumpus. Wren is not a yumpus.", + "query": "Prove: Wren is not a sterpus and Wren is not a lorpus.", + "chain_of_thought": [ + "Assume Wren is a sterpus.", + "Wren is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a sterpus.\n\n", + "Assume Wren is a lorpus.", + "Wren is a lorpus or a sterpus.", + "Everything that is a lorpus or a sterpus is a yumpus.", + "Wren is a yumpus.", + "This contradicts with Wren is not a yumpus.", + "Wren is not a lorpus.\n\n", + "Wren is not a sterpus and Wren is not a lorpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a shumpus or a gorpus is a zumpus. Fae is not a zumpus.", + "query": "Prove: Fae is not a gorpus and Fae is not a shumpus.", + "chain_of_thought": [ + "Assume Fae is a gorpus.", + "Fae is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a gorpus.\n\n", + "Assume Fae is a shumpus.", + "Fae is a shumpus or a gorpus.", + "Everything that is a shumpus or a gorpus is a zumpus.", + "Fae is a zumpus.", + "This contradicts with Fae is not a zumpus.", + "Fae is not a shumpus.\n\n", + "Fae is not a gorpus and Fae is not a shumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a grimpus or a lempus is an impus. Fae is not an impus.", + "query": "Prove: Fae is not a lempus and Fae is not a grimpus.", + "chain_of_thought": [ + "Assume Fae is a lempus.", + "Fae is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a lempus.\n\n", + "Assume Fae is a grimpus.", + "Fae is a grimpus or a lempus.", + "Everything that is a grimpus or a lempus is an impus.", + "Fae is an impus.", + "This contradicts with Fae is not an impus.", + "Fae is not a grimpus.\n\n", + "Fae is not a lempus and Fae is not a grimpus." + ] + }, + "in_context_example7": { + "question": "Everything that is an impus or a lorpus is a sterpus. Max is not a sterpus.", + "query": "Prove: Max is not a lorpus and Max is not an impus.", + "chain_of_thought": [ + "Assume Max is a lorpus.", + "Max is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not a lorpus.\n\n", + "Assume Max is an impus.", + "Max is an impus or a lorpus.", + "Everything that is an impus or a lorpus is a sterpus.", + "Max is a sterpus.", + "This contradicts with Max is not a sterpus.", + "Max is not an impus.\n\n", + "Max is not a lorpus and Max is not an impus." + ] + }, + "test_example": { + "question": "Everything that is a grimpus or a lorpus is a gorpus. Everything that is a vumpus or a brimpus is a gorpus. Everything that is a vumpus or a brimpus is a rompus. Alex is not a shumpus. Alex is not a gorpus.", + "query": "Prove: Alex is not a brimpus and Alex is not a vumpus.", + "chain_of_thought": [ + "Assume Alex is a brimpus.", + "Alex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a brimpus.\n\n", + "Assume Alex is a vumpus.", + "Alex is a vumpus or a brimpus.", + "Everything that is a vumpus or a brimpus is a gorpus.", + "Alex is a gorpus.", + "This contradicts with Alex is not a gorpus.", + "Alex is not a vumpus.\n\n", + "Alex is not a brimpus and Alex is not a vumpus." + ] + } + }, + "example100": { + "in_context_example0": { + "question": "Everything that is a lorpus or a dumpus is a tumpus. Stella is not a tumpus.", + "query": "Prove: Stella is not a dumpus and Stella is not a lorpus.", + "chain_of_thought": [ + "Assume Stella is a dumpus.", + "Stella is a lorpus or a dumpus.", + "Everything that is a lorpus or a dumpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a dumpus.\n\n", + "Assume Stella is a lorpus.", + "Stella is a lorpus or a dumpus.", + "Everything that is a lorpus or a dumpus is a tumpus.", + "Stella is a tumpus.", + "This contradicts with Stella is not a tumpus.", + "Stella is not a lorpus.\n\n", + "Stella is not a dumpus and Stella is not a lorpus." + ] + }, + "in_context_example1": { + "question": "Everything that is a rompus or a sterpus is a lorpus. Fae is not a lorpus.", + "query": "Prove: Fae is not a sterpus and Fae is not a rompus.", + "chain_of_thought": [ + "Assume Fae is a sterpus.", + "Fae is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a sterpus.\n\n", + "Assume Fae is a rompus.", + "Fae is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a lorpus.", + "Fae is a lorpus.", + "This contradicts with Fae is not a lorpus.", + "Fae is not a rompus.\n\n", + "Fae is not a sterpus and Fae is not a rompus." + ] + }, + "in_context_example2": { + "question": "Everything that is a yumpus or a vumpus is an impus. Sam is not an impus.", + "query": "Prove: Sam is not a vumpus and Sam is not a yumpus.", + "chain_of_thought": [ + "Assume Sam is a vumpus.", + "Sam is a yumpus or a vumpus.", + "Everything that is a yumpus or a vumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a vumpus.\n\n", + "Assume Sam is a yumpus.", + "Sam is a yumpus or a vumpus.", + "Everything that is a yumpus or a vumpus is an impus.", + "Sam is an impus.", + "This contradicts with Sam is not an impus.", + "Sam is not a yumpus.\n\n", + "Sam is not a vumpus and Sam is not a yumpus." + ] + }, + "in_context_example3": { + "question": "Everything that is a yumpus or a numpus is a wumpus. Wren is not a wumpus.", + "query": "Prove: Wren is not a numpus and Wren is not a yumpus.", + "chain_of_thought": [ + "Assume Wren is a numpus.", + "Wren is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a numpus.\n\n", + "Assume Wren is a yumpus.", + "Wren is a yumpus or a numpus.", + "Everything that is a yumpus or a numpus is a wumpus.", + "Wren is a wumpus.", + "This contradicts with Wren is not a wumpus.", + "Wren is not a yumpus.\n\n", + "Wren is not a numpus and Wren is not a yumpus." + ] + }, + "in_context_example4": { + "question": "Everything that is a numpus or a grimpus is an impus. Rex is not an impus.", + "query": "Prove: Rex is not a grimpus and Rex is not a numpus.", + "chain_of_thought": [ + "Assume Rex is a grimpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a grimpus.\n\n", + "Assume Rex is a numpus.", + "Rex is a numpus or a grimpus.", + "Everything that is a numpus or a grimpus is an impus.", + "Rex is an impus.", + "This contradicts with Rex is not an impus.", + "Rex is not a numpus.\n\n", + "Rex is not a grimpus and Rex is not a numpus." + ] + }, + "in_context_example5": { + "question": "Everything that is a vumpus or a zumpus is a gorpus. Sam is not a gorpus.", + "query": "Prove: Sam is not a zumpus and Sam is not a vumpus.", + "chain_of_thought": [ + "Assume Sam is a zumpus.", + "Sam is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a zumpus.\n\n", + "Assume Sam is a vumpus.", + "Sam is a vumpus or a zumpus.", + "Everything that is a vumpus or a zumpus is a gorpus.", + "Sam is a gorpus.", + "This contradicts with Sam is not a gorpus.", + "Sam is not a vumpus.\n\n", + "Sam is not a zumpus and Sam is not a vumpus." + ] + }, + "in_context_example6": { + "question": "Everything that is a rompus or a sterpus is a yumpus. Stella is not a yumpus.", + "query": "Prove: Stella is not a sterpus and Stella is not a rompus.", + "chain_of_thought": [ + "Assume Stella is a sterpus.", + "Stella is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a sterpus.\n\n", + "Assume Stella is a rompus.", + "Stella is a rompus or a sterpus.", + "Everything that is a rompus or a sterpus is a yumpus.", + "Stella is a yumpus.", + "This contradicts with Stella is not a yumpus.", + "Stella is not a rompus.\n\n", + "Stella is not a sterpus and Stella is not a rompus." + ] + }, + "in_context_example7": { + "question": "Everything that is a shumpus or a sterpus is a zumpus. Alex is not a zumpus.", + "query": "Prove: Alex is not a sterpus and Alex is not a shumpus.", + "chain_of_thought": [ + "Assume Alex is a sterpus.", + "Alex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a sterpus.\n\n", + "Assume Alex is a shumpus.", + "Alex is a shumpus or a sterpus.", + "Everything that is a shumpus or a sterpus is a zumpus.", + "Alex is a zumpus.", + "This contradicts with Alex is not a zumpus.", + "Alex is not a shumpus.\n\n", + "Alex is not a sterpus and Alex is not a shumpus." + ] + }, + "test_example": { + "question": "Everything that is a yumpus or a jompus is a brimpus. Everything that is a tumpus or a grimpus is a sterpus. Everything that is a tumpus or a grimpus is a brimpus. Alex is not a numpus. Alex is not a brimpus.", + "query": "Prove: Alex is not a grimpus and Alex is not a tumpus.", + "chain_of_thought": [ + "Assume Alex is a grimpus.", + "Alex is a tumpus or a grimpus.", + "Everything that is a tumpus or a grimpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a grimpus.\n\n", + "Assume Alex is a tumpus.", + "Alex is a tumpus or a grimpus.", + "Everything that is a tumpus or a grimpus is a brimpus.", + "Alex is a brimpus.", + "This contradicts with Alex is not a brimpus.", + "Alex is not a tumpus.\n\n", + "Alex is not a grimpus and Alex is not a tumpus." + ] + } + } +} \ No newline at end of file