%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 05:44:42 EDT 2022 % Result : Theorem 0.72s 0.90s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 02:19:37 EDT 2022 % 0.12/0.34 % CPUTime : % 0.72/0.90 % SZS status Theorem % 0.72/0.90 (* PROOF-FOUND *) % 0.72/0.90 (* BEGIN-PROOF *) % 0.72/0.90 % SZS output start Proof % 0.72/0.90 1. ((empty_set) != (empty_set)) ### NotEqual % 0.72/0.90 2. (in T_0 (empty_set)) (-. (in T_0 (empty_set))) ### Axiom % 0.72/0.90 3. (All B, (-. (in B (empty_set)))) (in T_0 (empty_set)) ### All 2 % 0.72/0.90 4. (((empty_set) = (empty_set)) <=> (All B, (-. (in B (empty_set))))) (in T_0 (empty_set)) ### Equiv 1 3 % 0.72/0.90 5. (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) (in T_0 (empty_set)) ### All 4 % 0.72/0.90 6. ((in T_1 T_0) /\ (in T_0 (empty_set))) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### And 5 % 0.72/0.90 7. (Ex D, ((in T_1 D) /\ (in D (empty_set)))) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### Exists 6 % 0.72/0.90 8. (in T_1 (empty_set)) (-. (in T_1 (empty_set))) ### Axiom % 0.72/0.90 9. (All B, (-. (in B (empty_set)))) (in T_1 (empty_set)) ### All 8 % 0.72/0.90 10. (((empty_set) = (empty_set)) <=> (All B, (-. (in B (empty_set))))) (in T_1 (empty_set)) ### Equiv 1 9 % 0.72/0.90 11. (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) (in T_1 (empty_set)) ### All 10 % 0.72/0.90 12. (-. ((in T_1 (empty_set)) <=> (Ex D, ((in T_1 D) /\ (in D (empty_set)))))) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### NotEquiv 7 11 % 0.72/0.90 13. (-. (All C, ((in C (empty_set)) <=> (Ex D, ((in C D) /\ (in D (empty_set))))))) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### NotAllEx 12 % 0.72/0.90 14. ((union (empty_set)) != (empty_set)) ((empty_set) = (union (empty_set))) ### Sym(=) % 0.72/0.90 15. (((empty_set) = (union (empty_set))) <=> (All C, ((in C (empty_set)) <=> (Ex D, ((in C D) /\ (in D (empty_set))))))) ((union (empty_set)) != (empty_set)) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### Equiv 13 14 % 0.72/0.90 16. (All B, ((B = (union (empty_set))) <=> (All C, ((in C B) <=> (Ex D, ((in C D) /\ (in D (empty_set)))))))) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ((union (empty_set)) != (empty_set)) ### All 15 % 0.72/0.90 17. (All A, (All B, ((B = (union A)) <=> (All C, ((in C B) <=> (Ex D, ((in C D) /\ (in D A)))))))) ((union (empty_set)) != (empty_set)) (All A, ((A = (empty_set)) <=> (All B, (-. (in B A))))) ### All 16 % 0.72/0.90 % SZS output end Proof % 0.72/0.90 (* END-PROOF *) %------------------------------------------------------------------------------