%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n029.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 14:48:39 EDT 2022 % Result : Theorem 1.85s 2.07s % Output : Proof 1.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0. % 0.08/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 22:22:29 EDT 2022 % 0.13/0.34 % CPUTime : % 1.85/2.07 % SZS status Theorem % 1.85/2.07 (* PROOF-FOUND *) % 1.85/2.07 (* BEGIN-PROOF *) % 1.85/2.07 % SZS output start Proof % 1.85/2.07 1. (subset T_0 (empty_set)) (-. (subset T_0 (empty_set))) ### Axiom % 1.85/2.07 2. ((singleton (empty_set)) != (singleton (empty_set))) ### Refl(=) % 1.85/2.07 3. (T_0 = (empty_set)) (T_0 != (empty_set)) ### Axiom % 1.85/2.07 4. (-. (in T_0 (singleton (empty_set)))) (in T_0 (singleton (empty_set))) ### Axiom % 1.85/2.07 5. ((in T_0 (singleton (empty_set))) <=> (T_0 = (empty_set))) (-. (in T_0 (singleton (empty_set)))) (T_0 = (empty_set)) ### Equiv 3 4 % 1.85/2.07 6. (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set)))) (T_0 = (empty_set)) (-. (in T_0 (singleton (empty_set)))) ### All 5 % 1.85/2.07 7. (((singleton (empty_set)) = (singleton (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set))))) (-. (in T_0 (singleton (empty_set)))) (T_0 = (empty_set)) ### Equiv 2 6 % 1.85/2.07 8. (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (T_0 = (empty_set)) (-. (in T_0 (singleton (empty_set)))) ### All 7 % 1.85/2.07 9. ((subset T_0 (empty_set)) => (T_0 = (empty_set))) (-. (in T_0 (singleton (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (subset T_0 (empty_set)) ### Imply 1 8 % 1.85/2.07 10. (All A, ((subset A (empty_set)) => (A = (empty_set)))) (subset T_0 (empty_set)) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (-. (in T_0 (singleton (empty_set)))) ### All 9 % 1.85/2.07 11. ((singleton (empty_set)) != (singleton (empty_set))) ### Refl(=) % 1.85/2.07 12. (in T_0 (singleton (empty_set))) (-. (in T_0 (singleton (empty_set)))) ### Axiom % 1.85/2.07 13. (T_0 != (empty_set)) (T_0 = (empty_set)) ### Axiom % 1.85/2.07 14. ((in T_0 (singleton (empty_set))) <=> (T_0 = (empty_set))) (T_0 != (empty_set)) (in T_0 (singleton (empty_set))) ### Equiv 12 13 % 1.85/2.07 15. (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set)))) (in T_0 (singleton (empty_set))) (T_0 != (empty_set)) ### All 14 % 1.85/2.07 16. (((singleton (empty_set)) = (singleton (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (C = (empty_set))))) (T_0 != (empty_set)) (in T_0 (singleton (empty_set))) ### Equiv 11 15 % 1.85/2.07 17. (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (in T_0 (singleton (empty_set))) (T_0 != (empty_set)) ### All 16 % 1.85/2.07 18. (-. (subset T_0 (empty_set))) (in T_0 (singleton (empty_set))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ### Refl(subset) 17 % 1.85/2.07 19. (-. ((in T_0 (singleton (empty_set))) <=> (subset T_0 (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ### NotEquiv 10 18 % 1.85/2.07 20. (-. (All C, ((in C (singleton (empty_set))) <=> (subset C (empty_set))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ### NotAllEx 19 % 1.85/2.07 21. ((powerset (empty_set)) != (singleton (empty_set))) ((singleton (empty_set)) = (powerset (empty_set))) ### Sym(=) % 1.85/2.07 22. (((singleton (empty_set)) = (powerset (empty_set))) <=> (All C, ((in C (singleton (empty_set))) <=> (subset C (empty_set))))) ((powerset (empty_set)) != (singleton (empty_set))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ### Equiv 20 21 % 1.85/2.07 23. (All B, ((B = (powerset (empty_set))) <=> (All C, ((in C B) <=> (subset C (empty_set)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (singleton (empty_set))) <=> (All C, ((in C B) <=> (C = (empty_set)))))) ((powerset (empty_set)) != (singleton (empty_set))) ### All 22 % 1.85/2.07 24. (All A, (All B, ((B = (singleton A)) <=> (All C, ((in C B) <=> (C = A)))))) ((powerset (empty_set)) != (singleton (empty_set))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) (All B, ((B = (powerset (empty_set))) <=> (All C, ((in C B) <=> (subset C (empty_set)))))) ### All 23 % 1.85/2.07 25. (All A, (All B, ((B = (powerset A)) <=> (All C, ((in C B) <=> (subset C A)))))) (All A, ((subset A (empty_set)) => (A = (empty_set)))) ((powerset (empty_set)) != (singleton (empty_set))) (All A, (All B, ((B = (singleton A)) <=> (All C, ((in C B) <=> (C = A)))))) ### All 24 % 1.85/2.07 % SZS output end Proof % 1.85/2.07 (* END-PROOF *) %------------------------------------------------------------------------------