%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n007.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 14:48:26 EDT 2022 % Result : Theorem 10.20s 10.47s % Output : Proof 10.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.36 % Computer : n007.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Mon Jun 20 11:38:44 EDT 2022 % 0.14/0.36 % CPUTime : % 10.20/10.47 % SZS status Theorem % 10.20/10.47 (* PROOF-FOUND *) % 10.20/10.47 (* BEGIN-PROOF *) % 10.20/10.47 % SZS output start Proof % 10.20/10.47 1. ((empty_set) != (set_intersection2 (empty_set) T_0)) ((set_intersection2 (empty_set) T_0) = (empty_set)) ### Sym(=) % 10.20/10.47 2. (disjoint (empty_set) T_0) ((empty_set) != (set_intersection2 (empty_set) T_0)) ### Definition-Pseudo(disjoint) 1 % 10.20/10.47 3. (-. (-. (disjoint (empty_set) T_0))) ((empty_set) != (set_intersection2 (empty_set) T_0)) ### NotNot 2 % 10.20/10.47 4. (in T_1 (empty_set)) (-. (in T_1 (empty_set))) ### Axiom % 10.20/10.47 5. (in T_1 (empty_set)) (-. (in T_1 (empty_set))) ### Axiom % 10.20/10.47 6. (-. ((in T_1 (empty_set)) /\ (in T_1 (empty_set)))) (in T_1 (empty_set)) ### NotAnd 4 5 % 10.20/10.47 7. (-. (Ex C, ((in C (empty_set)) /\ (in C (empty_set))))) (in T_1 (empty_set)) ### NotExists 6 % 10.20/10.47 8. (-. (in T_2 (empty_set))) (in T_2 (empty_set)) ### Axiom % 10.20/10.47 9. ((in T_2 (empty_set)) /\ (in T_2 (empty_set))) (-. (in T_2 (empty_set))) ### And 8 % 10.20/10.47 10. (in T_2 (empty_set)) (-. (in T_2 (empty_set))) ### Axiom % 10.20/10.47 11. (in T_2 (empty_set)) (-. (in T_2 (empty_set))) ### Axiom % 10.20/10.47 12. (-. ((in T_2 (empty_set)) /\ (in T_2 (empty_set)))) (in T_2 (empty_set)) ### NotAnd 10 11 % 10.20/10.47 13. (-. ((in T_2 (empty_set)) <=> ((in T_2 (empty_set)) /\ (in T_2 (empty_set))))) ### NotEquiv 9 12 % 10.20/10.47 14. (-. (All D, ((in D (empty_set)) <=> ((in D (empty_set)) /\ (in D (empty_set)))))) ### NotAllEx 13 % 10.20/10.47 15. ((set_intersection2 (empty_set) (empty_set)) != (empty_set)) ((empty_set) = (set_intersection2 (empty_set) (empty_set))) ### Sym(=) % 10.20/10.47 16. (((empty_set) = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D (empty_set)) <=> ((in D (empty_set)) /\ (in D (empty_set)))))) ((set_intersection2 (empty_set) (empty_set)) != (empty_set)) ### Equiv 14 15 % 10.20/10.47 17. (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ((set_intersection2 (empty_set) (empty_set)) != (empty_set)) ### All 16 % 10.20/10.47 18. (-. (disjoint (empty_set) (empty_set))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ### Definition-Pseudo(disjoint) 17 % 10.20/10.47 19. (-. ((Ex C, ((in C (empty_set)) /\ (in C (empty_set)))) /\ (disjoint (empty_set) (empty_set)))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (in T_1 (empty_set)) ### NotAnd 7 18 % 10.20/10.47 20. ((-. ((-. (disjoint (empty_set) (empty_set))) /\ (All C, (-. ((in C (empty_set)) /\ (in C (empty_set))))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C (empty_set)))) /\ (disjoint (empty_set) (empty_set))))) (in T_1 (empty_set)) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ### And 19 % 10.20/10.47 21. (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (in T_1 (empty_set)) ### All 20 % 10.20/10.47 22. ((in T_1 (empty_set)) /\ (in T_1 T_0)) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) ### And 21 % 10.20/10.47 23. (-. (-. ((in T_1 (empty_set)) /\ (in T_1 T_0)))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ### NotNot 22 % 10.20/10.47 24. (-. (All C, (-. ((in C (empty_set)) /\ (in C T_0))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) ### NotAllEx 23 % 10.20/10.47 25. (-. ((-. (disjoint (empty_set) T_0)) /\ (All C, (-. ((in C (empty_set)) /\ (in C T_0)))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ((empty_set) != (set_intersection2 (empty_set) T_0)) ### NotAnd 3 24 % 10.20/10.47 26. ((-. ((-. (disjoint (empty_set) T_0)) /\ (All C, (-. ((in C (empty_set)) /\ (in C T_0)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C T_0))) /\ (disjoint (empty_set) T_0)))) ((empty_set) != (set_intersection2 (empty_set) T_0)) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) ### And 25 % 10.20/10.47 27. (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) ((empty_set) != (set_intersection2 (empty_set) T_0)) ### All 26 % 10.20/10.47 28. (in T_3 (empty_set)) (-. (in T_3 (empty_set))) ### Axiom % 10.20/10.47 29. (-. (in T_3 T_0)) (in T_3 T_0) ### Axiom % 10.20/10.47 30. ((in T_3 (empty_set)) /\ (in T_3 T_0)) (-. (in T_3 T_0)) ### And 29 % 10.20/10.47 31. ((in T_3 (empty_set)) <=> ((in T_3 (empty_set)) /\ (in T_3 T_0))) (-. (in T_3 T_0)) (in T_3 (empty_set)) ### Equiv 28 30 % 10.20/10.47 32. (All D, ((in D (empty_set)) <=> ((in D (empty_set)) /\ (in D T_0)))) (in T_3 (empty_set)) (-. (in T_3 T_0)) ### All 31 % 10.20/10.47 33. (((empty_set) = (set_intersection2 (empty_set) T_0)) <=> (All D, ((in D (empty_set)) <=> ((in D (empty_set)) /\ (in D T_0))))) (-. (in T_3 T_0)) (in T_3 (empty_set)) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) ### Equiv 27 32 % 10.20/10.47 34. (All C, ((C = (set_intersection2 (empty_set) T_0)) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D T_0)))))) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) (empty_set))) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D (empty_set))))))) (in T_3 (empty_set)) (-. (in T_3 T_0)) ### All 33 % 10.20/10.47 35. (All B, (All C, ((C = (set_intersection2 (empty_set) B)) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D B))))))) (-. (in T_3 T_0)) (in T_3 (empty_set)) (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (All C, ((C = (set_intersection2 (empty_set) T_0)) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D T_0)))))) ### All 34 % 10.20/10.47 36. (All B, ((-. ((-. (disjoint (empty_set) B)) /\ (All C, (-. ((in C (empty_set)) /\ (in C B)))))) /\ (-. ((Ex C, ((in C (empty_set)) /\ (in C B))) /\ (disjoint (empty_set) B))))) (in T_3 (empty_set)) (-. (in T_3 T_0)) (All B, (All C, ((C = (set_intersection2 (empty_set) B)) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D B))))))) ### All 35 % 10.20/10.47 37. (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) (All B, (All C, ((C = (set_intersection2 (empty_set) B)) <=> (All D, ((in D C) <=> ((in D (empty_set)) /\ (in D B))))))) (-. (in T_3 T_0)) (in T_3 (empty_set)) ### All 36 % 10.20/10.48 38. (All A, (All B, (All C, ((C = (set_intersection2 A B)) <=> (All D, ((in D C) <=> ((in D A) /\ (in D B)))))))) (in T_3 (empty_set)) (-. (in T_3 T_0)) (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) ### All 37 % 10.20/10.48 39. (-. ((in T_3 (empty_set)) => (in T_3 T_0))) (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) (All A, (All B, (All C, ((C = (set_intersection2 A B)) <=> (All D, ((in D C) <=> ((in D A) /\ (in D B)))))))) ### NotImply 38 % 10.20/10.48 40. (-. (All C, ((in C (empty_set)) => (in C T_0)))) (All A, (All B, (All C, ((C = (set_intersection2 A B)) <=> (All D, ((in D C) <=> ((in D A) /\ (in D B)))))))) (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) ### NotAllEx 39 % 10.20/10.48 41. (-. (subset (empty_set) T_0)) (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) (All A, (All B, (All C, ((C = (set_intersection2 A B)) <=> (All D, ((in D C) <=> ((in D A) /\ (in D B)))))))) ### Definition-Pseudo(subset) 40 % 10.20/10.48 42. (-. (All A, (subset (empty_set) A))) (All A, (All B, (All C, ((C = (set_intersection2 A B)) <=> (All D, ((in D C) <=> ((in D A) /\ (in D B)))))))) (All A, (All B, ((-. ((-. (disjoint A B)) /\ (All C, (-. ((in C A) /\ (in C B)))))) /\ (-. ((Ex C, ((in C A) /\ (in C B))) /\ (disjoint A B)))))) ### NotAllEx 41 % 10.20/10.48 % SZS output end Proof % 10.20/10.48 (* END-PROOF *) %------------------------------------------------------------------------------