%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM390+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 : n026.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 : Mon Jul 18 14:42:07 EDT 2022 % Result : Theorem 0.99s 1.18s % Output : Proof 0.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n026.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 : Wed Jul 6 07:23:38 EDT 2022 % 0.12/0.34 % CPUTime : % 0.99/1.18 % SZS status Theorem % 0.99/1.18 (* PROOF-FOUND *) % 0.99/1.18 (* BEGIN-PROOF *) % 0.99/1.18 % SZS output start Proof % 0.99/1.18 1. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.99/1.18 2. (in T_1 T_0) (-. (in T_1 T_0)) ### Axiom % 0.99/1.18 3. (All B, ((in B T_0) => (subset B T_0))) (-. (All B, ((in B T_0) => (subset B T_0)))) ### Axiom % 0.99/1.18 4. (-. (epsilon_transitive T_0)) (All B, ((in B T_0) => (subset B T_0))) ### Definition-Pseudo(epsilon_transitive) 3 % 0.99/1.18 5. (All B, ((in B T_2) => (subset B T_2))) (-. (All B, ((in B T_2) => (subset B T_2)))) ### Axiom % 0.99/1.18 6. (-. (epsilon_transitive T_2)) (All B, ((in B T_2) => (subset B T_2))) ### Definition-Pseudo(epsilon_transitive) 5 % 0.99/1.18 7. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.99/1.18 8. (-. (subset T_0 T_0)) ### Refl(subset) % 0.99/1.18 9. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.99/1.18 10. (subset T_2 T_1) (-. (subset T_2 T_1)) ### Axiom % 0.99/1.18 11. (-. (T_0 != T_0)) (T_0 != T_0) ### Axiom % 0.99/1.18 12. (-. (subset T_2 T_0)) (subset T_1 T_0) (-. (T_0 != T_0)) (subset T_2 T_1) ### Trans 10 11 % 0.99/1.18 13. (T_0 != T_2) (T_2 = T_0) ### Sym(=) % 0.99/1.18 14. (-. (T_2 != T_0)) (T_0 != T_2) ### NotNot 13 % 0.99/1.18 15. (-. ((subset T_2 T_0) /\ (T_2 != T_0))) (T_0 != T_2) (subset T_2 T_1) (-. (T_0 != T_0)) (subset T_1 T_0) ### NotAnd 12 14 % 0.99/1.18 16. (-. (proper_subset T_2 T_0)) (subset T_1 T_0) (-. (T_0 != T_0)) (subset T_2 T_1) (T_0 != T_2) ### Definition-Pseudo(proper_subset) 15 % 0.99/1.18 17. (-. (in T_2 T_0)) (in T_2 T_0) ### Axiom % 0.99/1.18 18. ((ordinal T_0) => ((proper_subset T_2 T_0) => (in T_2 T_0))) (-. (in T_2 T_0)) (T_0 != T_2) (subset T_2 T_1) (-. (T_0 != T_0)) (subset T_1 T_0) (ordinal T_0) ### DisjTree 9 16 17 % 0.99/1.18 19. (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B)))) (ordinal T_0) (subset T_1 T_0) (-. (T_0 != T_0)) (subset T_2 T_1) (T_0 != T_2) (-. (in T_2 T_0)) ### All 18 % 0.99/1.18 20. (-. ((subset T_0 T_0) /\ (T_0 != T_0))) (-. (in T_2 T_0)) (T_0 != T_2) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B)))) ### NotAnd 8 19 % 0.99/1.18 21. (-. (proper_subset T_0 T_0)) (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B)))) (ordinal T_0) (subset T_1 T_0) (subset T_2 T_1) (T_0 != T_2) (-. (in T_2 T_0)) ### Definition-Pseudo(proper_subset) 20 % 0.99/1.18 22. (-. (in T_0 T_0)) (in T_0 T_0) ### Axiom % 0.99/1.18 23. ((ordinal T_0) => ((proper_subset T_0 T_0) => (in T_0 T_0))) (-. (in T_0 T_0)) (-. (in T_2 T_0)) (T_0 != T_2) (subset T_2 T_1) (subset T_1 T_0) (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B)))) (ordinal T_0) ### DisjTree 7 21 22 % 0.99/1.18 24. (All B, ((ordinal B) => ((proper_subset T_0 B) => (in T_0 B)))) (ordinal T_0) (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B)))) (subset T_1 T_0) (subset T_2 T_1) (T_0 != T_2) (-. (in T_2 T_0)) (-. (in T_0 T_0)) ### All 23 % 0.99/1.18 25. ((epsilon_transitive T_2) => (All B, ((ordinal B) => ((proper_subset T_2 B) => (in T_2 B))))) (-. (in T_0 T_0)) (-. (in T_2 T_0)) (T_0 != T_2) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((ordinal B) => ((proper_subset T_0 B) => (in T_0 B)))) (All B, ((in B T_2) => (subset B T_2))) ### Imply 6 24 % 0.99/1.18 26. (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (All B, ((ordinal B) => ((proper_subset T_0 B) => (in T_0 B)))) (ordinal T_0) (subset T_1 T_0) (subset T_2 T_1) (T_0 != T_2) (-. (in T_2 T_0)) (-. (in T_0 T_0)) ### All 25 % 0.99/1.18 27. ((epsilon_transitive T_0) => (All B, ((ordinal B) => ((proper_subset T_0 B) => (in T_0 B))))) (-. (in T_0 T_0)) (-. (in T_2 T_0)) (T_0 != T_2) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) ### Imply 4 26 % 0.99/1.18 28. (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_1 T_0) (subset T_2 T_1) (T_0 != T_2) (-. (in T_2 T_0)) (-. (in T_0 T_0)) ### All 27 % 0.99/1.18 29. (T_1 != T_1) ### Refl(=) % 0.99/1.18 30. (-. (subset T_0 T_1)) (-. (in T_0 T_0)) (-. (in T_2 T_0)) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) ### Trans 28 29 % 0.99/1.18 31. (in T_1 T_0) (-. (in T_1 T_0)) ### Axiom % 0.99/1.18 32. (subset T_0 T_1) (-. (subset T_0 T_1)) ### Axiom % 0.99/1.18 33. (-. ((in T_1 T_0) /\ (subset T_0 T_1))) (subset T_0 T_1) (in T_1 T_0) ### NotAnd 31 32 % 0.99/1.18 34. (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (in T_1 T_0) (subset T_0 T_1) ### All 33 % 0.99/1.18 35. ((element T_0 (powerset T_1)) <=> (subset T_0 T_1)) (in T_1 T_0) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_1 T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (-. (in T_0 T_0)) ### Equiv 30 34 % 0.99/1.18 36. (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) (-. (in T_0 T_0)) (-. (in T_2 T_0)) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (in T_1 T_0) ### All 35 % 0.99/1.18 37. (-. (subset T_0 T_0)) ### Refl(subset) % 0.99/1.18 38. (-. ((in T_0 T_0) /\ (subset T_0 T_0))) (in T_1 T_0) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_1 T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) ### NotAnd 36 37 % 0.99/1.18 39. (All B, (-. ((in T_0 B) /\ (subset B T_0)))) (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) (-. (in T_2 T_0)) (subset T_2 T_1) (subset T_1 T_0) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (in T_1 T_0) ### All 38 % 0.99/1.18 40. ((in T_1 T_0) => (subset T_1 T_0)) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) (All B, (-. ((in T_0 B) /\ (subset B T_0)))) (in T_1 T_0) ### Imply 2 39 % 0.99/1.18 41. (in T_1 T_0) (All B, (-. ((in T_0 B) /\ (subset B T_0)))) (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) (-. (in T_2 T_0)) (subset T_2 T_1) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) ### All 40 % 0.99/1.18 42. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (All B, (-. ((in T_0 B) /\ (subset B T_0)))) (in T_1 T_0) ### All 41 % 0.99/1.18 43. (All A, (All B, (-. ((in A B) /\ (subset B A))))) (in T_1 T_0) (-. (in T_2 T_0)) (subset T_2 T_1) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_0) => (subset B T_0))) (All B, (-. ((in T_1 B) /\ (subset B T_1)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### All 42 % 0.99/1.18 44. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All B, ((in B T_0) => (subset B T_0))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (in T_1 T_0) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### All 43 % 0.99/1.18 45. (epsilon_transitive T_0) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (in T_1 T_0) (-. (in T_2 T_0)) (subset T_2 T_1) (ordinal T_0) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### Definition-Pseudo(epsilon_transitive) 44 % 0.99/1.18 46. ((epsilon_transitive T_0) /\ (epsilon_connected T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (ordinal T_0) (subset T_2 T_1) (-. (in T_2 T_0)) (in T_1 T_0) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### And 45 % 0.99/1.18 47. ((ordinal T_0) => ((epsilon_transitive T_0) /\ (epsilon_connected T_0))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (in T_1 T_0) (-. (in T_2 T_0)) (subset T_2 T_1) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (ordinal T_0) ### Imply 1 46 % 0.99/1.18 48. (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (ordinal T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (subset T_2 T_1) (-. (in T_2 T_0)) (in T_1 T_0) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### All 47 % 0.99/1.18 49. (-. ((ordinal T_0) => (((subset T_2 T_1) /\ (in T_1 T_0)) => (in T_2 T_0)))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### ConjTree 48 % 0.99/1.18 50. (-. (All C, ((ordinal C) => (((subset T_2 T_1) /\ (in T_1 C)) => (in T_2 C))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### NotAllEx 49 % 0.99/1.18 51. (-. ((ordinal T_1) => (All C, ((ordinal C) => (((subset T_2 T_1) /\ (in T_1 C)) => (in T_2 C)))))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (All B, ((in B T_2) => (subset B T_2))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### NotImply 50 % 0.99/1.18 52. (-. (All B, ((ordinal B) => (All C, ((ordinal C) => (((subset T_2 B) /\ (in B C)) => (in T_2 C))))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All B, ((in B T_2) => (subset B T_2))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### NotAllEx 51 % 0.99/1.18 53. (epsilon_transitive T_2) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (-. (All B, ((ordinal B) => (All C, ((ordinal C) => (((subset T_2 B) /\ (in B C)) => (in T_2 C))))))) ### Definition-Pseudo(epsilon_transitive) 52 % 0.99/1.18 54. (-. ((epsilon_transitive T_2) => (All B, ((ordinal B) => (All C, ((ordinal C) => (((subset T_2 B) /\ (in B C)) => (in T_2 C)))))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) ### NotImply 53 % 0.99/1.18 55. (-. (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => (All C, ((ordinal C) => (((subset A B) /\ (in B C)) => (in A C))))))))) (All A, (All B, (-. ((in A B) /\ (subset B A))))) (All A, ((epsilon_transitive A) => (All B, ((ordinal B) => ((proper_subset A B) => (in A B)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### NotAllEx 54 % 0.99/1.18 % SZS output end Proof % 0.99/1.18 (* END-PROOF *) %------------------------------------------------------------------------------