%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n019.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 05:42:31 EDT 2022 % Result : Theorem 0.71s 0.90s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n019.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 : Sun Jul 10 11:42:38 EDT 2022 % 0.12/0.34 % CPUTime : % 0.71/0.90 % SZS status Theorem % 0.71/0.90 (* PROOF-FOUND *) % 0.71/0.90 (* BEGIN-PROOF *) % 0.71/0.90 % SZS output start Proof % 0.71/0.90 1. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 0.71/0.90 2. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom % 0.71/0.90 3. ((member T_0 T_1) /\ (-. (member T_0 T_2))) (-. (member T_0 T_1)) ### And 2 % 0.71/0.90 4. ((member T_0 (difference T_1 T_2)) <=> ((member T_0 T_1) /\ (-. (member T_0 T_2)))) (-. (member T_0 T_1)) (member T_0 (difference T_1 T_2)) ### Equiv 1 3 % 0.71/0.90 5. (All D, ((member D (difference T_1 T_2)) <=> ((member D T_1) /\ (-. (member D T_2))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_1)) ### All 4 % 0.71/0.90 6. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (-. (member T_0 T_1)) (member T_0 (difference T_1 T_2)) ### All 5 % 0.71/0.90 7. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_1)) ### All 6 % 0.71/0.90 8. (-. (member T_0 (union T_2 T_3))) (member T_0 (union T_2 T_3)) ### Axiom % 0.71/0.90 9. ((member T_0 T_1) => (member T_0 (union T_2 T_3))) (-. (member T_0 (union T_2 T_3))) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Imply 7 8 % 0.71/0.90 10. (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 (union T_2 T_3))) ### All 9 % 0.71/0.90 11. (member T_0 (difference T_1 T_2)) (-. (member T_0 (difference T_1 T_2))) ### Axiom % 0.71/0.90 12. (member T_0 T_2) (-. (member T_0 T_2)) ### Axiom % 0.71/0.90 13. ((member T_0 T_1) /\ (-. (member T_0 T_2))) (member T_0 T_2) ### And 12 % 0.71/0.90 14. ((member T_0 (difference T_1 T_2)) <=> ((member T_0 T_1) /\ (-. (member T_0 T_2)))) (member T_0 T_2) (member T_0 (difference T_1 T_2)) ### Equiv 11 13 % 0.71/0.90 15. (All D, ((member D (difference T_1 T_2)) <=> ((member D T_1) /\ (-. (member D T_2))))) (member T_0 (difference T_1 T_2)) (member T_0 T_2) ### All 14 % 0.71/0.90 16. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (member T_0 T_2) (member T_0 (difference T_1 T_2)) ### All 15 % 0.71/0.90 17. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (member T_0 T_2) ### All 16 % 0.71/0.90 18. (-. (member T_0 T_3)) (member T_0 T_3) ### Axiom % 0.71/0.90 19. ((member T_0 T_2) \/ (member T_0 T_3)) (-. (member T_0 T_3)) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Or 17 18 % 0.71/0.90 20. ((member T_0 (union T_2 T_3)) <=> ((member T_0 T_2) \/ (member T_0 T_3))) (-. (member T_0 T_3)) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) ### Equiv 10 19 % 0.71/0.90 21. (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_3)) ### All 20 % 0.71/0.90 22. (All C, (All D, ((member D (union T_2 C)) <=> ((member D T_2) \/ (member D C))))) (-. (member T_0 T_3)) (member T_0 (difference T_1 T_2)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) ### All 21 % 0.71/0.90 23. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_0 (difference T_1 T_2)) (-. (member T_0 T_3)) ### All 22 % 0.71/0.90 24. (-. ((member T_0 (difference T_1 T_2)) => (member T_0 T_3))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotImply 23 % 0.71/0.90 25. (-. (All D, ((member D (difference T_1 T_2)) => (member D T_3)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 24 % 0.71/0.90 26. (-. (subset (difference T_1 T_2) T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### Definition-Pseudo(subset) 25 % 0.71/0.90 27. (member T_4 (difference T_1 T_3)) (-. (member T_4 (difference T_1 T_3))) ### Axiom % 0.71/0.90 28. (-. (member T_4 T_1)) (member T_4 T_1) ### Axiom % 0.71/0.90 29. ((member T_4 T_1) /\ (-. (member T_4 T_3))) (-. (member T_4 T_1)) ### And 28 % 0.71/0.90 30. ((member T_4 (difference T_1 T_3)) <=> ((member T_4 T_1) /\ (-. (member T_4 T_3)))) (-. (member T_4 T_1)) (member T_4 (difference T_1 T_3)) ### Equiv 27 29 % 0.71/0.90 31. (All D, ((member D (difference T_1 T_3)) <=> ((member D T_1) /\ (-. (member D T_3))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_1)) ### All 30 % 0.71/0.90 32. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (-. (member T_4 T_1)) (member T_4 (difference T_1 T_3)) ### All 31 % 0.71/0.90 33. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_1)) ### All 32 % 0.71/0.90 34. (-. (member T_4 (union T_2 T_3))) (member T_4 (union T_2 T_3)) ### Axiom % 0.71/0.90 35. ((member T_4 T_1) => (member T_4 (union T_2 T_3))) (-. (member T_4 (union T_2 T_3))) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Imply 33 34 % 0.71/0.90 36. (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 (union T_2 T_3))) ### All 35 % 0.71/0.90 37. (-. (member T_4 T_2)) (member T_4 T_2) ### Axiom % 0.71/0.90 38. (-. (member T_4 T_3)) (member T_4 T_3) ### Axiom % 0.71/0.90 39. ((member T_4 T_2) \/ (member T_4 T_3)) (-. (member T_4 T_3)) (-. (member T_4 T_2)) ### Or 37 38 % 0.71/0.90 40. ((member T_4 (union T_2 T_3)) <=> ((member T_4 T_2) \/ (member T_4 T_3))) (-. (member T_4 T_2)) (-. (member T_4 T_3)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) ### Equiv 36 39 % 0.71/0.90 41. (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_3)) (-. (member T_4 T_2)) ### All 40 % 0.71/0.90 42. (-. ((member T_4 T_3) \/ (member T_4 T_2))) (-. (member T_4 T_2)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) ### NotOr 41 % 0.71/0.90 43. (member T_4 (difference T_1 T_3)) (-. (member T_4 (difference T_1 T_3))) ### Axiom % 0.71/0.90 44. (member T_4 T_3) (-. (member T_4 T_3)) ### Axiom % 0.71/0.90 45. ((member T_4 T_1) /\ (-. (member T_4 T_3))) (member T_4 T_3) ### And 44 % 0.71/0.90 46. ((member T_4 (difference T_1 T_3)) <=> ((member T_4 T_1) /\ (-. (member T_4 T_3)))) (member T_4 T_3) (member T_4 (difference T_1 T_3)) ### Equiv 43 45 % 0.71/0.90 47. (All D, ((member D (difference T_1 T_3)) <=> ((member D T_1) /\ (-. (member D T_3))))) (member T_4 (difference T_1 T_3)) (member T_4 T_3) ### All 46 % 0.71/0.90 48. (All C, (All D, ((member D (difference T_1 C)) <=> ((member D T_1) /\ (-. (member D C)))))) (member T_4 T_3) (member T_4 (difference T_1 T_3)) ### All 47 % 0.71/0.90 49. (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (member T_4 T_3) ### All 48 % 0.71/0.91 50. (-. (member T_4 T_2)) (member T_4 T_2) ### Axiom % 0.71/0.91 51. ((member T_4 T_3) \/ (member T_4 T_2)) (-. (member T_4 T_2)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### Or 49 50 % 0.71/0.91 52. ((member T_4 (union T_3 T_2)) <=> ((member T_4 T_3) \/ (member T_4 T_2))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_2)) ### Equiv 42 51 % 0.71/0.91 53. (All D, ((member D (union T_3 T_2)) <=> ((member D T_3) \/ (member D T_2)))) (-. (member T_4 T_2)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) ### All 52 % 0.71/0.91 54. (All C, (All D, ((member D (union T_3 C)) <=> ((member D T_3) \/ (member D C))))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_2)) ### All 53 % 0.71/0.91 55. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_4 T_2)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All D, ((member D (union T_2 T_3)) <=> ((member D T_2) \/ (member D T_3)))) ### All 54 % 0.71/0.91 56. (All C, (All D, ((member D (union T_2 C)) <=> ((member D T_2) \/ (member D C))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (member T_4 (difference T_1 T_3)) (-. (member T_4 T_2)) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### All 55 % 0.71/0.91 57. (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. (member T_4 T_2)) (member T_4 (difference T_1 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) ### All 56 % 0.71/0.91 58. (-. ((member T_4 (difference T_1 T_3)) => (member T_4 T_2))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotImply 57 % 0.71/0.91 59. (-. (All D, ((member D (difference T_1 T_3)) => (member D T_2)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) ### NotAllEx 58 % 0.71/0.91 60. (-. (subset (difference T_1 T_3) T_2)) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### Definition-Pseudo(subset) 59 % 0.71/0.91 61. (-. ((subset (difference T_1 T_2) T_3) /\ (subset (difference T_1 T_3) T_2))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All D, ((member D T_1) => (member D (union T_2 T_3)))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAnd 26 60 % 0.71/0.91 62. (subset T_1 (union T_2 T_3)) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (-. ((subset (difference T_1 T_2) T_3) /\ (subset (difference T_1 T_3) T_2))) ### Definition-Pseudo(subset) 61 % 0.71/0.91 63. (-. ((subset T_1 (union T_2 T_3)) => ((subset (difference T_1 T_2) T_3) /\ (subset (difference T_1 T_3) T_2)))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotImply 62 % 0.71/0.91 64. (-. (All D, ((subset T_1 (union T_2 D)) => ((subset (difference T_1 T_2) D) /\ (subset (difference T_1 D) T_2))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 63 % 0.71/0.91 65. (-. (All C, (All D, ((subset T_1 (union C D)) => ((subset (difference T_1 C) D) /\ (subset (difference T_1 D) C)))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) ### NotAllEx 64 % 0.71/0.91 66. (-. (All B, (All C, (All D, ((subset B (union C D)) => ((subset (difference B C) D) /\ (subset (difference B D) C))))))) (All B, (All C, (All D, ((member D (difference B C)) <=> ((member D B) /\ (-. (member D C))))))) (All B, (All C, (All D, ((member D (union B C)) <=> ((member D B) \/ (member D C)))))) ### NotAllEx 65 % 0.71/0.91 % SZS output end Proof % 0.71/0.91 (* END-PROOF *) %------------------------------------------------------------------------------