%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SYN548+1 : 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 : n004.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 : Thu Jul 21 12:45:06 EDT 2022 % Result : Theorem 27.03s 27.23s % Output : Proof 27.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN548+1 : TPTP v8.1.0. Released v2.2.0. % 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jul 11 22:54:07 EDT 2022 % 0.12/0.33 % CPUTime : % 27.03/27.23 % SZS status Theorem % 27.03/27.23 (* PROOF-FOUND *) % 27.03/27.23 (* BEGIN-PROOF *) % 27.03/27.23 % SZS output start Proof % 27.03/27.23 1. (-. (reachable (initial_world) (initial_world))) ### Refl(reachable) % 27.03/27.23 2. (reachable T_0 T_1) (-. (reachable T_0 T_1)) ### Axiom % 27.03/27.23 3. (-. (p T_1)) (p T_1) ### Axiom % 27.03/27.23 4. ((reachable T_0 T_1) => (p T_1)) (-. (p T_1)) (reachable T_0 T_1) ### Imply 2 3 % 27.03/27.23 5. (All W, ((reachable T_0 W) => (p W))) (reachable T_0 T_1) (-. (p T_1)) ### All 4 % 27.03/27.23 6. (reachable T_0 T_1) (-. (reachable T_0 T_1)) ### Axiom % 27.03/27.23 7. (T_2 != T_2) ### Refl(=) % 27.03/27.23 8. (-. (reachable T_0 T_2)) (reachable T_1 T_2) (reachable T_0 T_1) ### Trans 6 7 % 27.03/27.23 9. (-. (q T_2)) (q T_2) ### Axiom % 27.03/27.23 10. ((reachable T_0 T_2) => (q T_2)) (-. (q T_2)) (reachable T_0 T_1) (reachable T_1 T_2) ### Imply 8 9 % 27.03/27.23 11. (All W, ((reachable T_0 W) => (q W))) (reachable T_1 T_2) (reachable T_0 T_1) (-. (q T_2)) ### All 10 % 27.03/27.23 12. ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))) (-. (q T_2)) (reachable T_1 T_2) (-. (p T_1)) (reachable T_0 T_1) ### Or 5 11 % 27.03/27.23 13. (-. ((reachable T_1 T_2) => (q T_2))) (reachable T_0 T_1) (-. (p T_1)) ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))) ### NotImply 12 % 27.03/27.23 14. (-. (All V, ((reachable T_1 V) => (q V)))) ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))) (-. (p T_1)) (reachable T_0 T_1) ### NotAllEx 13 % 27.03/27.23 15. (-. ((reachable T_0 T_1) => ((p T_1) \/ (All V, ((reachable T_1 V) => (q V)))))) ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))) ### ConjTree 14 % 27.03/27.23 16. (-. (All Z, ((reachable T_0 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V))))))) ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))) ### NotAllEx 15 % 27.03/27.23 17. (reachable (initial_world) T_0) (-. (reachable (initial_world) T_0)) ### Axiom % 27.03/27.23 18. (T_3 != T_3) ### Refl(=) % 27.03/27.23 19. (-. (reachable (initial_world) T_3)) (reachable T_0 T_3) (reachable (initial_world) T_0) ### Trans 17 18 % 27.03/27.23 20. (reachable T_4 T_5) (-. (reachable T_4 T_5)) ### Axiom % 27.03/27.23 21. (-. (p T_5)) (p T_5) ### Axiom % 27.03/27.23 22. ((reachable T_4 T_5) => (p T_5)) (-. (p T_5)) (reachable T_4 T_5) ### Imply 20 21 % 27.03/27.23 23. (All W, ((reachable T_4 W) => (p W))) (reachable T_4 T_5) (-. (p T_5)) ### All 22 % 27.03/27.23 24. (reachable T_4 T_5) (-. (reachable T_4 T_5)) ### Axiom % 27.03/27.23 25. (T_6 != T_6) ### Refl(=) % 27.03/27.23 26. (-. (reachable T_4 T_6)) (reachable T_5 T_6) (reachable T_4 T_5) ### Trans 24 25 % 27.03/27.23 27. (-. (q T_6)) (q T_6) ### Axiom % 27.03/27.23 28. ((reachable T_4 T_6) => (q T_6)) (-. (q T_6)) (reachable T_4 T_5) (reachable T_5 T_6) ### Imply 26 27 % 27.03/27.23 29. (All W, ((reachable T_4 W) => (q W))) (reachable T_5 T_6) (reachable T_4 T_5) (-. (q T_6)) ### All 28 % 27.03/27.23 30. ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))) (-. (q T_6)) (reachable T_5 T_6) (-. (p T_5)) (reachable T_4 T_5) ### Or 23 29 % 27.03/27.23 31. (-. ((reachable T_5 T_6) => (q T_6))) (reachable T_4 T_5) (-. (p T_5)) ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))) ### NotImply 30 % 27.03/27.23 32. (-. (All V, ((reachable T_5 V) => (q V)))) ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))) (-. (p T_5)) (reachable T_4 T_5) ### NotAllEx 31 % 27.03/27.23 33. (-. ((reachable T_4 T_5) => ((p T_5) \/ (All V, ((reachable T_5 V) => (q V)))))) ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))) ### ConjTree 32 % 27.03/27.23 34. (-. (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V))))))) ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))) ### NotAllEx 33 % 27.03/27.23 35. (T_4 != T_4) ### Refl(=) % 27.03/27.23 36. (-. (reachable (initial_world) T_4)) (reachable T_3 T_4) (reachable (initial_world) T_0) (reachable T_0 T_3) ### Trans 19 35 % 27.03/27.23 37. (T_7 != T_7) ### Refl(=) % 27.03/27.23 38. (-. (reachable (initial_world) T_7)) (reachable T_4 T_7) (reachable T_0 T_3) (reachable (initial_world) T_0) (reachable T_3 T_4) ### Trans 36 37 % 27.03/27.23 39. (reachable T_8 T_9) (-. (reachable T_8 T_9)) ### Axiom % 27.03/27.23 40. (-. (p T_9)) (p T_9) ### Axiom % 27.03/27.23 41. ((reachable T_8 T_9) => (p T_9)) (-. (p T_9)) (reachable T_8 T_9) ### Imply 39 40 % 27.03/27.23 42. (All W, ((reachable T_8 W) => (p W))) (reachable T_8 T_9) (-. (p T_9)) ### All 41 % 27.03/27.23 43. (reachable T_8 T_9) (-. (reachable T_8 T_9)) ### Axiom % 27.03/27.23 44. (T_10 != T_10) ### Refl(=) % 27.03/27.23 45. (-. (reachable T_8 T_10)) (reachable T_9 T_10) (reachable T_8 T_9) ### Trans 43 44 % 27.03/27.23 46. (-. (q T_10)) (q T_10) ### Axiom % 27.03/27.23 47. ((reachable T_8 T_10) => (q T_10)) (-. (q T_10)) (reachable T_8 T_9) (reachable T_9 T_10) ### Imply 45 46 % 27.03/27.23 48. (All W, ((reachable T_8 W) => (q W))) (reachable T_9 T_10) (reachable T_8 T_9) (-. (q T_10)) ### All 47 % 27.03/27.23 49. ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))) (-. (q T_10)) (reachable T_9 T_10) (-. (p T_9)) (reachable T_8 T_9) ### Or 42 48 % 27.03/27.23 50. (-. ((reachable T_9 T_10) => (q T_10))) (reachable T_8 T_9) (-. (p T_9)) ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))) ### NotImply 49 % 27.03/27.23 51. (-. (All V, ((reachable T_9 V) => (q V)))) ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))) (-. (p T_9)) (reachable T_8 T_9) ### NotAllEx 50 % 27.03/27.23 52. (-. ((reachable T_8 T_9) => ((p T_9) \/ (All V, ((reachable T_9 V) => (q V)))))) ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))) ### ConjTree 51 % 27.03/27.23 53. (-. (All Z, ((reachable T_8 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V))))))) ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))) ### NotAllEx 52 % 27.03/27.23 54. (reachable T_4 T_7) (-. (reachable T_4 T_7)) ### Axiom % 27.03/27.23 55. (-. (p T_7)) (p T_7) ### Axiom % 27.03/27.23 56. (reachable T_7 T_8) (-. (reachable T_7 T_8)) ### Axiom % 27.03/27.23 57. (T_11 != T_11) ### Refl(=) % 27.03/27.23 58. (-. (reachable T_7 T_11)) (reachable T_8 T_11) (reachable T_7 T_8) ### Trans 56 57 % 27.03/27.23 59. (-. (q T_11)) (q T_11) ### Axiom % 27.03/27.23 60. ((reachable T_7 T_11) => (q T_11)) (-. (q T_11)) (reachable T_7 T_8) (reachable T_8 T_11) ### Imply 58 59 % 27.03/27.23 61. (All V, ((reachable T_7 V) => (q V))) (reachable T_8 T_11) (reachable T_7 T_8) (-. (q T_11)) ### All 60 % 27.03/27.23 62. ((reachable T_4 T_7) => ((p T_7) \/ (All V, ((reachable T_7 V) => (q V))))) (-. (q T_11)) (reachable T_7 T_8) (reachable T_8 T_11) (-. (p T_7)) (reachable T_4 T_7) ### DisjTree 54 55 61 % 27.03/27.23 63. (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_4 T_7) (-. (p T_7)) (reachable T_8 T_11) (reachable T_7 T_8) (-. (q T_11)) ### All 62 % 27.03/27.23 64. (-. ((reachable T_8 T_11) => (q T_11))) (reachable T_7 T_8) (-. (p T_7)) (reachable T_4 T_7) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) ### NotImply 63 % 27.03/27.23 65. (-. (All W, ((reachable T_8 W) => (q W)))) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_4 T_7) (-. (p T_7)) (reachable T_7 T_8) ### NotAllEx 64 % 27.03/27.23 66. (-. ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W))))) (reachable T_7 T_8) (-. (p T_7)) (reachable T_4 T_7) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) ### NotOr 65 % 27.03/27.23 67. (-. ((All Z, ((reachable T_8 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W)))))) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_4 T_7) (-. (p T_7)) (reachable T_7 T_8) ### NotEquiv 53 66 % 27.03/27.23 68. (-. ((reachable T_7 T_8) => ((All Z, ((reachable T_8 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_8 W) => (p W))) \/ (All W, ((reachable T_8 W) => (q W))))))) (-. (p T_7)) (reachable T_4 T_7) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) ### NotImply 67 % 27.03/27.23 69. (-. (All Y, ((reachable T_7 Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_4 T_7) (-. (p T_7)) ### NotAllEx 68 % 27.03/27.23 70. (-. ((reachable (initial_world) T_7) /\ (All Y, ((reachable T_7 Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W))))))))) (-. (p T_7)) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_3 T_4) (reachable (initial_world) T_0) (reachable T_0 T_3) (reachable T_4 T_7) ### NotAnd 38 69 % 27.03/27.25 71. (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable T_4 T_7) (reachable T_0 T_3) (reachable (initial_world) T_0) (reachable T_3 T_4) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (-. (p T_7)) ### NotExists 70 % 27.03/27.25 72. (-. ((reachable T_4 T_7) => (p T_7))) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_3 T_4) (reachable (initial_world) T_0) (reachable T_0 T_3) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotImply 71 % 27.03/27.25 73. (-. (All W, ((reachable T_4 W) => (p W)))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable T_0 T_3) (reachable (initial_world) T_0) (reachable T_3 T_4) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) ### NotAllEx 72 % 27.03/27.25 74. (-. ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W))))) (All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) (reachable T_3 T_4) (reachable (initial_world) T_0) (reachable T_0 T_3) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotOr 73 % 27.03/27.25 75. (-. ((All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W)))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable T_0 T_3) (reachable (initial_world) T_0) (reachable T_3 T_4) ### NotEquiv 34 74 % 27.03/27.25 76. (-. ((reachable T_3 T_4) => ((All Z, ((reachable T_4 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_4 W) => (p W))) \/ (All W, ((reachable T_4 W) => (q W))))))) (reachable (initial_world) T_0) (reachable T_0 T_3) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotImply 75 % 27.03/27.25 77. (-. (All Y, ((reachable T_3 Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable T_0 T_3) (reachable (initial_world) T_0) ### NotAllEx 76 % 27.03/27.25 78. (-. ((reachable (initial_world) T_3) /\ (All Y, ((reachable T_3 Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W))))))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable (initial_world) T_0) (reachable T_0 T_3) ### NotAnd 19 77 % 27.03/27.25 79. (reachable T_0 T_3) (reachable (initial_world) T_0) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotExists 78 % 27.03/27.25 80. (-. ((reachable T_0 T_3) => (q T_3))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable (initial_world) T_0) ### NotImply 79 % 27.03/27.25 81. (-. (All W, ((reachable T_0 W) => (q W)))) (reachable (initial_world) T_0) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotAllEx 80 % 27.03/27.25 82. (-. ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) (reachable (initial_world) T_0) ### NotOr 81 % 27.03/27.25 83. (-. ((All Z, ((reachable T_0 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W)))))) (reachable (initial_world) T_0) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotEquiv 16 82 % 27.03/27.25 84. (-. ((reachable (initial_world) T_0) => ((All Z, ((reachable T_0 Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable T_0 W) => (p W))) \/ (All W, ((reachable T_0 W) => (q W))))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotImply 83 % 27.03/27.25 85. (-. (All Y, ((reachable (initial_world) Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotAllEx 84 % 27.03/27.25 86. (-. ((reachable (initial_world) (initial_world)) /\ (All Y, ((reachable (initial_world) Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W))))))))) (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotAnd 1 85 % 27.03/27.25 87. (-. (Ex X, ((reachable (initial_world) X) /\ (All Y, ((reachable X Y) => ((All Z, ((reachable Y Z) => ((p Z) \/ (All V, ((reachable Z V) => (q V)))))) <=> ((All W, ((reachable Y W) => (p W))) \/ (All W, ((reachable Y W) => (q W)))))))))) ### NotExists 86 % 27.03/27.25 % SZS output end Proof % 27.03/27.25 (* END-PROOF *) %------------------------------------------------------------------------------