%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWC411+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n015.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 22:08:08 EDT 2022 % Result : Theorem 143.93s 144.19s % Output : Proof 143.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC411+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n015.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 Jun 12 15:02:37 EDT 2022 % 0.12/0.34 % CPUTime : % 143.93/144.19 % SZS status Theorem % 143.93/144.19 (* PROOF-FOUND *) % 143.93/144.19 (* BEGIN-PROOF *) % 143.93/144.19 % SZS output start Proof % 143.93/144.19 1. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 2. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 3. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 4. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 5. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 6. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 7. (ssList T_1) (-. (ssList T_1)) ### Axiom % 143.93/144.19 8. (ssList T_2) (-. (ssList T_2)) ### Axiom % 143.93/144.19 9. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 143.93/144.19 10. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 143.93/144.19 11. (memberP T_2 T_0) (-. (memberP T_2 T_0)) ### Axiom % 143.93/144.19 12. (-. ((memberP T_2 T_0) \/ (memberP (nil) T_0))) (memberP T_2 T_0) ### NotOr 11 % 143.93/144.19 13. (T_1 = T_2) (T_2 != T_1) ### Sym(=) % 143.93/144.19 14. ((nil) != (nil)) ### NotEqual % 143.93/144.19 15. ((app T_2 (nil)) != (app T_1 (nil))) (T_1 = T_2) ### NotEqual 13 14 % 143.93/144.19 16. (-. (T_0 != T_0)) (T_0 != T_0) ### Axiom % 143.93/144.19 17. (-. (memberP (app T_1 (nil)) T_0)) (memberP (app T_2 (nil)) T_0) (-. (T_0 != T_0)) (T_1 = T_2) ### P-NotP 15 16 % 143.93/144.19 18. ((memberP (app T_2 (nil)) T_0) <=> ((memberP T_2 T_0) \/ (memberP (nil) T_0))) (T_1 = T_2) (-. (T_0 != T_0)) (-. (memberP (app T_1 (nil)) T_0)) (memberP T_2 T_0) ### Equiv 12 17 % 143.93/144.19 19. ((ssList (nil)) => ((memberP (app T_2 (nil)) T_0) <=> ((memberP T_2 T_0) \/ (memberP (nil) T_0)))) (memberP T_2 T_0) (-. (memberP (app T_1 (nil)) T_0)) (-. (T_0 != T_0)) (T_1 = T_2) (ssList (nil)) ### Imply 10 18 % 143.93/144.19 20. (All W, ((ssList W) => ((memberP (app T_2 W) T_0) <=> ((memberP T_2 T_0) \/ (memberP W T_0))))) (ssList (nil)) (T_1 = T_2) (-. (T_0 != T_0)) (-. (memberP (app T_1 (nil)) T_0)) (memberP T_2 T_0) ### All 19 % 143.93/144.19 21. (-. (memberP T_1 T_0)) (memberP T_1 T_0) ### Axiom % 143.93/144.19 22. (-. (memberP (nil) T_0)) (memberP (nil) T_0) ### Axiom % 143.93/144.19 23. ((memberP T_1 T_0) \/ (memberP (nil) T_0)) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) ### Or 21 22 % 143.93/144.19 24. ((memberP (app T_1 (nil)) T_0) <=> ((memberP T_1 T_0) \/ (memberP (nil) T_0))) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (-. (T_0 != T_0)) (T_1 = T_2) (ssList (nil)) (All W, ((ssList W) => ((memberP (app T_2 W) T_0) <=> ((memberP T_2 T_0) \/ (memberP W T_0))))) ### Equiv 20 23 % 143.93/144.19 25. ((ssList (nil)) => ((memberP (app T_1 (nil)) T_0) <=> ((memberP T_1 T_0) \/ (memberP (nil) T_0)))) (All W, ((ssList W) => ((memberP (app T_2 W) T_0) <=> ((memberP T_2 T_0) \/ (memberP W T_0))))) (T_1 = T_2) (-. (T_0 != T_0)) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) ### Imply 9 24 % 143.93/144.19 26. (All W, ((ssList W) => ((memberP (app T_1 W) T_0) <=> ((memberP T_1 T_0) \/ (memberP W T_0))))) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (-. (T_0 != T_0)) (T_1 = T_2) (All W, ((ssList W) => ((memberP (app T_2 W) T_0) <=> ((memberP T_2 T_0) \/ (memberP W T_0))))) ### All 25 % 143.93/144.19 27. ((ssList T_2) => (All W, ((ssList W) => ((memberP (app T_2 W) T_0) <=> ((memberP T_2 T_0) \/ (memberP W T_0)))))) (T_1 = T_2) (-. (T_0 != T_0)) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) (All W, ((ssList W) => ((memberP (app T_1 W) T_0) <=> ((memberP T_1 T_0) \/ (memberP W T_0))))) (ssList T_2) ### Imply 8 26 % 143.93/144.19 28. (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (All W, ((ssList W) => ((memberP (app T_1 W) T_0) <=> ((memberP T_1 T_0) \/ (memberP W T_0))))) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (-. (T_0 != T_0)) (T_1 = T_2) ### All 27 % 143.93/144.19 29. ((ssList T_1) => (All W, ((ssList W) => ((memberP (app T_1 W) T_0) <=> ((memberP T_1 T_0) \/ (memberP W T_0)))))) (T_1 = T_2) (-. (T_0 != T_0)) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) ### Imply 7 28 % 143.93/144.19 30. (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (-. (T_0 != T_0)) (T_1 = T_2) ### All 29 % 143.93/144.19 31. (leq T_0 T_0) (-. (leq T_0 T_0)) ### Axiom % 143.93/144.19 32. (-. ((T_0 != T_0) /\ (leq T_0 T_0))) (leq T_0 T_0) (T_1 = T_2) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) ### NotAnd 30 31 % 143.93/144.19 33. (T_0 != T_0) ### Refl(=) % 143.93/144.19 34. ((T_0 != T_0) /\ (leq T_0 T_0)) ### And 33 % 143.93/144.19 35. ((lt T_0 T_0) <=> ((T_0 != T_0) /\ (leq T_0 T_0))) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (T_1 = T_2) (leq T_0 T_0) ### Equiv 32 34 % 143.93/144.19 36. ((ssItem T_0) => ((lt T_0 T_0) <=> ((T_0 != T_0) /\ (leq T_0 T_0)))) (leq T_0 T_0) (T_1 = T_2) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) (ssItem T_0) ### Imply 6 35 % 143.93/144.19 37. (All V, ((ssItem V) => ((lt T_0 V) <=> ((T_0 != V) /\ (leq T_0 V))))) (ssItem T_0) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (T_1 = T_2) (leq T_0 T_0) ### All 36 % 143.93/144.19 38. ((ssItem T_0) => (All V, ((ssItem V) => ((lt T_0 V) <=> ((T_0 != V) /\ (leq T_0 V)))))) (leq T_0 T_0) (T_1 = T_2) (memberP T_2 T_0) (-. (memberP (nil) T_0)) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) (ssItem T_0) ### Imply 5 37 % 143.93/144.19 39. (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssItem T_0) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (-. (memberP (nil) T_0)) (memberP T_2 T_0) (T_1 = T_2) (leq T_0 T_0) ### All 38 % 143.93/144.19 40. ((ssItem T_0) => (-. (memberP (nil) T_0))) (leq T_0 T_0) (T_1 = T_2) (memberP T_2 T_0) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssItem T_0) ### Imply 4 39 % 143.93/144.19 41. (All U, ((ssItem U) => (-. (memberP (nil) U)))) (ssItem T_0) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (memberP T_2 T_0) (T_1 = T_2) (leq T_0 T_0) ### All 40 % 143.93/144.19 42. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 43. (ssItem T_0) (-. (ssItem T_0)) ### Axiom % 143.93/144.19 44. (ssList T_3) (-. (ssList T_3)) ### Axiom % 143.93/144.19 45. (ssList T_3) (-. (ssList T_3)) ### Axiom % 143.93/144.19 46. (ssList T_4) (-. (ssList T_4)) ### Axiom % 143.93/144.19 47. (ssList T_3) (-. (ssList T_3)) ### Axiom % 143.93/144.19 48. (memberP T_4 T_0) (-. (memberP T_4 T_0)) ### Axiom % 143.93/144.19 49. (-. ((memberP T_4 T_0) \/ (memberP T_3 T_0))) (memberP T_4 T_0) ### NotOr 48 % 143.93/144.19 50. (T_4 = T_3) (T_4 != T_3) ### Axiom % 143.93/144.19 51. (T_3 != T_3) ### Refl(=) % 143.93/144.19 52. ((app T_4 T_3) != (app T_3 T_3)) (T_4 = T_3) ### NotEqual 50 51 % 143.93/144.19 53. (-. (T_0 != T_0)) (T_0 != T_0) ### Axiom % 143.93/144.19 54. (-. (memberP (app T_3 T_3) T_0)) (memberP (app T_4 T_3) T_0) (-. (T_0 != T_0)) (T_4 = T_3) ### P-NotP 52 53 % 143.93/144.19 55. ((memberP (app T_4 T_3) T_0) <=> ((memberP T_4 T_0) \/ (memberP T_3 T_0))) (T_4 = T_3) (-. (T_0 != T_0)) (-. (memberP (app T_3 T_3) T_0)) (memberP T_4 T_0) ### Equiv 49 54 % 143.93/144.19 56. ((ssList T_3) => ((memberP (app T_4 T_3) T_0) <=> ((memberP T_4 T_0) \/ (memberP T_3 T_0)))) (memberP T_4 T_0) (-. (memberP (app T_3 T_3) T_0)) (-. (T_0 != T_0)) (T_4 = T_3) (ssList T_3) ### Imply 47 55 % 143.93/144.22 57. (All W, ((ssList W) => ((memberP (app T_4 W) T_0) <=> ((memberP T_4 T_0) \/ (memberP W T_0))))) (ssList T_3) (T_4 = T_3) (-. (T_0 != T_0)) (-. (memberP (app T_3 T_3) T_0)) (memberP T_4 T_0) ### All 56 % 143.93/144.22 58. ((ssList T_4) => (All W, ((ssList W) => ((memberP (app T_4 W) T_0) <=> ((memberP T_4 T_0) \/ (memberP W T_0)))))) (memberP T_4 T_0) (-. (memberP (app T_3 T_3) T_0)) (-. (T_0 != T_0)) (T_4 = T_3) (ssList T_3) (ssList T_4) ### Imply 46 57 % 143.93/144.22 59. (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (ssList T_3) (T_4 = T_3) (-. (T_0 != T_0)) (-. (memberP (app T_3 T_3) T_0)) (memberP T_4 T_0) ### All 58 % 143.93/144.22 60. (-. (memberP T_3 T_0)) (memberP T_3 T_0) ### Axiom % 143.93/144.22 61. (-. (memberP T_3 T_0)) (memberP T_3 T_0) ### Axiom % 143.93/144.22 62. ((memberP T_3 T_0) \/ (memberP T_3 T_0)) (-. (memberP T_3 T_0)) ### Or 60 61 % 143.93/144.22 63. ((memberP (app T_3 T_3) T_0) <=> ((memberP T_3 T_0) \/ (memberP T_3 T_0))) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (-. (T_0 != T_0)) (T_4 = T_3) (ssList T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) ### Equiv 59 62 % 143.93/144.22 64. ((ssList T_3) => ((memberP (app T_3 T_3) T_0) <=> ((memberP T_3 T_0) \/ (memberP T_3 T_0)))) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (T_4 = T_3) (-. (T_0 != T_0)) (memberP T_4 T_0) (-. (memberP T_3 T_0)) (ssList T_3) ### Imply 45 63 % 143.93/144.22 65. (All W, ((ssList W) => ((memberP (app T_3 W) T_0) <=> ((memberP T_3 T_0) \/ (memberP W T_0))))) (ssList T_3) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (-. (T_0 != T_0)) (T_4 = T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) ### All 64 % 143.93/144.22 66. ((ssList T_3) => (All W, ((ssList W) => ((memberP (app T_3 W) T_0) <=> ((memberP T_3 T_0) \/ (memberP W T_0)))))) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (T_4 = T_3) (-. (T_0 != T_0)) (memberP T_4 T_0) (-. (memberP T_3 T_0)) (ssList T_3) ### Imply 44 65 % 143.93/144.22 67. (ssList T_3) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (-. (T_0 != T_0)) (T_4 = T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) ### All 66 % 143.93/144.22 68. (leq T_0 T_0) (-. (leq T_0 T_0)) ### Axiom % 143.93/144.22 69. (-. ((T_0 != T_0) /\ (leq T_0 T_0))) (leq T_0 T_0) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (-. (memberP T_3 T_0)) (ssList T_3) ### NotAnd 67 68 % 143.93/144.22 70. ((lt T_0 T_0) <=> ((T_0 != T_0) /\ (leq T_0 T_0))) (ssList T_3) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (leq T_0 T_0) ### Equiv 69 34 % 143.93/144.22 71. ((ssItem T_0) => ((lt T_0 T_0) <=> ((T_0 != T_0) /\ (leq T_0 T_0)))) (leq T_0 T_0) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (-. (memberP T_3 T_0)) (ssList T_3) (ssItem T_0) ### Imply 43 70 % 143.93/144.22 72. (All V, ((ssItem V) => ((lt T_0 V) <=> ((T_0 != V) /\ (leq T_0 V))))) (ssItem T_0) (ssList T_3) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (leq T_0 T_0) ### All 71 % 143.93/144.22 73. ((ssItem T_0) => (All V, ((ssItem V) => ((lt T_0 V) <=> ((T_0 != V) /\ (leq T_0 V)))))) (leq T_0 T_0) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (-. (memberP T_3 T_0)) (ssList T_3) (ssItem T_0) ### Imply 42 72 % 143.93/144.22 74. (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssItem T_0) (ssList T_3) (-. (memberP T_3 T_0)) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (leq T_0 T_0) ### All 73 % 143.93/144.22 75. (-. ((ssItem T_0) /\ ((-. (memberP T_2 T_0)) /\ (memberP T_3 T_0)))) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (ssList T_3) (leq T_0 T_0) (T_1 = T_2) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (ssItem T_0) ### DisjTree 3 41 74 % 143.93/144.22 76. (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (ssItem T_0) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0))))))) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (T_1 = T_2) (leq T_0 T_0) (ssList T_3) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) ### NotExists 75 % 143.93/144.22 77. ((ssItem T_0) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) T_0) <=> ((memberP V T_0) \/ (memberP W T_0)))))))) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (ssList T_3) (leq T_0 T_0) (T_1 = T_2) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (ssItem T_0) ### Imply 2 76 % 143.93/144.22 78. (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (ssItem T_0) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (T_1 = T_2) (leq T_0 T_0) (ssList T_3) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) ### All 77 % 143.93/144.22 79. ((ssItem T_0) => (leq T_0 T_0)) (ssList T_4) (T_4 = T_3) (memberP T_4 T_0) (ssList T_3) (T_1 = T_2) (-. (memberP T_1 T_0)) (ssList (nil)) (ssList T_2) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (ssItem T_0) ### Imply 1 78 % 143.93/144.22 80. (All U, ((ssItem U) => (leq U U))) (ssItem T_0) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList T_2) (ssList (nil)) (-. (memberP T_1 T_0)) (T_1 = T_2) (ssList T_3) (memberP T_4 T_0) (T_4 = T_3) (ssList T_4) ### All 79 % 143.93/144.22 81. (-. ((ssItem T_0) => ((-. (memberP T_4 T_0)) \/ (memberP T_1 T_0)))) (ssList T_4) (T_4 = T_3) (ssList T_3) (T_1 = T_2) (ssList (nil)) (ssList T_2) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (leq U U))) ### ConjTree 80 % 143.93/144.22 82. (-. (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z))))) (All U, ((ssItem U) => (leq U U))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (-. (Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList T_2) (ssList (nil)) (T_1 = T_2) (ssList T_3) (T_4 = T_3) (ssList T_4) ### NotAllEx 81 % 143.99/144.23 83. (-. ((ssList T_3) => ((T_4 != T_3) \/ ((T_1 != T_2) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP T_3 Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z))))))))) (ssList T_4) (ssList (nil)) (ssList T_2) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (leq U U))) ### ConjTree 82 % 143.99/144.23 84. (-. (All X, ((ssList X) => ((T_4 != X) \/ ((T_1 != T_2) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z)))))))))) (All U, ((ssItem U) => (leq U U))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList T_2) (ssList (nil)) (ssList T_4) ### NotAllEx 83 % 143.99/144.23 85. (-. ((ssList T_2) => (All X, ((ssList X) => ((T_4 != X) \/ ((T_1 != T_2) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP T_2 Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z))))))))))) (ssList T_4) (ssList (nil)) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (leq U U))) ### NotImply 84 % 143.99/144.23 86. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_4 != X) \/ ((T_1 != W) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP W Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z)))))))))))) (All U, ((ssItem U) => (leq U U))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList (nil)) (ssList T_4) ### NotAllEx 85 % 143.99/144.23 87. (-. ((ssList T_4) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_4 != X) \/ ((T_1 != W) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP W Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP T_4 Z)) \/ (memberP T_1 Z))))))))))))) (ssList (nil)) (ssList T_1) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (leq U U))) ### NotImply 86 % 143.99/144.23 88. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_1 != W) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP W Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP V Z)) \/ (memberP T_1 Z)))))))))))))) (All U, ((ssItem U) => (leq U U))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList T_1) (ssList (nil)) ### NotAllEx 87 % 143.99/144.23 89. (-. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_1 != W) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP W Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP V Z)) \/ (memberP T_1 Z))))))))))))))) (ssList (nil)) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (leq U U))) ### NotImply 88 % 143.99/144.23 90. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((Ex Y, ((ssItem Y) /\ ((-. (memberP W Y)) /\ (memberP X Y)))) \/ (All Z, ((ssItem Z) => ((-. (memberP V Z)) \/ (memberP U Z)))))))))))))))) (All U, ((ssItem U) => (leq U U))) (All U, ((ssItem U) => (All V, ((ssList V) => (All W, ((ssList W) => ((memberP (app V W) U) <=> ((memberP V U) \/ (memberP W U))))))))) (All U, ((ssItem U) => (-. (memberP (nil) U)))) (All U, ((ssItem U) => (All V, ((ssItem V) => ((lt U V) <=> ((U != V) /\ (leq U V))))))) (ssList (nil)) ### NotAllEx 89 % 143.99/144.23 % SZS output end Proof % 143.99/144.23 (* END-PROOF *) %------------------------------------------------------------------------------