TSTP Solution File: SWC209+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SWC209+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 : n013.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 22:07:07 EDT 2022
% Result : Theorem 6.01s 6.21s
% Output : Proof 6.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWC209+1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n013.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 : Sun Jun 12 05:11:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.01/6.21 % SZS status Theorem
% 6.01/6.21 (* PROOF-FOUND *)
% 6.01/6.21 (* BEGIN-PROOF *)
% 6.01/6.21 % SZS output start Proof
% 6.01/6.21 1. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 6.01/6.21 2. ((nil) = T_0) ((nil) != T_0) ### Axiom
% 6.01/6.21 3. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 6.01/6.21 4. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 5. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 6. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 7. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 6.01/6.21 8. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 9. (T_1 = (nil)) ((nil) != T_1) ### Sym(=)
% 6.01/6.21 10. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 11. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 12. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 6.01/6.21 13. (-. (frontsegP T_0 (nil))) (frontsegP T_0 (nil)) ### Axiom
% 6.01/6.21 14. ((ssList T_0) => (frontsegP T_0 (nil))) (-. (frontsegP T_0 (nil))) (ssList T_0) ### Imply 12 13
% 6.01/6.21 15. (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (-. (frontsegP T_0 (nil))) ### All 14
% 6.01/6.21 16. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 17. (-. (frontsegP (nil) (nil))) (ssList (nil)) ### Extension/test/ax42ctrp 16
% 6.01/6.21 18. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 19. (frontsegP T_0 (nil)) (-. (frontsegP T_0 (nil))) ### Axiom
% 6.01/6.21 20. (frontsegP (nil) T_1) (-. (frontsegP (nil) T_1)) ### Axiom
% 6.01/6.21 21. (-. (frontsegP T_0 T_1)) (frontsegP T_0 T_1) ### Axiom
% 6.01/6.21 22. ((ssList T_1) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) T_1)) => (frontsegP T_0 T_1))) (-. (frontsegP T_0 T_1)) (frontsegP (nil) T_1) (frontsegP T_0 (nil)) (ssList T_1) ### DisjTree 18 19 20 21
% 6.01/6.21 23. (All W, ((ssList W) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_0 W)))) (ssList T_1) (frontsegP T_0 (nil)) (frontsegP (nil) T_1) (-. (frontsegP T_0 T_1)) ### All 22
% 6.01/6.21 24. ((ssList (nil)) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) (nil))) => (frontsegP T_0 (nil)))) (-. (frontsegP T_0 T_1)) (frontsegP (nil) T_1) (ssList T_1) (All W, ((ssList W) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_0 W)))) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) ### DisjTree 11 15 17 23
% 6.01/6.21 25. (ssList (nil)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (All W, ((ssList W) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_0 W)))) (ssList T_1) (frontsegP (nil) T_1) (-. (frontsegP T_0 T_1)) ### All 24
% 6.01/6.21 26. ((ssList (nil)) => (All W, ((ssList W) => (((frontsegP T_0 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_0 W))))) (-. (frontsegP T_0 T_1)) (frontsegP (nil) T_1) (ssList T_1) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) ### Imply 10 25
% 6.01/6.21 27. (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_0 V) /\ (frontsegP V W)) => (frontsegP T_0 W)))))) (ssList (nil)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (ssList T_1) (frontsegP (nil) T_1) (-. (frontsegP T_0 T_1)) ### All 26
% 6.01/6.21 28. ((frontsegP (nil) T_1) <=> ((nil) = T_1)) (-. (frontsegP T_0 T_1)) (ssList T_1) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_0 V) /\ (frontsegP V W)) => (frontsegP T_0 W)))))) (T_1 = (nil)) ### Equiv 9 27
% 6.01/6.21 29. ((ssList T_1) => ((frontsegP (nil) T_1) <=> ((nil) = T_1))) (T_1 = (nil)) (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_0 V) /\ (frontsegP V W)) => (frontsegP T_0 W)))))) (ssList (nil)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (-. (frontsegP T_0 T_1)) (ssList T_1) ### Imply 8 28
% 6.01/6.21 30. (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_1) (-. (frontsegP T_0 T_1)) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_0 V) /\ (frontsegP V W)) => (frontsegP T_0 W)))))) (T_1 = (nil)) ### All 29
% 6.01/6.21 31. ((ssList T_0) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_0 V) /\ (frontsegP V W)) => (frontsegP T_0 W))))))) (T_1 = (nil)) (ssList (nil)) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_0 T_1)) (ssList T_1) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) ### Imply 7 30
% 6.01/6.21 32. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_1) (-. (frontsegP T_0 T_1)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) (T_1 = (nil)) ### All 31
% 6.01/6.21 33. (-. (T_1 != (nil))) (ssList (nil)) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_0 T_1)) (ssList T_1) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) ### NotNot 32
% 6.01/6.21 34. (-. (neq T_1 (nil))) (neq T_1 (nil)) ### Axiom
% 6.01/6.21 35. ((neq T_1 (nil)) <=> (T_1 != (nil))) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_1) (-. (frontsegP T_0 T_1)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList (nil)) ### Equiv 33 34
% 6.01/6.21 36. ((ssList (nil)) => ((neq T_1 (nil)) <=> (T_1 != (nil)))) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_0 T_1)) (ssList T_1) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) ### Imply 6 35
% 6.01/6.21 37. (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_1) (-. (frontsegP T_0 T_1)) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 36
% 6.01/6.21 38. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 39. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 40. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 41. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 6.01/6.21 42. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 6.01/6.21 43. (-. (frontsegP T_1 (nil))) (frontsegP T_1 (nil)) ### Axiom
% 6.01/6.21 44. ((ssList T_1) => (frontsegP T_1 (nil))) (-. (frontsegP T_1 (nil))) (ssList T_1) ### Imply 42 43
% 6.01/6.21 45. (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_1) (-. (frontsegP T_1 (nil))) ### All 44
% 6.01/6.21 46. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 6.01/6.21 47. (frontsegP T_1 (nil)) (-. (frontsegP T_1 (nil))) ### Axiom
% 6.01/6.21 48. (frontsegP (nil) T_0) (-. (frontsegP (nil) T_0)) ### Axiom
% 6.01/6.21 49. (-. (frontsegP T_1 T_0)) (frontsegP T_1 T_0) ### Axiom
% 6.01/6.21 50. ((ssList T_0) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) T_0)) => (frontsegP T_1 T_0))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (frontsegP T_1 (nil)) (ssList T_0) ### DisjTree 46 47 48 49
% 6.01/6.21 51. (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W)))) (ssList T_0) (frontsegP T_1 (nil)) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) ### All 50
% 6.01/6.21 52. ((frontsegP T_1 (nil)) <=> (Ex W, ((ssList W) /\ ((app (nil) W) = T_1)))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (ssList T_0) (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W)))) (ssList T_1) (All U, ((ssList U) => (frontsegP U (nil)))) ### Equiv 45 51
% 6.01/6.21 53. ((ssList (nil)) => ((frontsegP T_1 (nil)) <=> (Ex W, ((ssList W) /\ ((app (nil) W) = T_1))))) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_1) (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W)))) (ssList T_0) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) (ssList (nil)) ### Imply 41 52
% 6.01/6.21 54. (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (ssList (nil)) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (ssList T_0) (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W)))) (ssList T_1) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 53
% 6.01/6.21 55. ((ssList (nil)) => (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W))))) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_1) (ssList T_0) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (ssList (nil)) ### Imply 40 54
% 6.14/6.33 56. (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_1 V) /\ (frontsegP V W)) => (frontsegP T_1 W)))))) (ssList (nil)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (ssList T_0) (ssList T_1) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 55
% 6.14/6.33 57. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_1 V) /\ (frontsegP V W)) => (frontsegP T_1 W))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (ssList (nil)) (ssList T_1) ### Imply 39 56
% 6.14/6.33 58. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_1) (ssList (nil)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 57
% 6.14/6.33 59. ((ssList T_1) => (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_0) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_1) ### Imply 38 58
% 6.14/6.33 60. (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 59
% 6.14/6.33 61. (T_2 != T_2) ### Refl(=)
% 6.14/6.33 62. (T_0 = T_1) (T_0 != T_1) ### Axiom
% 6.14/6.33 63. (T_2 != T_1) (T_2 = T_0) (T_0 = T_1) ### Trans 61 62
% 6.14/6.33 64. ((ssList T_1) => (((frontsegP T_0 T_1) /\ (frontsegP T_1 T_0)) => (T_0 = T_1))) (T_2 = T_0) (T_2 != T_1) (frontsegP (nil) T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList T_1) ### DisjTree 5 37 60 63
% 6.14/6.33 65. (All V, ((ssList V) => (((frontsegP T_0 V) /\ (frontsegP V T_0)) => (T_0 = V)))) (ssList T_1) (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (frontsegP (nil) T_0) (T_2 != T_1) (T_2 = T_0) ### All 64
% 6.14/6.33 66. ((ssList T_1) => (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V))))) (T_2 = T_0) (T_2 != T_1) (frontsegP (nil) T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (All V, ((ssList V) => (((frontsegP T_0 V) /\ (frontsegP V T_0)) => (T_0 = V)))) (ssList T_1) ### Imply 4 65
% 6.14/6.33 67. (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (All V, ((ssList V) => (((frontsegP T_0 V) /\ (frontsegP V T_0)) => (T_0 = V)))) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (frontsegP (nil) T_0) (T_2 != T_1) (T_2 = T_0) ### All 66
% 6.14/6.33 68. ((ssList T_0) => (All V, ((ssList V) => (((frontsegP T_0 V) /\ (frontsegP V T_0)) => (T_0 = V))))) (T_2 = T_0) (T_2 != T_1) (frontsegP (nil) T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_0) ### Imply 3 67
% 6.14/6.33 69. (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (frontsegP (nil) T_0) (T_2 != T_1) (T_2 = T_0) ### All 68
% 6.14/6.33 70. ((frontsegP (nil) T_0) <=> ((nil) = T_0)) (T_2 = T_0) (T_2 != T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ((nil) = T_0) ### Equiv 2 69
% 6.14/6.33 71. ((ssList T_0) => ((frontsegP (nil) T_0) <=> ((nil) = T_0))) ((nil) = T_0) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (T_2 != T_1) (T_2 = T_0) (ssList T_0) ### Imply 1 70
% 6.14/6.33 72. (ssList T_0) (T_2 = T_0) (T_2 != T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ((nil) = T_0) ### All 71
% 6.14/6.34 73. ((nil) != (nil)) ### NotEqual
% 6.14/6.34 74. (neq T_2 (nil)) ((nil) = T_0) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (T_2 = T_0) (ssList T_0) ### P-NotP 72 73
% 6.14/6.34 75. (-. ((nil) != T_0)) (ssList T_0) (T_2 = T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (neq T_2 (nil)) ### NotNot 74
% 6.14/6.34 76. (-. (((nil) != T_0) \/ ((nil) != T_3))) (neq T_2 (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (-. (neq T_1 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (T_2 = T_0) (ssList T_0) ### NotOr 75
% 6.14/6.34 77. (T_1 = T_3) (T_3 != T_1) ### Sym(=)
% 6.14/6.34 78. (-. (neq T_1 (nil))) (neq T_3 (nil)) (T_1 = T_3) ### P-NotP 77 73
% 6.14/6.34 79. (-. (-. (neq T_3 (nil)))) (T_1 = T_3) (-. (neq T_1 (nil))) ### NotNot 78
% 6.14/6.34 80. (-. ((-. (neq T_3 (nil))) \/ (-. (segmentP T_0 T_3)))) (-. (neq T_1 (nil))) (T_1 = T_3) ### NotOr 79
% 6.14/6.34 81. (-. ((((nil) != T_0) \/ ((nil) != T_3)) /\ ((-. (neq T_3 (nil))) \/ (-. (segmentP T_0 T_3))))) (T_1 = T_3) (ssList T_0) (T_2 = T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (neq T_2 (nil)) ### NotAnd 76 80
% 6.14/6.34 82. (-. ((ssList T_0) => ((T_2 != T_0) \/ ((T_1 != T_3) \/ ((-. (neq T_2 (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != T_0) \/ ((nil) != T_3)) /\ ((-. (neq T_3 (nil))) \/ (-. (segmentP T_0 T_3)))))))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### ConjTree 81
% 6.14/6.34 83. (-. (All X, ((ssList X) => ((T_2 != X) \/ ((T_1 != T_3) \/ ((-. (neq T_2 (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != T_3)) /\ ((-. (neq T_3 (nil))) \/ (-. (segmentP X T_3))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ### NotAllEx 82
% 6.14/6.34 84. (-. ((ssList T_3) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_1 != T_3) \/ ((-. (neq T_2 (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != T_3)) /\ ((-. (neq T_3 (nil))) \/ (-. (segmentP X T_3)))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotImply 83
% 6.14/6.34 85. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_1 != W) \/ ((-. (neq T_2 (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ### NotAllEx 84
% 6.14/6.34 86. (-. ((ssList T_2) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_1 != W) \/ ((-. (neq T_2 (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotImply 85
% 6.14/6.34 87. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_1 != W) \/ ((-. (neq V (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ### NotAllEx 86
% 6.14/6.34 88. (-. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_1 != W) \/ ((-. (neq V (nil))) \/ ((neq T_1 (nil)) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotImply 87
% 6.14/6.34 89. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((-. (neq V (nil))) \/ ((neq U (nil)) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => (All V, ((ssList V) => (((frontsegP U V) /\ (frontsegP V U)) => (U = V)))))) ### NotAllEx 88
% 6.14/6.34 % SZS output end Proof
% 6.14/6.34 (* END-PROOF *)
%------------------------------------------------------------------------------