TSTP Solution File: SWC369+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SWC369+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 : n027.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 22:07:55 EDT 2022
% Result : Theorem 1.30s 1.53s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 20:32:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.30/1.53 % SZS status Theorem
% 1.30/1.53 (* PROOF-FOUND *)
% 1.30/1.53 (* BEGIN-PROOF *)
% 1.30/1.53 % SZS output start Proof
% 1.30/1.53 1. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 1.30/1.53 2. ((nil) = T_0) ((nil) != T_0) ### Axiom
% 1.30/1.53 3. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 1.30/1.53 4. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 1.30/1.53 5. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 1.30/1.53 6. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 1.30/1.53 7. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 1.30/1.53 8. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 1.30/1.53 9. (-. (segmentP T_1 (nil))) (segmentP T_1 (nil)) ### Axiom
% 1.30/1.53 10. ((ssList T_1) => (segmentP T_1 (nil))) (-. (segmentP T_1 (nil))) (ssList T_1) ### Imply 8 9
% 1.30/1.53 11. (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (-. (segmentP T_1 (nil))) ### All 10
% 1.30/1.53 12. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 1.30/1.53 13. (segmentP T_1 (nil)) (-. (segmentP T_1 (nil))) ### Axiom
% 1.30/1.53 14. (segmentP (nil) T_0) (-. (segmentP (nil) T_0)) ### Axiom
% 1.30/1.53 15. (-. (segmentP T_1 T_0)) (segmentP T_1 T_0) ### Axiom
% 1.30/1.53 16. ((ssList T_0) => (((segmentP T_1 (nil)) /\ (segmentP (nil) T_0)) => (segmentP T_1 T_0))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (segmentP T_1 (nil)) (ssList T_0) ### DisjTree 12 13 14 15
% 1.30/1.53 17. (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W)))) (ssList T_0) (segmentP T_1 (nil)) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) ### All 16
% 1.30/1.53 18. ((segmentP T_1 (nil)) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W (nil)) X) = T_1)))))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W)))) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) ### Equiv 11 17
% 1.30/1.53 19. ((ssList (nil)) => ((segmentP T_1 (nil)) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W (nil)) X) = T_1))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W)))) (ssList T_0) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) (ssList (nil)) ### Imply 7 18
% 1.30/1.53 20. (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList (nil)) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W)))) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) ### All 19
% 1.30/1.53 21. ((ssList (nil)) => (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (ssList T_0) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList (nil)) ### Imply 6 20
% 1.30/1.53 22. (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_1 V) /\ (segmentP V W)) => (segmentP T_1 W)))))) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) ### All 21
% 1.30/1.53 23. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_1 V) /\ (segmentP V W)) => (segmentP T_1 W))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList (nil)) (ssList T_1) ### Imply 5 22
% 1.30/1.53 24. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_1) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) ### All 23
% 1.30/1.53 25. (T_2 = T_1) (T_1 != T_2) ### Sym(=)
% 1.30/1.53 26. (T_3 = T_0) (T_0 != T_3) ### Sym(=)
% 1.30/1.53 27. (-. (segmentP T_2 T_3)) (segmentP T_1 T_0) (T_3 = T_0) (T_2 = T_1) ### P-NotP 25 26
% 1.30/1.53 28. ((segmentP T_1 T_0) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W T_0) X) = T_1)))))) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (segmentP (nil) T_0) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) ### Equiv 24 27
% 1.30/1.53 29. ((ssList T_0) => ((segmentP T_1 T_0) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W T_0) X) = T_1))))))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_1) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (segmentP (nil) T_0) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) ### Imply 4 28
% 1.30/1.53 30. (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (All U, ((ssList U) => (segmentP U (nil)))) (segmentP (nil) T_0) (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) ### All 29
% 1.30/1.53 31. ((ssList T_1) => (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1))))))))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (segmentP (nil) T_0) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) (ssList T_1) ### Imply 3 30
% 1.30/1.53 32. (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (ssList T_1) (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (All U, ((ssList U) => (segmentP U (nil)))) (segmentP (nil) T_0) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) ### All 31
% 1.30/1.53 33. ((segmentP (nil) T_0) <=> ((nil) = T_0)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ((nil) = T_0) ### Equiv 2 32
% 1.30/1.53 34. ((ssList T_0) => ((segmentP (nil) T_0) <=> ((nil) = T_0))) ((nil) = T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_0) ### Imply 1 33
% 1.30/1.53 35. (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ((nil) = T_0) ### All 34
% 1.30/1.53 36. (-. ((nil) != T_0)) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) ### NotNot 35
% 1.37/1.54 37. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 1.37/1.54 38. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 1.37/1.54 39. ((nil) != T_1) (T_1 = (nil)) ### Sym(=)
% 1.37/1.54 40. (-. (T_1 != (nil))) ((nil) != T_1) ### NotNot 39
% 1.37/1.54 41. (-. (neq T_1 (nil))) (neq T_1 (nil)) ### Axiom
% 1.37/1.54 42. ((neq T_1 (nil)) <=> (T_1 != (nil))) (-. (neq T_1 (nil))) ((nil) != T_1) ### Equiv 40 41
% 1.37/1.54 43. ((ssList (nil)) => ((neq T_1 (nil)) <=> (T_1 != (nil)))) ((nil) != T_1) (-. (neq T_1 (nil))) (ssList (nil)) ### Imply 38 42
% 1.37/1.54 44. (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList (nil)) (-. (neq T_1 (nil))) ((nil) != T_1) ### All 43
% 1.37/1.54 45. ((ssList T_1) => (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V))))) ((nil) != T_1) (-. (neq T_1 (nil))) (ssList (nil)) (ssList T_1) ### Imply 37 44
% 1.37/1.54 46. (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (ssList (nil)) (-. (neq T_1 (nil))) ((nil) != T_1) ### All 45
% 1.37/1.54 47. (-. (-. (segmentP T_1 T_0))) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) ### NotNot 27
% 1.37/1.54 48. (-. ((-. (neq T_0 (nil))) \/ (-. (segmentP T_1 T_0)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) ### NotOr 47
% 1.37/1.54 49. (-. ((neq T_1 (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP T_1 T_0))))) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) ((nil) != T_1) (ssList (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotAnd 46 48
% 1.37/1.54 50. (-. (((nil) != T_0) /\ ((nil) = T_1))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (-. ((neq T_1 (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP T_1 T_0))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ### NotAnd 36 49
% 1.37/1.54 51. (-. ((ssList T_1) => ((T_2 != T_1) \/ ((T_3 != T_0) \/ ((segmentP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = T_1)) \/ ((neq T_1 (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP T_1 T_0)))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### ConjTree 50
% 1.37/1.54 52. (-. (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((segmentP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP X T_0))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ### NotAllEx 51
% 1.37/1.54 53. (-. ((ssList T_0) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((segmentP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP X T_0)))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 52
% 1.37/1.54 54. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((segmentP T_2 T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ### NotAllEx 53
% 1.37/1.54 55. (-. ((ssList T_2) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((segmentP T_2 T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 54
% 1.37/1.54 56. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((segmentP V T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ### NotAllEx 55
% 1.37/1.54 57. (-. ((ssList T_3) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((segmentP V T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 56
% 1.37/1.54 58. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((segmentP V U) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W))))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((segmentP U V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = U)))))))))) ### NotAllEx 57
% 1.37/1.54 % SZS output end Proof
% 1.37/1.54 (* END-PROOF *)
%------------------------------------------------------------------------------