TSTP Solution File: SWC328+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SWC328+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 : n006.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 22:07:43 EDT 2022
% Result : Theorem 5.43s 5.61s
% Output : Proof 5.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC328+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n006.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 09:33:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.43/5.61 % SZS status Theorem
% 5.43/5.61 (* PROOF-FOUND *)
% 5.43/5.61 (* BEGIN-PROOF *)
% 5.43/5.61 % SZS output start Proof
% 5.43/5.61 1. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 5.43/5.61 2. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 5.43/5.61 3. ((nil) != (nil)) ### NotEqual
% 5.43/5.61 4. (T_1 = T_2) (T_2 != T_1) ### Sym(=)
% 5.43/5.61 5. ((nil) != T_1) ((nil) = T_2) (T_1 = T_2) ### Trans 3 4
% 5.43/5.61 6. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 5.43/5.61 7. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 5.43/5.61 8. (ssList (nil)) (-. (ssList (nil))) ### Axiom
% 5.43/5.61 9. (ssList T_0) (-. (ssList T_0)) ### Axiom
% 5.43/5.61 10. (-. (segmentP T_0 (nil))) (segmentP T_0 (nil)) ### Axiom
% 5.43/5.61 11. ((ssList T_0) => (segmentP T_0 (nil))) (-. (segmentP T_0 (nil))) (ssList T_0) ### Imply 9 10
% 5.43/5.61 12. (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (-. (segmentP T_0 (nil))) ### All 11
% 5.43/5.61 13. (ssList T_1) (-. (ssList T_1)) ### Axiom
% 5.43/5.61 14. (segmentP T_0 (nil)) (-. (segmentP T_0 (nil))) ### Axiom
% 5.43/5.61 15. (segmentP (nil) T_1) (-. (segmentP (nil) T_1)) ### Axiom
% 5.43/5.61 16. (-. (segmentP T_0 T_1)) (segmentP T_0 T_1) ### Axiom
% 5.43/5.61 17. ((ssList T_1) => (((segmentP T_0 (nil)) /\ (segmentP (nil) T_1)) => (segmentP T_0 T_1))) (-. (segmentP T_0 T_1)) (segmentP (nil) T_1) (segmentP T_0 (nil)) (ssList T_1) ### DisjTree 13 14 15 16
% 5.43/5.61 18. (All W, ((ssList W) => (((segmentP T_0 (nil)) /\ (segmentP (nil) W)) => (segmentP T_0 W)))) (ssList T_1) (segmentP T_0 (nil)) (segmentP (nil) T_1) (-. (segmentP T_0 T_1)) ### All 17
% 5.43/5.61 19. ((segmentP T_0 (nil)) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W (nil)) X) = T_0)))))) (-. (segmentP T_0 T_1)) (segmentP (nil) T_1) (ssList T_1) (All W, ((ssList W) => (((segmentP T_0 (nil)) /\ (segmentP (nil) W)) => (segmentP T_0 W)))) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) ### Equiv 12 18
% 5.43/5.61 20. ((ssList (nil)) => ((segmentP T_0 (nil)) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W (nil)) X) = T_0))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (All W, ((ssList W) => (((segmentP T_0 (nil)) /\ (segmentP (nil) W)) => (segmentP T_0 W)))) (ssList T_1) (segmentP (nil) T_1) (-. (segmentP T_0 T_1)) (ssList (nil)) ### Imply 8 19
% 5.43/5.61 21. (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (ssList (nil)) (-. (segmentP T_0 T_1)) (segmentP (nil) T_1) (ssList T_1) (All W, ((ssList W) => (((segmentP T_0 (nil)) /\ (segmentP (nil) W)) => (segmentP T_0 W)))) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) ### All 20
% 5.43/5.61 22. ((ssList (nil)) => (All W, ((ssList W) => (((segmentP T_0 (nil)) /\ (segmentP (nil) W)) => (segmentP T_0 W))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (ssList T_1) (segmentP (nil) T_1) (-. (segmentP T_0 T_1)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (ssList (nil)) ### Imply 7 21
% 5.43/5.61 23. (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_0 V) /\ (segmentP V W)) => (segmentP T_0 W)))))) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (-. (segmentP T_0 T_1)) (segmentP (nil) T_1) (ssList T_1) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) ### All 22
% 5.43/5.61 24. ((ssList T_0) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_0 V) /\ (segmentP V W)) => (segmentP T_0 W))))))) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (segmentP (nil) T_1) (-. (segmentP T_0 T_1)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (ssList (nil)) (ssList T_0) ### Imply 6 23
% 5.43/5.61 25. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_0) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (-. (segmentP T_0 T_1)) (segmentP (nil) T_1) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) ### All 24
% 5.43/5.61 26. ((segmentP (nil) T_1) <=> ((nil) = T_1)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (-. (segmentP T_0 T_1)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (ssList (nil)) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (T_1 = T_2) ((nil) = T_2) ### Equiv 5 25
% 5.43/5.61 27. ((ssList T_1) => ((segmentP (nil) T_1) <=> ((nil) = T_1))) ((nil) = T_2) (T_1 = T_2) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList T_0) (ssList (nil)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (-. (segmentP T_0 T_1)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) ### Imply 2 26
% 5.43/5.61 28. (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_0 T_1)) (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0)))))))) (ssList (nil)) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (T_1 = T_2) ((nil) = T_2) ### All 27
% 5.43/5.61 29. ((ssList T_0) => (All V, ((ssList V) => ((segmentP T_0 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_0))))))))) ((nil) = T_2) (T_1 = T_2) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (ssList (nil)) (-. (segmentP T_0 T_1)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_0) ### Imply 1 28
% 5.43/5.61 30. (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_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) (-. (segmentP T_0 T_1)) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP U V) /\ (segmentP V W)) => (segmentP U W)))))))) (T_1 = T_2) ((nil) = T_2) ### All 29
% 5.43/5.61 31. (-. (equalelemsP T_1)) (equalelemsP (nil)) (T_1 = T_2) ((nil) = T_2) ### P-NotP 5
% 5.43/5.61 32. (-. ((segmentP T_0 T_1) /\ (equalelemsP T_1))) (equalelemsP (nil)) ((nil) = T_2) (T_1 = T_2) (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)))) (ssList T_1) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))))) ### NotAnd 30 31
% 5.43/5.61 33. (-. ((ssList T_3) => (((nil) != T_2) \/ ((T_0 != T_3) \/ ((T_1 != T_2) \/ ((segmentP T_0 T_1) /\ (equalelemsP 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)))))))))) (ssList T_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_1) (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)))))))) (equalelemsP (nil)) ### ConjTree 32
% 5.43/5.61 34. (-. (All X, ((ssList X) => (((nil) != T_2) \/ ((T_0 != X) \/ ((T_1 != T_2) \/ ((segmentP T_0 T_1) /\ (equalelemsP T_1)))))))) (equalelemsP (nil)) (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)))) (ssList T_1) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))))) ### NotAllEx 33
% 5.43/5.61 35. (-. ((ssList T_2) => (All X, ((ssList X) => (((nil) != T_2) \/ ((T_0 != X) \/ ((T_1 != T_2) \/ ((segmentP T_0 T_1) /\ (equalelemsP 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)))))))))) (ssList T_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_1) (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)))))))) (equalelemsP (nil)) ### NotImply 34
% 5.43/5.61 36. (-. (All W, ((ssList W) => (All X, ((ssList X) => (((nil) != W) \/ ((T_0 != X) \/ ((T_1 != W) \/ ((segmentP T_0 T_1) /\ (equalelemsP T_1)))))))))) (equalelemsP (nil)) (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)))) (ssList T_1) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))))) ### NotAllEx 35
% 5.43/5.61 37. (-. ((ssList T_0) => (All W, ((ssList W) => (All X, ((ssList X) => (((nil) != W) \/ ((T_0 != X) \/ ((T_1 != W) \/ ((segmentP T_0 T_1) /\ (equalelemsP 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)))))))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (ssList T_1) (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)))))))) (equalelemsP (nil)) ### NotImply 36
% 5.43/5.61 38. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => (((nil) != W) \/ ((V != X) \/ ((T_1 != W) \/ ((segmentP V T_1) /\ (equalelemsP T_1)))))))))))) (equalelemsP (nil)) (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)))) (ssList T_1) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) (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 37
% 5.43/5.61 39. (-. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => (((nil) != W) \/ ((V != X) \/ ((T_1 != W) \/ ((segmentP V T_1) /\ (equalelemsP 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)))))))))) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = 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)))))))) (equalelemsP (nil)) ### NotImply 38
% 5.43/5.61 40. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => (((nil) != W) \/ ((V != X) \/ ((U != W) \/ ((segmentP V U) /\ (equalelemsP U)))))))))))))) (equalelemsP (nil)) (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) => ((segmentP (nil) U) <=> ((nil) = U)))) (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 39
% 5.43/5.61 % SZS output end Proof
% 5.43/5.61 (* END-PROOF *)
%------------------------------------------------------------------------------