%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWC358+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 : n024.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 22:07:52 EDT 2022 % Result : Theorem 1.21s 1.44s % Output : Proof 1.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC358+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n024.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 08:55:49 EDT 2022 % 0.12/0.34 % CPUTime : % 1.21/1.44 % SZS status Theorem % 1.21/1.44 (* PROOF-FOUND *) % 1.21/1.44 (* BEGIN-PROOF *) % 1.21/1.44 % SZS output start Proof % 1.21/1.44 1. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.21/1.44 2. ((nil) = T_0) ((nil) != T_0) ### Axiom % 1.21/1.44 3. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.21/1.44 4. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.21/1.44 5. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.21/1.44 6. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.21/1.44 7. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.21/1.44 8. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.21/1.44 9. (-. (segmentP T_1 (nil))) (segmentP T_1 (nil)) ### Axiom % 1.21/1.44 10. ((ssList T_1) => (segmentP T_1 (nil))) (-. (segmentP T_1 (nil))) (ssList T_1) ### Imply 8 9 % 1.21/1.44 11. (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (-. (segmentP T_1 (nil))) ### All 10 % 1.21/1.44 12. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.21/1.44 13. (-. (segmentP (nil) (nil))) (ssList (nil)) ### Extension/test/ax55ctrp 12 % 1.21/1.44 14. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.21/1.44 15. (segmentP T_1 (nil)) (-. (segmentP T_1 (nil))) ### Axiom % 1.21/1.44 16. (segmentP (nil) T_0) (-. (segmentP (nil) T_0)) ### Axiom % 1.21/1.44 17. (-. (segmentP T_1 T_0)) (segmentP T_1 T_0) ### Axiom % 1.21/1.44 18. ((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 14 15 16 17 % 1.21/1.44 19. (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 18 % 1.21/1.44 20. ((ssList (nil)) => (((segmentP T_1 (nil)) /\ (segmentP (nil) (nil))) => (segmentP T_1 (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)))) (ssList (nil)) ### DisjTree 7 11 13 19 % 1.21/1.44 21. (ssList (nil)) (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)) ### All 20 % 1.21/1.44 22. ((ssList (nil)) => (All W, ((ssList W) => (((segmentP T_1 (nil)) /\ (segmentP (nil) W)) => (segmentP T_1 W))))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (ssList T_1) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) ### Imply 6 21 % 1.21/1.44 23. (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_1 V) /\ (segmentP V W)) => (segmentP T_1 W)))))) (ssList (nil)) (All U, ((ssList U) => (segmentP U (nil)))) (ssList T_1) (ssList T_0) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) ### All 22 % 1.21/1.44 24. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (((segmentP T_1 V) /\ (segmentP V W)) => (segmentP T_1 W))))))) (-. (segmentP T_1 T_0)) (segmentP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) (ssList (nil)) (ssList T_1) ### Imply 5 23 % 1.21/1.44 25. (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 U, ((ssList U) => (segmentP U (nil)))) (ssList T_0) (segmentP (nil) T_0) (-. (segmentP T_1 T_0)) ### All 24 % 1.21/1.44 26. (T_2 = T_1) (T_1 != T_2) ### Sym(=) % 1.21/1.44 27. (T_3 = T_0) (T_0 != T_3) ### Sym(=) % 1.21/1.44 28. (-. (segmentP T_2 T_3)) (segmentP T_1 T_0) (T_3 = T_0) (T_2 = T_1) ### P-NotP 26 27 % 1.21/1.44 29. ((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)) (segmentP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (segmentP U (nil)))) (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 25 28 % 1.21/1.44 30. ((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 U, ((ssList U) => (segmentP U (nil)))) (segmentP (nil) T_0) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) ### Imply 4 29 % 1.21/1.44 31. (All V, ((ssList V) => ((segmentP T_1 V) <=> (Ex W, ((ssList W) /\ (Ex X, ((ssList X) /\ ((app (app W V) X) = T_1)))))))) (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) (segmentP (nil) T_0) (All U, ((ssList U) => (segmentP U (nil)))) (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 30 % 1.21/1.44 32. ((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)) (All U, ((ssList U) => (segmentP U (nil)))) (segmentP (nil) T_0) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) (ssList T_1) ### Imply 3 31 % 1.21/1.44 33. (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)) (segmentP (nil) T_0) (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 32 % 1.21/1.44 34. ((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 33 % 1.21/1.44 35. ((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 34 % 1.21/1.44 36. (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 35 % 1.21/1.44 37. (-. ((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 36 % 1.21/1.44 38. (-. (((nil) != T_1) \/ ((nil) != 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)))))))))) ### NotOr 37 % 1.21/1.44 39. (-. (-. (segmentP T_1 T_0))) (T_2 = T_1) (T_3 = T_0) (-. (segmentP T_2 T_3)) ### NotNot 28 % 1.21/1.44 40. (-. ((-. (neq T_0 (nil))) \/ (-. (segmentP T_1 T_0)))) (-. (segmentP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) ### NotOr 39 % 1.21/1.44 41. (-. ((((nil) != T_1) \/ ((nil) != T_0)) /\ ((-. (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)))))))))) (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)))) ### NotAnd 38 40 % 1.21/1.44 42. (-. ((ssList T_1) => ((T_2 != T_1) \/ ((T_3 != T_0) \/ ((-. (neq T_2 (nil))) \/ ((segmentP T_2 T_3) \/ ((((nil) != T_1) \/ ((nil) != T_0)) /\ ((-. (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)))) (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)))))))))) ### ConjTree 41 % 1.21/1.44 43. (-. (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((-. (neq T_2 (nil))) \/ ((segmentP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != T_0)) /\ ((-. (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)))))))) (ssList T_0) (All U, ((ssList U) => ((segmentP (nil) U) <=> ((nil) = U)))) ### NotAllEx 42 % 1.21/1.44 44. (-. ((ssList T_0) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((-. (neq T_2 (nil))) \/ ((segmentP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != T_0)) /\ ((-. (neq T_0 (nil))) \/ (-. (segmentP X T_0)))))))))))) (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)))))))))) ### NotImply 43 % 1.21/1.44 45. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((-. (neq T_2 (nil))) \/ ((segmentP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (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)))) ### NotAllEx 44 % 1.21/1.44 46. (-. ((ssList T_2) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((-. (neq T_2 (nil))) \/ ((segmentP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))) (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)))))))))) ### NotImply 45 % 1.21/1.44 47. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((-. (neq V (nil))) \/ ((segmentP V T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (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)))) ### NotAllEx 46 % 1.21/1.44 48. (-. ((ssList T_3) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((-. (neq V (nil))) \/ ((segmentP V T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (segmentP X W)))))))))))))))) (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)))))))))) ### NotImply 47 % 1.21/1.44 49. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((-. (neq V (nil))) \/ ((segmentP V U) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (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)))) ### NotAllEx 48 % 1.21/1.44 % SZS output end Proof % 1.21/1.44 (* END-PROOF *) %------------------------------------------------------------------------------