%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWC352+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 22:07:50 EDT 2022 % Result : Theorem 1.96s 2.19s % Output : Proof 1.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC352+1 : TPTP v8.1.0. Released v2.4.0. % 0.13/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n024.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 : Sat Jun 11 22:53:19 EDT 2022 % 0.13/0.34 % CPUTime : % 1.96/2.19 % SZS status Theorem % 1.96/2.19 (* PROOF-FOUND *) % 1.96/2.19 (* BEGIN-PROOF *) % 1.96/2.19 % SZS output start Proof % 1.96/2.19 1. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.96/2.19 2. ((nil) = T_0) ((nil) != T_0) ### Axiom % 1.96/2.19 3. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.96/2.19 4. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.96/2.19 5. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.96/2.19 6. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.96/2.19 7. (-. (frontsegP T_1 (nil))) (frontsegP T_1 (nil)) ### Axiom % 1.96/2.19 8. ((ssList T_1) => (frontsegP T_1 (nil))) (-. (frontsegP T_1 (nil))) (ssList T_1) ### Imply 6 7 % 1.96/2.19 9. (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_1) (-. (frontsegP T_1 (nil))) ### All 8 % 1.96/2.19 10. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.96/2.19 11. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.96/2.19 12. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.96/2.19 13. (frontsegP T_1 (nil)) (-. (frontsegP T_1 (nil))) ### Axiom % 1.96/2.19 14. (frontsegP (nil) T_0) (-. (frontsegP (nil) T_0)) ### Axiom % 1.96/2.19 15. (-. (frontsegP T_1 T_0)) (frontsegP T_1 T_0) ### Axiom % 1.96/2.19 16. ((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 12 13 14 15 % 1.96/2.19 17. (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 16 % 1.96/2.19 18. ((ssList (nil)) => (All W, ((ssList W) => (((frontsegP T_1 (nil)) /\ (frontsegP (nil) W)) => (frontsegP T_1 W))))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (frontsegP T_1 (nil)) (ssList T_0) (ssList (nil)) ### Imply 11 17 % 1.96/2.19 19. (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_1 V) /\ (frontsegP V W)) => (frontsegP T_1 W)))))) (ssList (nil)) (ssList T_0) (frontsegP T_1 (nil)) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) ### All 18 % 1.96/2.19 20. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP T_1 V) /\ (frontsegP V W)) => (frontsegP T_1 W))))))) (-. (frontsegP T_1 T_0)) (frontsegP (nil) T_0) (frontsegP T_1 (nil)) (ssList T_0) (ssList (nil)) (ssList T_1) ### Imply 10 19 % 1.96/2.19 21. (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)) (ssList T_0) (frontsegP T_1 (nil)) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) ### All 20 % 1.96/2.19 22. ((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) (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) (All U, ((ssList U) => (frontsegP U (nil)))) ### Equiv 9 21 % 1.96/2.19 23. ((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 U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_0) (frontsegP (nil) T_0) (-. (frontsegP T_1 T_0)) (ssList (nil)) ### Imply 5 22 % 1.96/2.19 24. (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 U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_1) (All U, ((ssList U) => (frontsegP U (nil)))) ### All 23 % 1.96/2.19 25. (T_2 = T_1) (T_1 != T_2) ### Sym(=) % 1.96/2.19 26. (T_3 = T_0) (T_0 != T_3) ### Sym(=) % 1.96/2.19 27. (-. (frontsegP T_2 T_3)) (frontsegP T_1 T_0) (T_3 = T_0) (T_2 = T_1) ### P-NotP 25 26 % 1.96/2.19 28. ((frontsegP T_1 T_0) <=> (Ex W, ((ssList W) /\ ((app T_0 W) = T_1)))) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) (All U, ((ssList U) => (frontsegP U (nil)))) (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 T_0) (frontsegP (nil) T_0) (ssList (nil)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) ### Equiv 24 27 % 1.96/2.19 29. ((ssList T_0) => ((frontsegP T_1 T_0) <=> (Ex W, ((ssList W) /\ ((app T_0 W) = T_1))))) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) (ssList (nil)) (frontsegP (nil) T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList T_1) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) ### Imply 4 28 % 1.96/2.19 30. (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) (All U, ((ssList U) => (frontsegP U (nil)))) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (frontsegP (nil) T_0) (ssList (nil)) (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1)))))) ### All 29 % 1.96/2.19 31. ((ssList T_1) => (All V, ((ssList V) => ((frontsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app V W) = T_1))))))) (ssList (nil)) (frontsegP (nil) T_0) (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 U (nil)))) (-. (frontsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) (ssList T_1) ### Imply 3 30 % 1.96/2.19 32. (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (ssList T_1) (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) (All U, ((ssList U) => (frontsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (frontsegP (nil) T_0) (ssList (nil)) ### All 31 % 1.96/2.19 33. ((frontsegP (nil) T_0) <=> ((nil) = 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)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP 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) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ((nil) = T_0) ### Equiv 2 32 % 1.96/2.19 34. ((ssList T_0) => ((frontsegP (nil) T_0) <=> ((nil) = T_0))) ((nil) = T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) (All U, ((ssList U) => (frontsegP U (nil)))) (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_0) ### Imply 1 33 % 1.96/2.19 35. (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ((nil) = T_0) ### All 34 % 1.96/2.19 36. (-. ((nil) != T_0)) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) (All U, ((ssList U) => (frontsegP U (nil)))) (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_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) ### NotNot 35 % 1.96/2.19 37. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.96/2.19 38. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.96/2.19 39. ((nil) != T_1) (T_1 = (nil)) ### Sym(=) % 1.96/2.19 40. (-. (T_1 != (nil))) ((nil) != T_1) ### NotNot 39 % 1.96/2.19 41. (-. (neq T_1 (nil))) (neq T_1 (nil)) ### Axiom % 1.96/2.19 42. ((neq T_1 (nil)) <=> (T_1 != (nil))) (-. (neq T_1 (nil))) ((nil) != T_1) ### Equiv 40 41 % 1.96/2.19 43. ((ssList (nil)) => ((neq T_1 (nil)) <=> (T_1 != (nil)))) ((nil) != T_1) (-. (neq T_1 (nil))) (ssList (nil)) ### Imply 38 42 % 1.96/2.20 44. (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList (nil)) (-. (neq T_1 (nil))) ((nil) != T_1) ### All 43 % 1.96/2.20 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 % 1.96/2.20 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 % 1.96/2.20 47. (-. (-. (frontsegP T_1 T_0))) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP T_2 T_3)) ### NotNot 27 % 1.96/2.20 48. (-. ((-. (neq T_0 (nil))) \/ (-. (frontsegP T_1 T_0)))) (-. (frontsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) ### NotOr 47 % 1.96/2.20 49. (-. ((neq T_1 (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (frontsegP T_1 T_0))))) (T_2 = T_1) (T_3 = T_0) (-. (frontsegP 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 % 1.96/2.20 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))) \/ (-. (frontsegP T_1 T_0))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))) (All U, ((ssList U) => (frontsegP U (nil)))) (-. (frontsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotAnd 36 49 % 1.96/2.21 51. (-. ((ssList T_1) => ((T_2 != T_1) \/ ((T_3 != T_0) \/ ((frontsegP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = T_1)) \/ ((neq T_1 (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (frontsegP T_1 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) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (ssList T_0) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### ConjTree 50 % 1.96/2.21 52. (-. (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((frontsegP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (frontsegP X T_0))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (ssList 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)))))))) (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)))))))) ### NotAllEx 51 % 1.96/2.21 53. (-. ((ssList T_0) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((frontsegP T_2 T_3) \/ ((((nil) != T_0) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq T_0 (nil))) \/ (-. (frontsegP X 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) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 52 % 1.96/2.21 54. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((frontsegP T_2 T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (frontsegP X W))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (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 U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotAllEx 53 % 1.96/2.21 55. (-. ((ssList T_2) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((frontsegP T_2 T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (frontsegP 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) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 54 % 1.96/2.21 56. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((frontsegP V T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (frontsegP X W))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (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 U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotAllEx 55 % 1.96/2.21 57. (-. ((ssList T_3) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((frontsegP V T_3) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (frontsegP 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) => (All V, ((ssList V) => (All W, ((ssList W) => (((frontsegP U V) /\ (frontsegP V W)) => (frontsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotImply 56 % 1.96/2.21 58. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((frontsegP V U) \/ ((((nil) != W) /\ ((nil) = X)) \/ ((neq X (nil)) /\ ((-. (neq W (nil))) \/ (-. (frontsegP X W))))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (All U, ((ssList U) => ((frontsegP (nil) U) <=> ((nil) = U)))) (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 U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((frontsegP U V) <=> (Ex W, ((ssList W) /\ ((app V W) = U)))))))) ### NotAllEx 57 % 1.96/2.21 % SZS output end Proof % 1.96/2.21 (* END-PROOF *) %------------------------------------------------------------------------------