%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWC367+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 : n005.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 1.20s 1.39s % Output : Proof 1.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC367+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n005.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 12:44:09 EDT 2022 % 0.12/0.33 % CPUTime : % 1.20/1.39 % SZS status Theorem % 1.20/1.39 (* PROOF-FOUND *) % 1.20/1.39 (* BEGIN-PROOF *) % 1.20/1.39 % SZS output start Proof % 1.20/1.39 1. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.20/1.39 2. ((nil) = T_0) ((nil) != T_0) ### Axiom % 1.20/1.39 3. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.20/1.39 4. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.20/1.39 5. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.20/1.39 6. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.20/1.39 7. (ssList T_1) (-. (ssList T_1)) ### Axiom % 1.20/1.39 8. (-. (rearsegP T_1 (nil))) (rearsegP T_1 (nil)) ### Axiom % 1.20/1.39 9. ((ssList T_1) => (rearsegP T_1 (nil))) (-. (rearsegP T_1 (nil))) (ssList T_1) ### Imply 7 8 % 1.20/1.39 10. (All U, ((ssList U) => (rearsegP U (nil)))) (ssList T_1) (-. (rearsegP T_1 (nil))) ### All 9 % 1.20/1.39 11. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 1.20/1.39 12. (ssList T_0) (-. (ssList T_0)) ### Axiom % 1.20/1.39 13. (rearsegP T_1 (nil)) (-. (rearsegP T_1 (nil))) ### Axiom % 1.20/1.39 14. (rearsegP (nil) T_0) (-. (rearsegP (nil) T_0)) ### Axiom % 1.20/1.39 15. (-. (rearsegP T_1 T_0)) (rearsegP T_1 T_0) ### Axiom % 1.20/1.39 16. ((ssList T_0) => (((rearsegP T_1 (nil)) /\ (rearsegP (nil) T_0)) => (rearsegP T_1 T_0))) (-. (rearsegP T_1 T_0)) (rearsegP (nil) T_0) (rearsegP T_1 (nil)) (ssList T_0) ### DisjTree 12 13 14 15 % 1.20/1.39 17. (All W, ((ssList W) => (((rearsegP T_1 (nil)) /\ (rearsegP (nil) W)) => (rearsegP T_1 W)))) (ssList T_0) (rearsegP T_1 (nil)) (rearsegP (nil) T_0) (-. (rearsegP T_1 T_0)) ### All 16 % 1.20/1.39 18. ((ssList (nil)) => (All W, ((ssList W) => (((rearsegP T_1 (nil)) /\ (rearsegP (nil) W)) => (rearsegP T_1 W))))) (-. (rearsegP T_1 T_0)) (rearsegP (nil) T_0) (rearsegP T_1 (nil)) (ssList T_0) (ssList (nil)) ### Imply 11 17 % 1.20/1.39 19. (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP T_1 V) /\ (rearsegP V W)) => (rearsegP T_1 W)))))) (ssList (nil)) (ssList T_0) (rearsegP T_1 (nil)) (rearsegP (nil) T_0) (-. (rearsegP T_1 T_0)) ### All 18 % 1.20/1.39 20. ((rearsegP T_1 (nil)) <=> (Ex W, ((ssList W) /\ ((app W (nil)) = T_1)))) (-. (rearsegP T_1 T_0)) (rearsegP (nil) T_0) (ssList T_0) (ssList (nil)) (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP T_1 V) /\ (rearsegP V W)) => (rearsegP T_1 W)))))) (ssList T_1) (All U, ((ssList U) => (rearsegP U (nil)))) ### Equiv 10 19 % 1.20/1.39 21. ((ssList (nil)) => ((rearsegP T_1 (nil)) <=> (Ex W, ((ssList W) /\ ((app W (nil)) = T_1))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList T_1) (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP T_1 V) /\ (rearsegP V W)) => (rearsegP T_1 W)))))) (ssList T_0) (rearsegP (nil) T_0) (-. (rearsegP T_1 T_0)) (ssList (nil)) ### Imply 6 20 % 1.20/1.39 22. (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList (nil)) (-. (rearsegP T_1 T_0)) (rearsegP (nil) T_0) (ssList T_0) (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP T_1 V) /\ (rearsegP V W)) => (rearsegP T_1 W)))))) (ssList T_1) (All U, ((ssList U) => (rearsegP U (nil)))) ### All 21 % 1.20/1.39 23. ((ssList T_1) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP T_1 V) /\ (rearsegP V W)) => (rearsegP T_1 W))))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList T_0) (rearsegP (nil) T_0) (-. (rearsegP T_1 T_0)) (ssList (nil)) (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList T_1) ### Imply 5 22 % 1.20/1.39 24. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_1) (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList (nil)) (-. (rearsegP T_1 T_0)) (rearsegP (nil) T_0) (ssList T_0) (All U, ((ssList U) => (rearsegP U (nil)))) ### All 23 % 1.20/1.39 25. (T_2 = T_1) (T_1 != T_2) ### Sym(=) % 1.20/1.39 26. (T_3 = T_0) (T_0 != T_3) ### Sym(=) % 1.20/1.39 27. (-. (rearsegP T_2 T_3)) (rearsegP T_1 T_0) (T_3 = T_0) (T_2 = T_1) ### P-NotP 25 26 % 1.20/1.39 28. ((rearsegP T_1 T_0) <=> (Ex W, ((ssList W) /\ ((app W T_0) = T_1)))) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList T_0) (rearsegP (nil) T_0) (ssList (nil)) (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) ### Equiv 24 27 % 1.20/1.39 29. ((ssList T_0) => ((rearsegP T_1 T_0) <=> (Ex W, ((ssList W) /\ ((app W T_0) = T_1))))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_1) (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList (nil)) (rearsegP (nil) T_0) (All U, ((ssList U) => (rearsegP U (nil)))) (-. (rearsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) ### Imply 4 28 % 1.20/1.39 30. (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (rearsegP (nil) T_0) (ssList (nil)) (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1)))))) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) ### All 29 % 1.20/1.39 31. ((ssList T_1) => (All V, ((ssList V) => ((rearsegP T_1 V) <=> (Ex W, ((ssList W) /\ ((app W V) = T_1))))))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (rearsegP (nil) T_0) (All U, ((ssList U) => (rearsegP U (nil)))) (-. (rearsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_0) (ssList T_1) ### Imply 3 30 % 1.20/1.39 32. (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (ssList T_1) (ssList T_0) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (rearsegP (nil) T_0) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) ### All 31 % 1.20/1.39 33. ((rearsegP (nil) T_0) <=> ((nil) = T_0)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (-. (rearsegP 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) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ((nil) = T_0) ### Equiv 2 32 % 1.20/1.39 34. ((ssList T_0) => ((rearsegP (nil) T_0) <=> ((nil) = T_0))) ((nil) = T_0) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_0) ### Imply 1 33 % 1.20/1.39 35. (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (-. (rearsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ((nil) = T_0) ### All 34 % 1.20/1.39 36. (-. ((nil) != T_0)) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotNot 35 % 1.20/1.39 37. (-. (((nil) != T_1) \/ ((nil) != T_0))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (-. (rearsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ### NotOr 36 % 1.20/1.40 38. (-. (-. (rearsegP T_1 T_0))) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) ### NotNot 27 % 1.20/1.40 39. (-. ((-. (neq T_0 (nil))) \/ (-. (rearsegP T_1 T_0)))) (-. (rearsegP T_2 T_3)) (T_3 = T_0) (T_2 = T_1) ### NotOr 38 % 1.20/1.40 40. (-. ((((nil) != T_1) \/ ((nil) != T_0)) /\ ((-. (neq T_0 (nil))) \/ (-. (rearsegP T_1 T_0))))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (ssList T_1) (T_2 = T_1) (T_3 = T_0) (-. (rearsegP T_2 T_3)) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotAnd 37 39 % 1.20/1.40 41. (-. ((ssList T_1) => ((T_2 != T_1) \/ ((T_3 != T_0) \/ ((rearsegP T_2 T_3) \/ ((((nil) != T_1) \/ ((nil) != T_0)) /\ ((-. (neq T_0 (nil))) \/ (-. (rearsegP T_1 T_0))))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (ssList T_0) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ### ConjTree 40 % 1.20/1.40 42. (-. (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((rearsegP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != T_0)) /\ ((-. (neq T_0 (nil))) \/ (-. (rearsegP X T_0)))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList T_0) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotAllEx 41 % 1.20/1.40 43. (-. ((ssList T_0) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != T_0) \/ ((rearsegP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != T_0)) /\ ((-. (neq T_0 (nil))) \/ (-. (rearsegP X T_0))))))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ### NotImply 42 % 1.20/1.40 44. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((rearsegP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (rearsegP X W)))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotAllEx 43 % 1.20/1.40 45. (-. ((ssList T_2) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_2 != X) \/ ((T_3 != W) \/ ((rearsegP T_2 T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (rearsegP X W))))))))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ### NotImply 44 % 1.20/1.40 46. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((rearsegP V T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (rearsegP X W)))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotAllEx 45 % 1.20/1.40 47. (-. ((ssList T_3) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_3 != W) \/ ((rearsegP V T_3) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (rearsegP X W))))))))))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (ssList (nil)) (All U, ((ssList U) => (rearsegP U (nil)))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) ### NotImply 46 % 1.20/1.40 48. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((rearsegP V U) \/ ((((nil) != X) \/ ((nil) != W)) /\ ((-. (neq W (nil))) \/ (-. (rearsegP X W)))))))))))))))) (All U, ((ssList U) => (All V, ((ssList V) => ((rearsegP U V) <=> (Ex W, ((ssList W) /\ ((app W V) = U)))))))) (All U, ((ssList U) => (rearsegP U (nil)))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (((rearsegP U V) /\ (rearsegP V W)) => (rearsegP U W)))))))) (All U, ((ssList U) => ((rearsegP (nil) U) <=> ((nil) = U)))) ### NotAllEx 47 % 1.20/1.40 % SZS output end Proof % 1.20/1.40 (* END-PROOF *) %------------------------------------------------------------------------------