%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWC131+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 : n016.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 22:06:44 EDT 2022 % Result : Theorem 2.79s 2.96s % Output : Proof 2.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWC131+1 : TPTP v8.1.0. Released v2.4.0. % 0.04/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 12 20:04:43 EDT 2022 % 0.12/0.34 % CPUTime : % 2.79/2.96 % SZS status Theorem % 2.79/2.96 (* PROOF-FOUND *) % 2.79/2.96 (* BEGIN-PROOF *) % 2.79/2.96 % SZS output start Proof % 2.79/2.96 1. (ssList T_0) (-. (ssList T_0)) ### Axiom % 2.79/2.96 2. (ssList (nil)) (-. (ssList (nil))) ### Axiom % 2.79/2.96 3. (ssList T_1) (-. (ssList T_1)) ### Axiom % 2.79/2.96 4. (ssList T_1) (-. (ssList T_1)) ### Axiom % 2.79/2.96 5. (-. (T_1 != T_1)) (T_1 != T_1) ### Axiom % 2.79/2.96 6. (T_0 = (nil)) (T_0 != (nil)) ### Axiom % 2.79/2.96 7. ((nil) != T_1) (T_1 = T_0) (T_0 = (nil)) (-. (T_1 != T_1)) ### Trans-sym 5 6 % 2.79/2.96 8. (T_1 != T_1) ### Refl(=) % 2.79/2.96 9. ((neq T_1 T_1) <=> (T_1 != T_1)) (T_0 = (nil)) (T_1 = T_0) ((nil) != T_1) ### Equiv 7 8 % 2.79/2.96 10. ((ssList T_1) => ((neq T_1 T_1) <=> (T_1 != T_1))) ((nil) != T_1) (T_1 = T_0) (T_0 = (nil)) (ssList T_1) ### Imply 4 9 % 2.79/2.96 11. (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V)))) (ssList T_1) (T_0 = (nil)) (T_1 = T_0) ((nil) != T_1) ### All 10 % 2.79/2.96 12. ((ssList T_1) => (All V, ((ssList V) => ((neq T_1 V) <=> (T_1 != V))))) ((nil) != T_1) (T_1 = T_0) (T_0 = (nil)) (ssList T_1) ### Imply 3 11 % 2.79/2.96 13. (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (T_0 = (nil)) (T_1 = T_0) ((nil) != T_1) ### All 12 % 2.79/2.96 14. (-. (T_0 != (nil))) ((nil) != T_1) (T_1 = T_0) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) ### NotNot 13 % 2.79/2.96 15. (-. (neq T_0 (nil))) (neq T_0 (nil)) ### Axiom % 2.79/2.96 16. ((neq T_0 (nil)) <=> (T_0 != (nil))) (-. (neq T_0 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (T_1 = T_0) ((nil) != T_1) ### Equiv 14 15 % 2.79/2.96 17. ((ssList (nil)) => ((neq T_0 (nil)) <=> (T_0 != (nil)))) ((nil) != T_1) (T_1 = T_0) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (-. (neq T_0 (nil))) (ssList (nil)) ### Imply 2 16 % 2.79/2.96 18. (All V, ((ssList V) => ((neq T_0 V) <=> (T_0 != V)))) (ssList (nil)) (-. (neq T_0 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (T_1 = T_0) ((nil) != T_1) ### All 17 % 2.79/2.96 19. ((ssList T_0) => (All V, ((ssList V) => ((neq T_0 V) <=> (T_0 != V))))) ((nil) != T_1) (T_1 = T_0) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (-. (neq T_0 (nil))) (ssList (nil)) (ssList T_0) ### Imply 1 18 % 2.79/2.96 20. (ssList T_0) (ssList (nil)) (-. (neq T_0 (nil))) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (T_1 = T_0) ((nil) != T_1) ### All 19 % 2.79/2.96 21. (-. (cyclefreeP T_1)) (cyclefreeP (nil)) (T_1 = T_0) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (-. (neq T_0 (nil))) (ssList (nil)) (ssList T_0) ### P-NotP 20 % 2.79/2.96 22. (-. ((ssList T_0) => ((T_1 != T_0) \/ ((T_2 != T_3) \/ ((neq T_0 (nil)) \/ (cyclefreeP T_1)))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (cyclefreeP (nil)) ### ConjTree 21 % 2.79/2.96 23. (-. (All X, ((ssList X) => ((T_1 != X) \/ ((T_2 != T_3) \/ ((neq X (nil)) \/ (cyclefreeP T_1))))))) (cyclefreeP (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList (nil)) ### NotAllEx 22 % 2.79/2.97 24. (-. ((ssList T_3) => (All X, ((ssList X) => ((T_1 != X) \/ ((T_2 != T_3) \/ ((neq X (nil)) \/ (cyclefreeP T_1)))))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList T_1) (cyclefreeP (nil)) ### NotImply 23 % 2.79/2.97 25. (-. (All W, ((ssList W) => (All X, ((ssList X) => ((T_1 != X) \/ ((T_2 != W) \/ ((neq X (nil)) \/ (cyclefreeP T_1))))))))) (cyclefreeP (nil)) (ssList T_1) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList (nil)) ### NotAllEx 24 % 2.79/2.97 26. (-. ((ssList T_1) => (All W, ((ssList W) => (All X, ((ssList X) => ((T_1 != X) \/ ((T_2 != W) \/ ((neq X (nil)) \/ (cyclefreeP T_1)))))))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (cyclefreeP (nil)) ### NotImply 25 % 2.79/2.97 27. (-. (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_2 != W) \/ ((neq X (nil)) \/ (cyclefreeP V))))))))))) (cyclefreeP (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList (nil)) ### NotAllEx 26 % 2.79/2.97 28. (-. ((ssList T_2) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((T_2 != W) \/ ((neq X (nil)) \/ (cyclefreeP V)))))))))))) (ssList (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (cyclefreeP (nil)) ### NotImply 27 % 2.79/2.97 29. (-. (All U, ((ssList U) => (All V, ((ssList V) => (All W, ((ssList W) => (All X, ((ssList X) => ((V != X) \/ ((U != W) \/ ((neq X (nil)) \/ (cyclefreeP V))))))))))))) (cyclefreeP (nil)) (All U, ((ssList U) => (All V, ((ssList V) => ((neq U V) <=> (U != V)))))) (ssList (nil)) ### NotAllEx 28 % 2.79/2.97 % SZS output end Proof % 2.79/2.97 (* END-PROOF *) %------------------------------------------------------------------------------