%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n023.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 : Mon Jul 18 14:43:22 EDT 2022 % Result : Theorem 29.30s 29.48s % Output : Proof 29.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.31 % Computer : n023.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 600 % 0.12/0.31 % DateTime : Wed Jul 6 20:07:41 EDT 2022 % 0.12/0.31 % CPUTime : % 29.30/29.48 % SZS status Theorem % 29.30/29.48 (* PROOF-FOUND *) % 29.30/29.48 (* BEGIN-PROOF *) % 29.30/29.48 % SZS output start Proof % 29.30/29.48 1. (aSet0 (xS)) (-. (aSet0 (xS))) ### Axiom % 29.30/29.48 2. (aElementOf0 T_0 (xS)) (-. (aElementOf0 T_0 (xS))) ### Axiom % 29.30/29.48 3. (-. (aElement0 T_0)) (aElement0 T_0) ### Axiom % 29.30/29.48 4. ((aElementOf0 T_0 (xS)) => (aElement0 T_0)) (-. (aElement0 T_0)) (aElementOf0 T_0 (xS)) ### Imply 2 3 % 29.30/29.48 5. (All W1, ((aElementOf0 W1 (xS)) => (aElement0 W1))) (aElementOf0 T_0 (xS)) (-. (aElement0 T_0)) ### All 4 % 29.30/29.48 6. ((aSet0 (xS)) => (All W1, ((aElementOf0 W1 (xS)) => (aElement0 W1)))) (-. (aElement0 T_0)) (aElementOf0 T_0 (xS)) (aSet0 (xS)) ### Imply 1 5 % 29.30/29.48 7. (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) (aElementOf0 T_0 (xS)) (-. (aElement0 T_0)) ### All 6 % 29.30/29.48 8. (aElementOf0 T_0 (xS)) (-. (aElementOf0 T_0 (xS))) ### Axiom % 29.30/29.48 9. (T_0 != (xx)) (T_0 = (xx)) ### Axiom % 29.30/29.48 10. (-. ((aElement0 T_0) /\ ((aElementOf0 T_0 (xS)) /\ (T_0 != (xx))))) (T_0 != (xx)) (aElementOf0 T_0 (xS)) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### DisjTree 7 8 9 % 29.30/29.48 11. (-. (aElementOf0 T_0 (sdtmndt0 (xS) (xx)))) (aElementOf0 T_0 (sdtmndt0 (xS) (xx))) ### Axiom % 29.30/29.48 12. ((aElementOf0 T_0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 T_0) /\ ((aElementOf0 T_0 (xS)) /\ (T_0 != (xx))))) (-. (aElementOf0 T_0 (sdtmndt0 (xS) (xx)))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) (aElementOf0 T_0 (xS)) (T_0 != (xx)) ### Equiv 10 11 % 29.30/29.48 13. (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (T_0 != (xx)) (aElementOf0 T_0 (xS)) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aElementOf0 T_0 (sdtmndt0 (xS) (xx)))) ### All 12 % 29.30/29.48 14. (-. ((aElementOf0 T_0 (sdtmndt0 (xS) (xx))) \/ (T_0 = (xx)))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) (aElementOf0 T_0 (xS)) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) ### NotOr 13 % 29.30/29.48 15. (-. ((aElement0 T_0) /\ ((aElementOf0 T_0 (sdtmndt0 (xS) (xx))) \/ (T_0 = (xx))))) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (aElementOf0 T_0 (xS)) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### NotAnd 7 14 % 29.30/29.48 16. (-. (aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))) (aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) ### Axiom % 29.30/29.48 17. ((aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 T_0) /\ ((aElementOf0 T_0 (sdtmndt0 (xS) (xx))) \/ (T_0 = (xx))))) (-. (aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) (aElementOf0 T_0 (xS)) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) ### Equiv 15 16 % 29.30/29.48 18. (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (aElementOf0 T_0 (xS)) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (-. (aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))) ### All 17 % 29.30/29.48 19. (-. ((aElementOf0 T_0 (xS)) => (aElementOf0 T_0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) ### NotImply 18 % 29.30/29.48 20. (-. (All W0, ((aElementOf0 W0 (xS)) => (aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))))) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### NotAllEx 19 % 29.30/29.48 21. (-. (((aSet0 (sdtmndt0 (xS) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx))))))) => (((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx))))))) => ((All W0, ((aElementOf0 W0 (xS)) => (aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))) \/ (aSubsetOf0 (xS) (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))))) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) (aSet0 (xS)) ### ConjTree 20 % 29.30/29.48 22. (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) (-. (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))) ### Axiom % 29.30/29.48 23. (-. (aElementOf0 T_1 (sdtmndt0 (xS) (xx)))) (aElementOf0 T_1 (sdtmndt0 (xS) (xx))) ### Axiom % 29.30/29.48 24. (T_1 = (xx)) ((xx) != T_1) ### Sym(=) % 29.30/29.48 25. ((xS) != (xS)) ### NotEqual % 29.30/29.48 26. (-. (aElementOf0 T_1 (xS))) (aElementOf0 (xx) (xS)) (T_1 = (xx)) ### P-NotP 24 25 % 29.30/29.48 27. ((aElementOf0 T_1 (sdtmndt0 (xS) (xx))) \/ (T_1 = (xx))) (aElementOf0 (xx) (xS)) (-. (aElementOf0 T_1 (xS))) (-. (aElementOf0 T_1 (sdtmndt0 (xS) (xx)))) ### Or 23 26 % 29.30/29.48 28. ((aElement0 T_1) /\ ((aElementOf0 T_1 (sdtmndt0 (xS) (xx))) \/ (T_1 = (xx)))) (-. (aElementOf0 T_1 (sdtmndt0 (xS) (xx)))) (-. (aElementOf0 T_1 (xS))) (aElementOf0 (xx) (xS)) ### And 27 % 29.30/29.48 29. ((aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 T_1) /\ ((aElementOf0 T_1 (sdtmndt0 (xS) (xx))) \/ (T_1 = (xx))))) (aElementOf0 (xx) (xS)) (-. (aElementOf0 T_1 (xS))) (-. (aElementOf0 T_1 (sdtmndt0 (xS) (xx)))) (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) ### Equiv 22 28 % 29.30/29.48 30. (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) (-. (aElementOf0 T_1 (sdtmndt0 (xS) (xx)))) (-. (aElementOf0 T_1 (xS))) (aElementOf0 (xx) (xS)) ### All 29 % 29.30/29.48 31. (-. (aElementOf0 T_1 (xS))) (aElementOf0 T_1 (xS)) ### Axiom % 29.30/29.48 32. ((aElement0 T_1) /\ ((aElementOf0 T_1 (xS)) /\ (T_1 != (xx)))) (-. (aElementOf0 T_1 (xS))) ### ConjTree 31 % 29.30/29.48 33. ((aElementOf0 T_1 (sdtmndt0 (xS) (xx))) <=> ((aElement0 T_1) /\ ((aElementOf0 T_1 (xS)) /\ (T_1 != (xx))))) (aElementOf0 (xx) (xS)) (-. (aElementOf0 T_1 (xS))) (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) ### Equiv 30 32 % 29.30/29.48 34. (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) (-. (aElementOf0 T_1 (xS))) (aElementOf0 (xx) (xS)) ### All 33 % 29.30/29.48 35. (-. ((aElementOf0 T_1 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) => (aElementOf0 T_1 (xS)))) (aElementOf0 (xx) (xS)) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) ### NotImply 34 % 29.30/29.48 36. (-. (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) => (aElementOf0 W0 (xS))))) (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx)))))) (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx)))))) (aElementOf0 (xx) (xS)) ### NotAllEx 35 % 29.30/29.48 37. (-. (((aSet0 (sdtmndt0 (xS) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx))))))) => (((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx))))))) => ((All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) => (aElementOf0 W0 (xS)))) \/ (aSubsetOf0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)) (xS)))))) (aElementOf0 (xx) (xS)) ### ConjTree 36 % 29.30/29.48 38. (-. ((((aSet0 (sdtmndt0 (xS) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx))))))) => (((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx))))))) => ((All W0, ((aElementOf0 W0 (xS)) => (aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))) \/ (aSubsetOf0 (xS) (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))))) /\ (((aSet0 (sdtmndt0 (xS) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (xS)) /\ (W0 != (xx))))))) => (((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) /\ (All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) <=> ((aElement0 W0) /\ ((aElementOf0 W0 (sdtmndt0 (xS) (xx))) \/ (W0 = (xx))))))) => ((All W0, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))) => (aElementOf0 W0 (xS)))) \/ (aSubsetOf0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)) (xS))))))) (aElementOf0 (xx) (xS)) (aSet0 (xS)) (All W0, ((aSet0 W0) => (All W1, ((aElementOf0 W1 W0) => (aElement0 W1))))) ### NotAnd 21 37 % 29.30/29.48 % SZS output end Proof % 29.30/29.48 (* END-PROOF *) %------------------------------------------------------------------------------