TSTP Solution File: NUM535+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% 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 *)
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