%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET786+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : 300s
% DateTime : Sat Jun 21 05:26:20 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET786+1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 05:41:50 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(element_type, type, (
% 0.12/0.36 element: ( $i * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.12/0.36 tptp_fun_Z_1: $i > $i)).
% 0.12/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.36 tptp_fun_Y_0: $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i] : refl((~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))) <=> (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))) <=> ![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (^[X: $i] : rewrite((~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))) <=> (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))) <=> ![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))) <=> ![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X)) <=> (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))), ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) <=> (element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))))), rewrite((element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))) <=> (element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))), ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) <=> (element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))))), trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((element(X, Z) & element(Z, X)) <=> (~((~element(X, Z)) | (~element(Z, X))))), ((~(element(X, Z) & element(Z, X))) <=> (~(~((~element(X, Z)) | (~element(Z, X))))))), rewrite((~(~((~element(X, Z)) | (~element(Z, X))))) <=> ((~element(X, Z)) | (~element(Z, X)))), ((~(element(X, Z) & element(Z, X))) <=> ((~element(X, Z)) | (~element(Z, X)))))), (![Z: $i] : (~(element(X, Z) & element(Z, X))) <=> ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))), ((![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0))) <=> (![Z: $i] : ((~element(X, Z)) | (~element(Z, X))) | (~element(X, Y!0))))), rewrite((![Z: $i] : ((~element(X, Z)) | (~element(Z, X))) | (~element(X, Y!0))) <=> ((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))), ((![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0))) <=> ((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))), (((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))) <=> ((element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))) & ((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))))), rewrite(((element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X))))) & ((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))) <=> (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))), (((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))) <=> (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (![X: $i] : ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))) <=> ![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (^[X: $i] : rewrite((((element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X)) | element(X, Y!0)) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))) <=> ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (![X: $i] : (((element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X)) | element(X, Y!0)) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))) <=> ![X: $i] : ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y))) <=> ?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 ((~(~?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y))))) <=> ?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))) <=> (~?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))) <=> (~(~?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 ((~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))) <=> ?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))),
% 0.12/0.36 inference(transitivity,[status(thm)],[13, 11])).
% 0.12/0.36 tff(15,axiom,(~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm25')).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (?[Y: $i] : ![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.12/0.36 tff(18,plain,(
% 0.12/0.36 $oeq(![X: $i] : (~(?[Z: $i] : (element(X, Z) & element(Z, X)) <=> element(X, Y!0))), ![X: $i] : (((element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X)) | element(X, Y!0)) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0)))))),
% 0.12/0.37 inference(transitivity,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X: $i] : ((element(X, Y!0) | (element(X, tptp_fun_Z_1(X)) & element(tptp_fun_Z_1(X), X))) & (![Z: $i] : (~(element(X, Z) & element(Z, X))) | (~element(X, Y!0))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 9])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 7])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 5])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0)))))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~((~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))) | (~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))))) <=> (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0)))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))) | (~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))) | (~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))) | (~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0)))))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (~((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0))))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~(element(tptp_fun_Z_1(Y!0), Y!0) | (~((~element(tptp_fun_Z_1(Y!0), tptp_fun_Z_1(tptp_fun_Z_1(Y!0)))) | (~element(tptp_fun_Z_1(tptp_fun_Z_1(Y!0)), tptp_fun_Z_1(Y!0)))))))) | ((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.37 tff(31,assumption,(element(Y!0, Y!0)), introduced(assumption)).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~((~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))) | (~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))))) <=> (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))) | (~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))) | (~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))))))) <=> ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))) | (~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((~![X: $i] : (~((~(element(X, Y!0) | (~((~element(X, tptp_fun_Z_1(X))) | (~element(tptp_fun_Z_1(X), X)))))) | (~((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X)))))))) | (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (~((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 21])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))))) | ((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 ((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[42, 31])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0))) <=> ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~element(Y!0, Y!0)) | (~element(Y!0, Y!0))) <=> (~element(Y!0, Y!0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | ((~element(Y!0, Y!0)) | (~element(Y!0, Y!0)))) <=> ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | ((~element(Y!0, Y!0)) | (~element(Y!0, Y!0)))) <=> ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | ((~element(Y!0, Y!0)) | (~element(Y!0, Y!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 31, 43])).
% 0.12/0.38 tff(51,plain,(~element(Y!0, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (((~((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0))))) | (~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))))) | (element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[52, 38])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 ((~(element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))))) | element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 51])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))) | element(tptp_fun_Z_1(Y!0), Y!0)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (element(tptp_fun_Z_1(Y!0), Y!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 ((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | (~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((~((~element(tptp_fun_Z_1(Y!0), Y!0)) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0)))))) | ![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[60, 30])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))) | element(Y!0, tptp_fun_Z_1(Y!0))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (element(Y!0, tptp_fun_Z_1(Y!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | ((~element(tptp_fun_Z_1(Y!0), Y!0)) | (~element(Y!0, tptp_fun_Z_1(Y!0))))) <=> ((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | (~element(tptp_fun_Z_1(Y!0), Y!0)) | (~element(Y!0, tptp_fun_Z_1(Y!0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 ((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | ((~element(tptp_fun_Z_1(Y!0), Y!0)) | (~element(Y!0, tptp_fun_Z_1(Y!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 ((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | (~element(tptp_fun_Z_1(Y!0), Y!0)) | (~element(Y!0, tptp_fun_Z_1(Y!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[66, 63, 58, 61])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------