TSTP Solution File: SET046+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET046+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Tue Sep 20 05:05:08 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET046+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 01:43:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(element_type, type, (
% 0.13/0.39 element: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.39 tptp_fun_Y_0: $i)).
% 0.13/0.39 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.39 tptp_fun_Z_1: $i > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[X: $i] : refl((~((~((~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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![X: $i] : (~((~((~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)))))))) <=> ![X: $i] : (~((~((~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))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[X: $i] : rewrite((~((~((~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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![X: $i] : (~((~((~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)))))))) <=> ![X: $i] : (~((~((~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))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![X: $i] : (~((~((~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)))))))) <=> ![X: $i] : (~((~((~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))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~element(X, Y!0)) | ![Z: $i] : (~(element(X, Z) & element(Z, X)))) <=> ((~element(X, Y!0)) | ![Z: $i] : ((~element(X, Z)) | (~element(Z, X))))), 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))))))), ((((~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)))))))), rewrite((((~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))))))))), ((((~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))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i] : (((~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)))) <=> ![X: $i] : (~((~((~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))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))) <=> ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))) <=> ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))) <=> (~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))) <=> (~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 ((~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))) <=> ?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[11, 9])).
% 0.13/0.40 tff(13,axiom,(~(~?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel42')).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (?[Y: $i] : ![X: $i] : (element(X, Y) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.13/0.40 tff(16,plain,(
% 0.13/0.40 $oeq(![X: $i] : (element(X, Y!0) <=> (~?[Z: $i] : (element(X, Z) & element(Z, X)))), ![X: $i] : (((~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)))))),
% 0.13/0.40 inference(transitivity,[status(sab)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![X: $i] : (~((~((~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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![X: $i] : (~((~((~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))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ((~![X: $i] : (~((~((~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(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))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (~((~((~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)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (((~((~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))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~element(Y!0, Y!0)) | ![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (((~((~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)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (element(Y!0, Y!0) | (~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![X: $i] : (~((~((~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(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)))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (~((~((~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))))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[25, 18])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (((~((~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)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 ((~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))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,assumption,(~((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))), introduced(assumption)).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (((~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)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (element(tptp_fun_Z_1(Y!0), Y!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~((~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))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~((~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))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[33, 28])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (((~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))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (element(Y!0, tptp_fun_Z_1(Y!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[35, 29])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | ((~element(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(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (((~element(tptp_fun_Z_1(Y!0), Y!0)) | (~element(Y!0, tptp_fun_Z_1(Y!0)))) <=> ((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (((~![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(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (((~![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(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ((~![Z: $i] : ((~element(tptp_fun_Z_1(Y!0), Z)) | (~element(Z, tptp_fun_Z_1(Y!0))))) | (~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[42, 36, 31, 34])).
% 0.13/0.40 tff(44,plain,((~element(Y!0, tptp_fun_Z_1(Y!0))) | (~element(tptp_fun_Z_1(Y!0), Y!0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~(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))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (element(Y!0, Y!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44, 24])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~((~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)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 46, 22])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (((~![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (((~element(Y!0, Y!0)) | (~element(Y!0, Y!0))) <=> (~element(Y!0, Y!0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (((~![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)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~![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)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | ((~element(Y!0, Y!0)) | (~element(Y!0, Y!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~![Z: $i] : ((~element(Y!0, Z)) | (~element(Z, Y!0)))) | (~element(Y!0, Y!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 46, 48])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------