%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET047+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:24:59 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET047+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:08:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(element_type, type, (
% 0.11/0.36 element: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: $i)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.36 tptp_fun_Y_1: $i)).
% 0.11/0.36 tff(set_equal_type, type, (
% 0.11/0.36 set_equal: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,assumption,(~set_equal(Y!1, X!2)), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2))) <=> (~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))) <=> (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel43')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![X: $i, Y: $i] : (set_equal(X, Y) <=> set_equal(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,(
% 0.11/0.36 ~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2))),
% 0.11/0.36 inference(skolemize,[status(sab)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~(set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 ((set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2)) | set_equal(X!2, Y!1) | set_equal(Y!1, X!2)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (set_equal(X!2, Y!1) | set_equal(Y!1, X!2)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (set_equal(X!2, Y!1)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : refl((~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : rewrite((~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[17, 15])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) <=> ((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))), trans(monotonicity(rewrite((~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))) <=> (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))), ((set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))), rewrite((set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))), ((set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))) <=> (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))), ((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))))), rewrite((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))), ((((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y))) <=> ![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(22,axiom,(![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel43_1')).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (set_equal(X, Y) <=> ![Z: $i] : (element(Z, X) <=> element(Z, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.36 tff(24,plain,(
% 0.11/0.36 ![X: $i, Y: $i] : (((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y))) & (set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[23])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (~((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))))) | ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 ((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 ((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[32, 13])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 ((~![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1))) | (element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (~((~((~set_equal(X, Y)) | ![Z: $i] : (element(Z, X) <=> element(Z, Y)))) | (~(set_equal(X, Y) | (~(element(tptp_fun_Z_0(Y, X), X) <=> element(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (~((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[36, 26])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))))) | (set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 ((~(set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))))) | set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.11/0.36 tff(43,assumption,(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.11/0.36 tff(44,assumption,(~element(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.11/0.36 tff(45,assumption,(~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))), introduced(assumption)).
% 0.18/0.36 tff(46,plain,
% 0.18/0.36 ((element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)) | element(tptp_fun_Z_0(X!2, Y!1), Y!1) | element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(47,plain,
% 0.18/0.36 (element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[46, 44, 45])).
% 0.18/0.36 tff(48,plain,
% 0.18/0.36 ((~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (~element(tptp_fun_Z_0(X!2, Y!1), X!2)) | element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(49,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[48, 47, 44, 43])).
% 0.18/0.36 tff(50,plain,(element(tptp_fun_Z_0(X!2, Y!1), Y!1) | (~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.36 tff(51,plain,
% 0.18/0.36 (element(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[50, 35, 42])).
% 0.18/0.36 tff(52,plain,
% 0.18/0.36 ((element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)) | (~element(tptp_fun_Z_0(X!2, Y!1), Y!1)) | (~element(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(53,plain,
% 0.18/0.36 (~element(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[52, 51, 42])).
% 0.18/0.36 tff(54,plain,
% 0.18/0.36 ((~(element(tptp_fun_Z_0(X!2, Y!1), X!2) <=> element(tptp_fun_Z_0(X!2, Y!1), Y!1))) | element(tptp_fun_Z_0(X!2, Y!1), X!2) | (~element(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(55,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[54, 53, 51, 35])).
% 0.18/0.36 tff(56,plain,(set_equal(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.36 tff(57,plain,
% 0.18/0.36 (((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~(set_equal(Y!1, X!2) | (~(element(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> element(tptp_fun_Z_0(X!2, Y!1), X!2)))))) | ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(58,plain,
% 0.18/0.36 ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[57, 37])).
% 0.18/0.36 tff(59,plain,
% 0.18/0.36 ((~((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2)))) | (~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(60,plain,
% 0.18/0.36 ((~set_equal(Y!1, X!2)) | ![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.36 tff(61,plain,
% 0.18/0.36 (![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.18/0.36 tff(62,plain,
% 0.18/0.36 ((~![Z: $i] : (element(Z, Y!1) <=> element(Z, X!2))) | (element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(63,plain,
% 0.18/0.36 (element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.36 tff(64,assumption,(~element(tptp_fun_Z_0(Y!1, X!2), X!2)), introduced(assumption)).
% 0.18/0.36 tff(65,plain,
% 0.18/0.36 ((set_equal(X!2, Y!1) <=> set_equal(Y!1, X!2)) | (~set_equal(X!2, Y!1)) | (~set_equal(Y!1, X!2))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(66,plain,
% 0.18/0.36 ((~set_equal(X!2, Y!1)) | (~set_equal(Y!1, X!2))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[65, 10])).
% 0.18/0.36 tff(67,plain,
% 0.18/0.36 (~set_equal(X!2, Y!1)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[66, 56])).
% 0.18/0.36 tff(68,plain,
% 0.18/0.36 (((~((~set_equal(X!2, Y!1)) | ![Z: $i] : (element(Z, X!2) <=> element(Z, Y!1)))) | (~(set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))))) | (set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(69,plain,
% 0.18/0.36 (set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[68, 28])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 ((~(set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))))) | set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (set_equal(X!2, Y!1) | (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (~(element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[71, 67])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 ((element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)) | element(tptp_fun_Z_0(Y!1, X!2), X!2) | element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 (element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[73, 64, 72])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 ((~(element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))) | (~element(tptp_fun_Z_0(Y!1, X!2), Y!1)) | element(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[75, 74, 64, 63])).
% 0.18/0.37 tff(77,plain,(element(tptp_fun_Z_0(Y!1, X!2), X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 ((element(tptp_fun_Z_0(Y!1, X!2), X!2) <=> element(tptp_fun_Z_0(Y!1, X!2), Y!1)) | (~element(tptp_fun_Z_0(Y!1, X!2), X!2)) | (~element(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(79,plain,
% 0.18/0.37 (~element(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[78, 77, 72])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 ((~(element(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> element(tptp_fun_Z_0(Y!1, X!2), X!2))) | element(tptp_fun_Z_0(Y!1, X!2), Y!1) | (~element(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(81,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[80, 79, 77, 63])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------