%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET788+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:21 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET788+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.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 : Fri Jun 20 05:44:31 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(a_member_of_type, type, (
% 0.13/0.38 a_member_of: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_X_2_type, type, (
% 0.13/0.38 tptp_fun_X_2: $i)).
% 0.13/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.38 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38 tptp_fun_Y_1: $i)).
% 0.13/0.38 tff(equalish_type, type, (
% 0.13/0.38 equalish: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,assumption,(~equalish(Y!1, X!2)), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2))) <=> (~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ((~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))) <=> (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 ((~(![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X)))) <=> (~((~![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,axiom,(~(![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~((~![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.13/0.38 inference(or_elim,[status(thm)],[6])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.13/0.38 tff(11,plain,(
% 0.13/0.38 ~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2))),
% 0.13/0.38 inference(skolemize,[status(sab)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 ((equalish(X!2, Y!1) <=> equalish(Y!1, X!2)) | equalish(X!2, Y!1) | equalish(Y!1, X!2)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (equalish(X!2, Y!1) | equalish(Y!1, X!2)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (equalish(X!2, Y!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[14, 1])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : refl((~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : rewrite((~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) <=> (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))), trans(monotonicity(rewrite((~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))) <=> (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))), ((equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))), rewrite((equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))), ((equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))), ((((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))) <=> (((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))), rewrite((((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))), ((((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))) <=> (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[6])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : (((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~(equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~(equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~(equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))))) | ((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 15])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))) | (a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~equalish(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(equalish(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))))) | (~((~((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))) | (~(equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (~((~((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))) | (~(equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 28])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (((~((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))) | (~(equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))))) | (equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~(equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))))) | equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 1])).
% 0.13/0.39 tff(45,assumption,(a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.13/0.39 tff(46,assumption,(~a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.13/0.39 tff(47,assumption,(~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))), introduced(assumption)).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)) | a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) | a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[48, 46, 47])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ((~(a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (~a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)) | a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[50, 49, 46, 45])).
% 0.13/0.39 tff(52,plain,(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1))) | (a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 37, 44])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)) | (~a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)) | (~a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 53, 44])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~(a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1))) | a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2) | (~a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 55, 53, 37])).
% 0.13/0.39 tff(58,plain,(equalish(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (((~((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))) | (~(equalish(Y!1, X!2) | (~(a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1) <=> a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)))))) | ((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 39])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((~((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2)))) | (~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))) | (a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.13/0.40 tff(66,assumption,(~a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)), introduced(assumption)).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 ((equalish(X!2, Y!1) <=> equalish(Y!1, X!2)) | (~equalish(X!2, Y!1)) | (~equalish(Y!1, X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ((~equalish(X!2, Y!1)) | (~equalish(Y!1, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[67, 12])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (~equalish(X!2, Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 58])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~(equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))))) | (equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[70, 30])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~(equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1))))) | equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (equalish(X!2, Y!1) | (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (~(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[73, 69])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 ((a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)) | a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) | a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[75, 66, 74])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 ((~(a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2))) | (~a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)) | a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[77, 76, 66, 65])).
% 0.13/0.40 tff(79,plain,(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 ((a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)) | (~a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)) | (~a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (~a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[80, 79, 74])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 ((~(a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1) <=> a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2))) | a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1) | (~a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[82, 81, 79, 65])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------