TSTP Solution File: SET788+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 05:08:01 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.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 07:59:03 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.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(a_member_of_type, type, (
% 0.21/0.40 a_member_of: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_X_2_type, type, (
% 0.21/0.40 tptp_fun_X_2: $i)).
% 0.21/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.40 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.40 tptp_fun_Y_1: $i)).
% 0.21/0.40 tff(equalish_type, type, (
% 0.21/0.40 equalish: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,assumption,(~equalish(Y!1, X!2)), introduced(assumption)).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 ((~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2))) <=> ((~equalish(X!2, Y!1)) <=> equalish(Y!1, X!2))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))) <=> (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 ((~(![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 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/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (~((~![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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(or_elim,[status(thm)],[6])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (~![X: $i, Y: $i] : (equalish(X, Y) <=> equalish(Y, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.21/0.40 tff(14,plain,(
% 0.21/0.40 ~(equalish(X!2, Y!1) <=> equalish(Y!1, X!2))),
% 0.21/0.40 inference(skolemize,[status(sab)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~equalish(X!2, Y!1)) <=> equalish(Y!1, X!2)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (equalish(X!2, Y!1) | equalish(Y!1, X!2) | (~((~equalish(X!2, Y!1)) <=> equalish(Y!1, X!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (equalish(X!2, Y!1) | equalish(Y!1, X!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (equalish(X!2, Y!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (^[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)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (^[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)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[22, 20])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (^[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)))), ((((~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))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.21/0.40 inference(or_elim,[status(thm)],[6])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (equalish(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40 tff(31,plain,(
% 0.21/0.40 ![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)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![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))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~![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))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (~((~((~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)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (((~((~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)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1)))) | (~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((~equalish(X!2, Y!1)) | ![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (![Z: $i] : (a_member_of(Z, X!2) <=> a_member_of(Z, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 18])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((~![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))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 ((~![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))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (~((~((~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)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[44, 34])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (((~((~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)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (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))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 ((~(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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (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))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ((~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)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[49, 1])).
% 0.21/0.40 tff(51,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)).
% 0.21/0.40 tff(52,assumption,(~a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)), introduced(assumption)).
% 0.21/0.40 tff(53,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)).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~((~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)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[54, 52, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ((~(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)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[56, 55, 52, 51])).
% 0.21/0.40 tff(58,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,[]))).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (a_member_of(tptp_fun_Z_0(X!2, Y!1), Y!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[58, 43, 50])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 ((~((~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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (~a_member_of(tptp_fun_Z_0(X!2, Y!1), X!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 59, 50])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 ((~(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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[62, 61, 59, 43])).
% 0.21/0.40 tff(64,plain,(equalish(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (((~((~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)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 45])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~((~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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~equalish(Y!1, X!2)) | ![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![Z: $i] : (a_member_of(Z, Y!1) <=> a_member_of(Z, X!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 64])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.41 tff(72,assumption,(~a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)), introduced(assumption)).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~equalish(X!2, Y!1)) | (~equalish(Y!1, X!2)) | (~((~equalish(X!2, Y!1)) <=> equalish(Y!1, X!2)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 ((~equalish(X!2, Y!1)) | (~equalish(Y!1, X!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[73, 15])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (~equalish(X!2, Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[74, 64])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (((~((~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)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (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))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 36])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ((~(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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (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))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((~((~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)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[81, 72, 80])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~(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)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 82, 72, 71])).
% 0.21/0.41 tff(85,plain,(a_member_of(tptp_fun_Z_0(Y!1, X!2), X!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~((~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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (~a_member_of(tptp_fun_Z_0(Y!1, X!2), Y!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[86, 85, 80])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~(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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[88, 87, 85, 71])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------