TSTP Solution File: SYN966+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Fri Sep 30 00:01:25 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
% 0.11/0.12 % Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 09:47:47 EDT 2022
% 0.13/0.34 % 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(a_member_of_type, type, (
% 0.13/0.39 a_member_of: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_1_type, type, (
% 0.13/0.39 tptp_fun_B_1: $i)).
% 0.13/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.39 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_A_2_type, type, (
% 0.13/0.39 tptp_fun_A_2: $i)).
% 0.13/0.39 tff(eq_type, type, (
% 0.13/0.39 eq: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl((~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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(3,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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(5,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))), rewrite((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))), ((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))) <=> (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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(8,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(X, Y) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))) <=> (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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(10,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) <=> ![X: $i, Y: $i] : (eq(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(12,plain,
% 0.13/0.39 ((~(![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))) <=> (~((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,axiom,(~(![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) => ![A: $i, B: $i] : (eq(A, B) => eq(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~((~![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | ![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.39 tff(17,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y))) & (eq(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)],[17, 10])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[18, 8])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(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)],[19, 6])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) | (~((~((~eq(B!1, A!2)) | ![Z: $i] : (a_member_of(Z, B!1) <=> a_member_of(Z, A!2)))) | (~(eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~((~((~eq(B!1, A!2)) | ![Z: $i] : (a_member_of(Z, B!1) <=> a_member_of(Z, A!2)))) | (~(eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~((~eq(B!1, A!2)) | ![Z: $i] : (a_member_of(Z, B!1) <=> a_member_of(Z, A!2)))) | (~(eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))))) | (eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) <=> (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(or_elim,[status(thm)],[14])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.39 tff(33,plain,(
% 0.13/0.39 ~((~eq(A!2, B!1)) | eq(B!1, A!2))),
% 0.13/0.39 inference(skolemize,[status(sab)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (~eq(B!1, A!2)),
% 0.13/0.39 inference(or_elim,[status(thm)],[33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~(eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)))) | eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~(eq(B!1, A!2) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)))) | ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[36, 24])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))) | a_member_of(tptp_fun_Z_0(A!2, B!1), B!1) | a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (a_member_of(tptp_fun_Z_0(A!2, B!1), B!1) | a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (~((~((~eq(X, Y)) | ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))) | (~(eq(X, Y) | ((~a_member_of(tptp_fun_Z_0(Y, X), X)) <=> a_member_of(tptp_fun_Z_0(Y, X), Y))))))) | (~((~((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))) | (~(eq(A!2, B!1) | ((~a_member_of(tptp_fun_Z_0(B!1, A!2), A!2)) <=> a_member_of(tptp_fun_Z_0(B!1, A!2), B!1))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (~((~((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))) | (~(eq(A!2, B!1) | ((~a_member_of(tptp_fun_Z_0(B!1, A!2), A!2)) <=> a_member_of(tptp_fun_Z_0(B!1, A!2), B!1)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[41, 20])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (((~((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))) | (~(eq(A!2, B!1) | ((~a_member_of(tptp_fun_Z_0(B!1, A!2), A!2)) <=> a_member_of(tptp_fun_Z_0(B!1, A!2), B!1))))) | ((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 ((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (eq(A!2, B!1)),
% 0.13/0.40 inference(or_elim,[status(thm)],[33])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))) | (~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1)))) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ((~![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))) | (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~(a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)) | a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)) | a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 40, 1])).
% 0.13/0.40 tff(54,plain,(a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 37])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 54])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((~(a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))) | a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 50])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[59, 57, 54])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------