%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN966+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:41:05 AM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN966+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 13:02:03 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 tff(a_member_of_type, type, (
% 0.13/0.37 a_member_of: ( $i * $i ) > $o)).
% 0.13/0.37 tff(tptp_fun_B_1_type, type, (
% 0.13/0.37 tptp_fun_B_1: $i)).
% 0.13/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.37 tptp_fun_Z_0: ( $i * $i ) > $i)).
% 0.13/0.37 tff(tptp_fun_A_2_type, type, (
% 0.13/0.37 tptp_fun_A_2: $i)).
% 0.13/0.37 tff(eq_type, type, (
% 0.13/0.37 eq: ( $i * $i ) > $o)).
% 0.13/0.37 tff(1,assumption,(~a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)), introduced(assumption)).
% 0.13/0.37 tff(2,plain,
% 0.13/0.37 (^[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))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(3,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.37 tff(4,plain,
% 0.13/0.37 (^[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))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(5,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.37 tff(6,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.37 tff(7,plain,
% 0.13/0.37 (^[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)))), 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)))), ((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) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), Y)))))), rewrite((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) | (~(a_member_of(tptp_fun_Z_0(Y, X), X) <=> a_member_of(tptp_fun_Z_0(Y, X), 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) | (~(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))))))), 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)))))))))),
% 0.13/0.37 inference(bind,[status(th)],[])).
% 0.13/0.37 tff(8,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.13/0.37 tff(9,plain,
% 0.13/0.37 (![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)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(10,plain,
% 0.13/0.37 ((~(![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))))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(11,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/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.37 tff(12,plain,
% 0.13/0.37 (~((~![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)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.37 tff(13,plain,
% 0.13/0.37 (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.37 inference(or_elim,[status(thm)],[12])).
% 0.13/0.37 tff(14,plain,
% 0.13/0.37 (![X: $i, Y: $i] : (eq(X, Y) <=> ![Z: $i] : (a_member_of(Z, X) <=> a_member_of(Z, Y)))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.13/0.37 tff(15,plain,(
% 0.13/0.37 ![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)))))),
% 0.13/0.37 inference(skolemize,[status(sab)],[14])).
% 0.13/0.37 tff(16,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.13/0.37 tff(17,plain,
% 0.13/0.37 (![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)))))))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.13/0.37 tff(18,plain,
% 0.13/0.37 ((~![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)))))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(19,plain,
% 0.13/0.37 (~((~((~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))))))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.37 tff(20,plain,
% 0.13/0.37 (((~((~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))))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(21,plain,
% 0.13/0.37 (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)))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.37 tff(22,plain,
% 0.13/0.37 ((~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))) <=> (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A)))),
% 0.13/0.37 inference(rewrite,[status(thm)],[])).
% 0.13/0.37 tff(23,plain,
% 0.13/0.37 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.37 inference(or_elim,[status(thm)],[12])).
% 0.13/0.37 tff(24,plain,
% 0.13/0.37 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.37 tff(25,plain,
% 0.13/0.37 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.13/0.37 tff(26,plain,
% 0.13/0.37 (~![A: $i, B: $i] : ((~eq(A, B)) | eq(B, A))),
% 0.13/0.37 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.13/0.37 tff(27,plain,(
% 0.13/0.37 ~((~eq(A!2, B!1)) | eq(B!1, A!2))),
% 0.13/0.37 inference(skolemize,[status(sab)],[26])).
% 0.13/0.37 tff(28,plain,
% 0.13/0.37 (~eq(B!1, A!2)),
% 0.13/0.37 inference(or_elim,[status(thm)],[27])).
% 0.13/0.37 tff(29,plain,
% 0.13/0.37 ((~(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)))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(30,plain,
% 0.13/0.37 ((~(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)))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.37 tff(31,plain,
% 0.13/0.37 (~(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))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[30, 21])).
% 0.13/0.37 tff(32,plain,
% 0.13/0.37 ((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)),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(33,plain,
% 0.13/0.37 (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)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.37 tff(34,plain,
% 0.13/0.37 (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.13/0.37 tff(35,plain,
% 0.13/0.37 ((~![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)))))))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(36,plain,
% 0.13/0.37 (~((~((~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))))))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[35, 17])).
% 0.13/0.37 tff(37,plain,
% 0.13/0.37 (((~((~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)))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(38,plain,
% 0.13/0.37 ((~eq(A!2, B!1)) | ![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.13/0.37 tff(39,plain,
% 0.13/0.37 (eq(A!2, B!1)),
% 0.13/0.37 inference(or_elim,[status(thm)],[27])).
% 0.13/0.37 tff(40,plain,
% 0.13/0.37 ((~((~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))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(41,plain,
% 0.13/0.37 ((~((~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))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.37 tff(42,plain,
% 0.13/0.37 (![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.13/0.37 tff(43,plain,
% 0.13/0.37 ((~![Z: $i] : (a_member_of(Z, A!2) <=> a_member_of(Z, B!1))) | (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))),
% 0.13/0.37 inference(quant_inst,[status(thm)],[])).
% 0.13/0.37 tff(44,plain,
% 0.13/0.37 (a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.13/0.37 tff(45,plain,
% 0.13/0.37 ((~(a_member_of(tptp_fun_Z_0(A!2, B!1), A!2) <=> a_member_of(tptp_fun_Z_0(A!2, B!1), B!1))) | (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)) | a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(46,plain,
% 0.13/0.37 ((~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)) | a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.37 tff(47,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[46, 34, 1])).
% 0.13/0.37 tff(48,plain,(a_member_of(tptp_fun_Z_0(A!2, B!1), B!1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.37 tff(49,plain,
% 0.13/0.37 ((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))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(50,plain,
% 0.13/0.37 ((~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))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[49, 31])).
% 0.13/0.37 tff(51,plain,
% 0.13/0.37 (~a_member_of(tptp_fun_Z_0(A!2, B!1), A!2)),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[50, 48])).
% 0.13/0.37 tff(52,plain,
% 0.13/0.37 ((~(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))),
% 0.13/0.37 inference(tautology,[status(thm)],[])).
% 0.13/0.37 tff(53,plain,
% 0.13/0.37 (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))),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[52, 44])).
% 0.13/0.37 tff(54,plain,
% 0.13/0.37 ($false),
% 0.13/0.37 inference(unit_resolution,[status(thm)],[53, 51, 48])).
% 0.13/0.37 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------