TSTP Solution File: SET755+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 05:07:53 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:54:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_39_type, type, (
% 0.20/0.41 tptp_fun_Y_39: $i)).
% 0.20/0.41 tff(tptp_fun_Y_25_type, type, (
% 0.20/0.41 tptp_fun_Y_25: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_F_43_type, type, (
% 0.20/0.41 tptp_fun_F_43: $i)).
% 0.20/0.41 tff(tptp_fun_X_40_type, type, (
% 0.20/0.41 tptp_fun_X_40: $i)).
% 0.20/0.41 tff(tptp_fun_X_0_type, type, (
% 0.20/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(inverse_image2_type, type, (
% 0.20/0.41 inverse_image2: ( $i * $i ) > $i)).
% 0.20/0.41 tff(apply_type, type, (
% 0.20/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(subset_type, type, (
% 0.20/0.41 subset: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_B_41_type, type, (
% 0.20/0.41 tptp_fun_B_41: $i)).
% 0.20/0.41 tff(maps_type, type, (
% 0.20/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_A_42_type, type, (
% 0.20/0.41 tptp_fun_A_42: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[F: $i, B: $i, X: $i] : refl((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (^[F: $i, B: $i, X: $i] : rewrite((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[F: $i, B: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) <=> ((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))), rewrite((member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) <=> ![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(9,axiom,(![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_image2')).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.42 tff(11,plain,(
% 0.20/0.42 ![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))))) | ((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 ((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.42 tff(28,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.42 tff(31,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | ![X: $i] : ((~member(X, inverse_image2(F!43, X!40))) | member(X, inverse_image2(F!43, Y!39))))) | (~(subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~((~((~subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | ![X: $i] : ((~member(X, inverse_image2(F!43, X!40))) | member(X, inverse_image2(F!43, Y!39))))) | (~(subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~((~subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | ![X: $i] : ((~member(X, inverse_image2(F!43, X!40))) | member(X, inverse_image2(F!43, Y!39))))) | (~(subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))))))) | (subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & subset(X, B)) & subset(Y, B)) & subset(X, Y)) => subset(inverse_image2(F, X), inverse_image2(F, Y)))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & subset(X, B)) & subset(Y, B)) & subset(X, Y)) => subset(inverse_image2(F, X), inverse_image2(F, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa05')).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B) & subset(X, Y))) | subset(inverse_image2(F, X), inverse_image2(F, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.20/0.43 tff(48,plain,(
% 0.20/0.43 ~((~(maps(F!43, A!42, B!41) & subset(X!40, B!41) & subset(Y!39, B!41) & subset(X!40, Y!39))) | subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[47])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (~subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))),
% 0.20/0.43 inference(or_elim,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((~(subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))))) | subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~(subset(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 37])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))) | (~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[56, 17])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))) | apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 13])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))))) | (member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (((~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, X!40))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))) | (~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (~member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 52])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y))))) | member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y))))) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[67, 63])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))) <=> ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 68, 59])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43)))) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 57])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (~((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[75, 33])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39)))))) | ((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (maps(F!43, A!42, B!41) & subset(X!40, B!41) & subset(Y!39, B!41) & subset(X!40, Y!39)),
% 0.20/0.44 inference(or_elim,[status(thm)],[48])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (subset(X!40, Y!39)),
% 0.20/0.44 inference(and_elim,[status(thm)],[79])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 ((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 ((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[82, 78])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39))) <=> ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, Y!39), inverse_image2(F!43, X!40)), X!40, F!43), Y!39)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 83, 74, 72])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------