TSTP Solution File: SET754+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET754+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 05:07:52 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET754+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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 : Sat Sep 3 07:41:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(apply_type, type, (
% 0.19/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.41 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_F_42_type, type, (
% 0.19/0.41 tptp_fun_F_42: $i)).
% 0.19/0.41 tff(tptp_fun_B_40_type, type, (
% 0.19/0.41 tptp_fun_B_40: $i)).
% 0.19/0.41 tff(tptp_fun_X_0_type, type, (
% 0.19/0.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_C_39_type, type, (
% 0.19/0.41 tptp_fun_C_39: $i)).
% 0.19/0.41 tff(inverse_image2_type, type, (
% 0.19/0.41 inverse_image2: ( $i * $i ) > $i)).
% 0.19/0.41 tff(image2_type, type, (
% 0.19/0.41 image2: ( $i * $i ) > $i)).
% 0.19/0.41 tff(member_type, type, (
% 0.19/0.41 member: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X_23_type, type, (
% 0.19/0.41 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_A_41_type, type, (
% 0.19/0.41 tptp_fun_A_41: $i)).
% 0.19/0.41 tff(subset_type, type, (
% 0.19/0.41 subset: ( $i * $i ) > $o)).
% 0.19/0.41 tff(maps_type, type, (
% 0.19/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X_4_type, type, (
% 0.19/0.41 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.41 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.41 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X_7_type, type, (
% 0.19/0.41 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y_25_type, type, (
% 0.19/0.41 tptp_fun_Y_25: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : refl((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : rewrite((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[F: $i, A: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) <=> ((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))), rewrite((member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y))) <=> ![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,axiom,(![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image2')).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,(
% 0.19/0.41 ![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), C!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), C!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), C!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), C!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))) | (member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (^[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)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.42 tff(28,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.42 tff(31,plain,(
% 0.19/0.42 ![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)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[30])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~![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(C!39, inverse_image2(F!42, image2(F!42, C!39)))) | ![X: $i] : ((~member(X, C!39)) | member(X, inverse_image2(F!42, image2(F!42, C!39)))))) | (~(subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (~((~((~subset(C!39, inverse_image2(F!42, image2(F!42, C!39)))) | ![X: $i] : ((~member(X, C!39)) | member(X, inverse_image2(F!42, image2(F!42, C!39)))))) | (~(subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (((~((~subset(C!39, inverse_image2(F!42, image2(F!42, C!39)))) | ![X: $i] : ((~member(X, C!39)) | member(X, inverse_image2(F!42, image2(F!42, C!39)))))) | (~(subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))))))) | (subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 ((~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))) <=> (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 ((~![F: $i, A: $i, B: $i, C: $i] : ((maps(F, A, B) & subset(C, A)) => subset(C, inverse_image2(F, image2(F, C))))) <=> (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(40,axiom,(~![F: $i, A: $i, B: $i, C: $i] : ((maps(F, A, B) & subset(C, A)) => subset(C, inverse_image2(F, image2(F, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa04')).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (~![F: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & subset(C, A))) | subset(C, inverse_image2(F, image2(F, C))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.19/0.42 tff(48,plain,(
% 0.19/0.42 ~((~(maps(F!42, A!41, B!40) & subset(C!39, A!41))) | subset(C!39, inverse_image2(F!42, image2(F!42, C!39))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (~subset(C!39, inverse_image2(F!42, image2(F!42, C!39)))),
% 0.19/0.42 inference(or_elim,[status(thm)],[48])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~(subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))))) | subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~(subset(C!39, inverse_image2(F!42, image2(F!42, C!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[51, 37])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![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(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))) | (~(subset(C!39, A!41) | (~((~member(tptp_fun_X_0(A!41, C!39), C!39)) | member(tptp_fun_X_0(A!41, C!39), A!41)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (~((~((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))) | (~(subset(C!39, A!41) | (~((~member(tptp_fun_X_0(A!41, C!39), C!39)) | member(tptp_fun_X_0(A!41, C!39), A!41))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 33])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))) | (~(subset(C!39, A!41) | (~((~member(tptp_fun_X_0(A!41, C!39), C!39)) | member(tptp_fun_X_0(A!41, C!39), A!41)))))) | ((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (maps(F!42, A!41, B!40) & subset(C!39, A!41)),
% 0.19/0.42 inference(or_elim,[status(thm)],[48])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (subset(C!39, A!41)),
% 0.19/0.42 inference(and_elim,[status(thm)],[59])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 ((~((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))) | (~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~((~subset(C!39, A!41)) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41)))) | ![X: $i] : ((~member(X, C!39)) | member(X, A!41))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![X: $i] : ((~member(X, C!39)) | member(X, A!41))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (((~![X: $i] : ((~member(X, C!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41))) <=> ((~![X: $i] : ((~member(X, C!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, C!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 ((~![X: $i] : ((~member(X, C!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[66, 63, 54])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))), rewrite((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.44 tff(82,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.44 tff(85,plain,(
% 0.19/0.44 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[84])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[88, 69])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (maps(F!42, A!41, B!40)),
% 0.19/0.45 inference(and_elim,[status(thm)],[59])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[102, 99, 67])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))) | apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (^[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))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (^[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))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (^[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)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(114,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/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image2')).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.45 tff(116,plain,(
% 0.19/0.45 ![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)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[115])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 ((~![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!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (~((~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (((~((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), image2(F!42, C!39), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))))) | (member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[123, 52])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y))))) | member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 ((~(member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), inverse_image2(F!42, image2(F!42, C!39))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y))))) | ![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (((~![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) <=> ((~![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 ((~![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 ((~![Y: $i] : ((~member(Y, image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[130, 127, 105])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))))) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 ((~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42), image2(F!42, C!39)) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))))) | ![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[133, 17])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (((~![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) <=> ((~![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((~![X: $i] : ((~member(X, C!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), C!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image2(F!42, image2(F!42, C!39)), C!39), B!40, F!42)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[137, 54, 105, 134])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------