TSTP Solution File: SET758+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET758+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET758+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 08:09:07 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(member_type, type, (
% 0.22/0.43 member: ( $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_Y_39_type, type, (
% 0.22/0.43 tptp_fun_Y_39: $i)).
% 0.22/0.43 tff(tptp_fun_Y_26_type, type, (
% 0.22/0.43 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_F_42_type, type, (
% 0.22/0.43 tptp_fun_F_42: $i)).
% 0.22/0.43 tff(tptp_fun_X_24_type, type, (
% 0.22/0.43 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(inverse_image3_type, type, (
% 0.22/0.43 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_A_41_type, type, (
% 0.22/0.43 tptp_fun_A_41: $i)).
% 0.22/0.43 tff(tptp_fun_X_0_type, type, (
% 0.22/0.43 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.22/0.43 tff(image3_type, type, (
% 0.22/0.43 image3: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_B_40_type, type, (
% 0.22/0.43 tptp_fun_B_40: $i)).
% 0.22/0.43 tff(apply_type, type, (
% 0.22/0.43 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.43 tff(subset_type, type, (
% 0.22/0.43 subset: ( $i * $i ) > $o)).
% 0.22/0.43 tff(maps_type, type, (
% 0.22/0.43 maps: ( $i * $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.22/0.43 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_X_4_type, type, (
% 0.22/0.43 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Y2_5_type, type, (
% 0.22/0.43 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_Y1_6_type, type, (
% 0.22/0.43 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_X_7_type, type, (
% 0.22/0.43 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 (^[F: $i, B: $i, A: $i, X: $i] : refl((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.44 tff(6,plain,
% 0.22/0.44 (^[F: $i, B: $i, A: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) <=> ((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, X, Y)) <=> (~((~member(Y, B)) | (~apply(F, X, Y))))), ((~(member(Y, B) & apply(F, X, Y))) <=> (~(~((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, X, Y))))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))), ((~(member(Y, B) & apply(F, X, Y))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, X, Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), rewrite((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(7,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.44 tff(8,plain,
% 0.22/0.44 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))) <=> ![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(11,axiom,(![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image3')).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.44 tff(13,plain,(
% 0.22/0.44 ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[12])).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 (((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y)))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(20,plain,
% 0.22/0.45 ((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.45 tff(21,plain,
% 0.22/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(22,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.45 tff(23,plain,
% 0.22/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(24,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[24, 22])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(27,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.45 tff(28,plain,
% 0.22/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.45 tff(30,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(31,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image3')).
% 0.22/0.45 tff(32,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.45 tff(33,plain,(
% 0.22/0.45 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[32])).
% 0.22/0.45 tff(34,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(38,plain,
% 0.22/0.46 (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.22/0.46 tff(39,plain,
% 0.22/0.46 (((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(40,plain,
% 0.22/0.46 ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.22/0.46 tff(41,plain,
% 0.22/0.46 (^[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))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(42,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.46 tff(43,plain,
% 0.22/0.46 (^[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))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(44,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.46 tff(45,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[44, 42])).
% 0.22/0.46 tff(46,plain,
% 0.22/0.46 (^[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)))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(47,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.46 tff(48,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(49,plain,
% 0.22/0.46 (^[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))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(50,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[49])).
% 0.22/0.46 tff(51,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')).
% 0.22/0.46 tff(52,plain,
% 0.22/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.46 tff(53,plain,
% 0.22/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.46 tff(54,plain,(
% 0.22/0.46 ![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)))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[53])).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 (![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)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 (~((~((~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 (((~((~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))))) | (subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 (subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 ((~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 ((~![F: $i, A: $i, B: $i, Y: $i] : ((maps(F, A, B) & subset(Y, B)) => subset(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(63,axiom,(~![F: $i, A: $i, B: $i, Y: $i] : ((maps(F, A, B) & subset(Y, B)) => subset(image3(F, inverse_image3(F, Y, A), B), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa08')).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.22/0.46 tff(67,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.22/0.46 tff(68,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.22/0.46 tff(69,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.22/0.46 tff(70,plain,
% 0.22/0.46 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[69, 61])).
% 0.22/0.46 tff(71,plain,(
% 0.22/0.46 ~((~(maps(F!42, A!41, B!40) & subset(Y!39, B!40))) | subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.22/0.46 inference(skolemize,[status(sab)],[70])).
% 0.22/0.46 tff(72,plain,
% 0.22/0.46 (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)),
% 0.22/0.46 inference(or_elim,[status(thm)],[71])).
% 0.22/0.46 tff(73,plain,
% 0.22/0.46 ((~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))) | subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(74,plain,
% 0.22/0.46 ((~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.46 tff(75,plain,
% 0.22/0.46 (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.22/0.46 tff(76,plain,
% 0.22/0.47 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(77,plain,
% 0.22/0.47 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.22/0.47 tff(78,plain,
% 0.22/0.47 ((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(79,plain,
% 0.22/0.47 ((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.22/0.47 tff(80,plain,
% 0.22/0.47 (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[79, 40])).
% 0.22/0.47 tff(81,plain,
% 0.22/0.47 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(82,plain,
% 0.22/0.47 (member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.47 tff(83,plain,
% 0.22/0.47 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(84,plain,
% 0.22/0.47 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.47 tff(85,plain,
% 0.22/0.47 (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[84, 20])).
% 0.22/0.47 tff(86,plain,
% 0.22/0.47 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(87,plain,
% 0.22/0.47 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.22/0.47 tff(88,plain,
% 0.22/0.47 ((~![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(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40)))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(89,plain,
% 0.22/0.47 (~((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[88, 56])).
% 0.22/0.47 tff(90,plain,
% 0.22/0.47 (((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40)))))) | ((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(91,plain,
% 0.22/0.47 ((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.22/0.47 tff(92,plain,
% 0.22/0.47 (maps(F!42, A!41, B!40) & subset(Y!39, B!40)),
% 0.22/0.47 inference(or_elim,[status(thm)],[71])).
% 0.22/0.47 tff(93,plain,
% 0.22/0.47 (subset(Y!39, B!40)),
% 0.22/0.47 inference(and_elim,[status(thm)],[92])).
% 0.22/0.47 tff(94,plain,
% 0.22/0.47 ((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(95,plain,
% 0.22/0.47 ((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.22/0.47 tff(96,plain,
% 0.22/0.47 (![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.22/0.47 tff(97,plain,
% 0.22/0.47 (((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(98,plain,
% 0.22/0.48 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(99,plain,
% 0.22/0.48 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.22/0.48 tff(100,plain,
% 0.22/0.48 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[99, 96, 87])).
% 0.22/0.48 tff(101,plain,
% 0.22/0.48 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(102,plain,
% 0.22/0.48 (apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[101, 85])).
% 0.22/0.48 tff(103,plain,
% 0.22/0.48 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(104,plain,
% 0.22/0.48 (member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[103, 85])).
% 0.22/0.48 tff(105,plain,
% 0.22/0.48 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(106,plain,
% 0.22/0.48 (apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[105, 80])).
% 0.22/0.48 tff(107,plain,
% 0.22/0.48 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(108,plain,
% 0.22/0.48 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[107, 80])).
% 0.22/0.48 tff(109,plain,
% 0.22/0.48 (^[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)))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(110,plain,
% 0.22/0.48 (![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))))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.22/0.48 tff(111,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(112,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[111])).
% 0.22/0.48 tff(113,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(114,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[113])).
% 0.22/0.48 tff(115,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[114, 112])).
% 0.22/0.48 tff(116,plain,
% 0.22/0.48 (^[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))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(117,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.48 tff(118,plain,
% 0.22/0.48 (^[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)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(119,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[118])).
% 0.22/0.48 tff(120,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(121,plain,
% 0.22/0.48 (^[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)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(122,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[121])).
% 0.22/0.48 tff(123,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')).
% 0.22/0.48 tff(124,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.48 tff(125,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.22/0.48 tff(126,plain,(
% 0.22/0.48 ![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))))))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[125])).
% 0.22/0.48 tff(127,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.22/0.48 tff(128,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.22/0.48 tff(129,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[128, 115])).
% 0.22/0.48 tff(130,plain,
% 0.22/0.48 (![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))))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[129, 110])).
% 0.22/0.49 tff(131,plain,
% 0.22/0.49 ((~![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))))))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(132,plain,
% 0.22/0.49 (~((~((~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)))))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.22/0.49 tff(133,plain,
% 0.22/0.49 (((~((~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)))))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(134,plain,
% 0.22/0.49 ((~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))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.22/0.49 tff(135,plain,
% 0.22/0.49 (maps(F!42, A!41, B!40)),
% 0.22/0.49 inference(and_elim,[status(thm)],[92])).
% 0.22/0.49 tff(136,plain,
% 0.22/0.49 ((~((~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))))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(137,plain,
% 0.22/0.49 ((~((~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))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.22/0.49 tff(138,plain,
% 0.22/0.49 (~((~![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)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.22/0.49 tff(139,plain,
% 0.22/0.49 (((~![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, 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)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(140,plain,
% 0.22/0.49 (![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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.22/0.49 tff(141,plain,
% 0.22/0.49 (((~![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)))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))) <=> ((~![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)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(142,plain,
% 0.22/0.49 (((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40))) <=> ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(143,plain,
% 0.22/0.50 (((~![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)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))) <=> ((~![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)))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[142])).
% 0.22/0.50 tff(144,plain,
% 0.22/0.50 (((~![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)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))) <=> ((~![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)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[143, 141])).
% 0.22/0.50 tff(145,plain,
% 0.22/0.50 ((~![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)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(146,plain,
% 0.22/0.50 ((~![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)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.22/0.50 tff(147,plain,
% 0.22/0.50 ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[146, 140, 108, 106, 104, 102])).
% 0.22/0.50 tff(148,plain,
% 0.22/0.50 (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[147, 100])).
% 0.22/0.50 tff(149,plain,
% 0.22/0.50 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39) <=> member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[148])).
% 0.22/0.50 tff(150,plain,
% 0.22/0.50 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39) <=> member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.22/0.50 inference(symmetry,[status(thm)],[149])).
% 0.22/0.50 tff(151,plain,
% 0.22/0.50 ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) <=> (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[150])).
% 0.22/0.50 tff(152,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(153,plain,
% 0.22/0.50 (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[152, 75])).
% 0.22/0.50 tff(154,plain,
% 0.22/0.50 (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.22/0.50 tff(155,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[87, 154])).
% 0.22/0.50 % SZS output end Proof
%------------------------------------------------------------------------------