TSTP Solution File: SET760+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET760+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:07:54 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET760+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:49:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(apply_type, type, (
% 0.19/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_E_19_type, type, (
% 0.19/0.42 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_F_42_type, type, (
% 0.19/0.42 tptp_fun_F_42: $i)).
% 0.19/0.42 tff(tptp_fun_A_41_type, type, (
% 0.19/0.42 tptp_fun_A_41: $i)).
% 0.19/0.42 tff(tptp_fun_X_0_type, type, (
% 0.19/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_39_type, type, (
% 0.19/0.42 tptp_fun_Y_39: $i)).
% 0.19/0.42 tff(image3_type, type, (
% 0.19/0.42 image3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_B_40_type, type, (
% 0.19/0.42 tptp_fun_B_40: $i)).
% 0.19/0.42 tff(inverse_image3_type, type, (
% 0.19/0.42 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(member_type, type, (
% 0.19/0.42 member: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Y_26_type, type, (
% 0.19/0.42 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(subset_type, type, (
% 0.19/0.42 subset: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_X_24_type, type, (
% 0.19/0.42 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(surjective_type, type, (
% 0.19/0.42 surjective: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(maps_type, type, (
% 0.19/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(equal_set_type, type, (
% 0.19/0.42 equal_set: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_4_type, type, (
% 0.19/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_7_type, type, (
% 0.19/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_20_type, type, (
% 0.19/0.42 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[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))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (^[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))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 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')).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.43 tff(13,plain,(
% 0.19/0.43 ![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))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[12])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (((~![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)))))))) | (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), 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)))))))) | (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~(member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))))) <=> (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (((~![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_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~(member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), 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)))))))) | (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (((~![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_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~(member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), 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)))))))) | (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 ((~![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_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~(member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 ((~![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_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (~((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_Y_26(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 ((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.46 tff(36,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.46 tff(39,plain,(
% 0.19/0.46 ![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)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[38])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 ((~![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(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | ![X: $i] : ((~member(X, Y!39)) | member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~(subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (~((~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | ![X: $i] : ((~member(X, Y!39)) | member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~(subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (((~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | ![X: $i] : ((~member(X, Y!39)) | member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~(subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))) | (subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.46 tff(46,assumption,((~((~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)))))), introduced(assumption)).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 ((~![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: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[47, 41, 46])).
% 0.19/0.46 tff(49,plain,(~((~((~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))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 (((~((~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))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (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)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 ((~![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)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (~((~((~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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[52, 16])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (((~((~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))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (^[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))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (^[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))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(66,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')).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.47 tff(68,plain,(
% 0.19/0.47 ![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))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[67])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 ((~![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)))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (~((~((~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)) | ![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))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (((~((~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)) | ![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)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 ((~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))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.47 tff(76,assumption,(~((~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))), introduced(assumption)).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (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))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 ((~((~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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~((~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))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (~((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (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), inverse_image3(F!42, Y!39, A!41))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 ((~((~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), 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)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 ((~((~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), 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)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (~((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[85, 55])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (((~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_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)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (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), Y!39)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 ((~![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)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (~((~((~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))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[89, 41])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (((~((~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)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 ((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : (((maps(F, A, B) & surjective(F, A, B)) & subset(Y, B)) => equal_set(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(95,axiom,(~![F: $i, A: $i, B: $i, Y: $i] : (((maps(F, A, B) & surjective(F, A, B)) & subset(Y, B)) => equal_set(image3(F, inverse_image3(F, Y, A), B), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa10')).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[99, 93])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & surjective(F, A, B) & subset(Y, B))) | equal_set(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[101, 93])).
% 0.19/0.48 tff(103,plain,(
% 0.19/0.48 ~((~(maps(F!42, A!41, B!40) & surjective(F!42, A!41, B!40) & subset(Y!39, B!40))) | equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.48 inference(skolemize,[status(sab)],[102])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (maps(F!42, A!41, B!40) & surjective(F!42, A!41, B!40) & subset(Y!39, B!40)),
% 0.19/0.48 inference(or_elim,[status(thm)],[103])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (subset(Y!39, B!40)),
% 0.19/0.48 inference(and_elim,[status(thm)],[104])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 ((~((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 ((~((~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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[107, 92])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![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))) <=> ((~![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))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![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)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (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)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[111, 108, 88])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (((~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))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (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))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[113, 86])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (((~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)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (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)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[115, 86])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (((~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)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (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)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[117, 81])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (((~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)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[119, 81])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))), rewrite((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (![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)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (![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) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.49 tff(135,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.49 tff(138,plain,(
% 0.19/0.49 ![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) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[137])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (![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))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[140, 127])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (![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))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[141, 122])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 ((~![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))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (maps(F!42, A!41, B!40)),
% 0.19/0.50 inference(and_elim,[status(thm)],[104])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 (((~![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)))) <=> ((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 (((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))) | (~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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.51 tff(156,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[155, 153])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(158,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 ((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))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[158, 152, 120, 118, 116, 114])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 (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))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[159, 112])).
% 0.19/0.51 tff(161,plain,
% 0.19/0.51 (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)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.51 tff(162,plain,
% 0.19/0.51 (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)),
% 0.19/0.51 inference(symmetry,[status(thm)],[161])).
% 0.19/0.51 tff(163,plain,
% 0.19/0.51 ((~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))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.51 tff(164,plain,
% 0.19/0.51 (((~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))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(165,plain,
% 0.19/0.51 (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[164, 76])).
% 0.19/0.51 tff(166,plain,
% 0.19/0.51 (~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)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[165, 163])).
% 0.19/0.51 tff(167,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[88, 166])).
% 0.19/0.51 tff(168,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 ((~(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)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(170,plain,
% 0.19/0.51 ((~(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)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.51 tff(171,plain,
% 0.19/0.51 (subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[170, 51])).
% 0.19/0.51 tff(172,plain,
% 0.19/0.51 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(173,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[174])).
% 0.19/0.51 tff(176,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(177,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.51 tff(178,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.51 tff(179,plain,(
% 0.19/0.51 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[178])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 ((equal_set(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)) | (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))) <=> (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(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)) | (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[183])).
% 0.19/0.51 tff(185,plain,
% 0.19/0.51 (((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(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)) | (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))) <=> ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[184, 182])).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(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)) | (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[187, 181])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 (~equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)),
% 0.19/0.52 inference(or_elim,[status(thm)],[103])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 ((~(equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))) | equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | ((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 ((~(equal_set(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) <=> (~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))) | ((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.19/0.52 tff(192,plain,
% 0.19/0.52 ((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.19/0.52 tff(193,plain,
% 0.19/0.52 ((~((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))) | (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(194,plain,
% 0.19/0.52 ((~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.52 tff(195,plain,
% 0.19/0.52 (~subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[194, 171])).
% 0.19/0.52 tff(196,plain,
% 0.19/0.52 ((~(subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))) | subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(197,plain,
% 0.19/0.52 ((~(subset(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.52 tff(198,plain,
% 0.19/0.52 (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[197, 45])).
% 0.19/0.52 tff(199,plain,
% 0.19/0.52 (((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(200,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.19/0.52 tff(201,plain,
% 0.19/0.52 (((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(202,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(203,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.52 tff(204,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[203, 108, 200])).
% 0.19/0.52 tff(205,plain,
% 0.19/0.52 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(206,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.52 tff(207,plain,
% 0.19/0.52 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(208,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.52 tff(209,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[208, 206])).
% 0.19/0.52 tff(210,plain,
% 0.19/0.52 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(211,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 (^[F: $i, A: $i, B: $i] : rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(213,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.52 tff(214,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(215,plain,
% 0.19/0.52 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(216,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[215])).
% 0.19/0.52 tff(217,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.19/0.52 tff(218,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.52 tff(219,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.19/0.52 tff(220,plain,(
% 0.19/0.52 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[219])).
% 0.19/0.52 tff(221,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.19/0.52 tff(222,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[221, 211])).
% 0.19/0.52 tff(223,plain,
% 0.19/0.52 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[222, 209])).
% 0.19/0.52 tff(224,plain,
% 0.19/0.52 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))) | (~(surjective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!42), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!42, E, tptp_fun_Y_20(B!40, A!41, F!42)))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(225,plain,
% 0.19/0.52 (~((~((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))) | (~(surjective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!42), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!42, E, tptp_fun_Y_20(B!40, A!41, F!42))))))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.19/0.53 tff(226,plain,
% 0.19/0.53 (((~((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))) | (~(surjective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!42), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!42, E, tptp_fun_Y_20(B!40, A!41, F!42)))))))))) | ((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(227,plain,
% 0.19/0.53 ((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.19/0.53 tff(228,plain,
% 0.19/0.53 (surjective(F!42, A!41, B!40)),
% 0.19/0.53 inference(and_elim,[status(thm)],[104])).
% 0.19/0.53 tff(229,plain,
% 0.19/0.53 ((~((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))) | (~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(230,plain,
% 0.19/0.53 ((~((~surjective(F!42, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y))))))) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.53 tff(231,plain,
% 0.19/0.53 (![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.19/0.53 tff(232,plain,
% 0.19/0.53 (((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(233,plain,
% 0.19/0.53 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(234,plain,
% 0.19/0.53 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(Y, A!41, F!42), Y)))))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.53 tff(235,plain,
% 0.19/0.53 (~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[234, 231, 204])).
% 0.19/0.53 tff(236,plain,
% 0.19/0.53 (((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))) | apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(237,plain,
% 0.19/0.53 (apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.19/0.53 tff(238,plain,
% 0.19/0.53 (((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))) <=> ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(239,plain,
% 0.19/0.53 ((~((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~(member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))))) <=> (~((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(240,plain,
% 0.19/0.53 (((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~(member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))) <=> ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[239])).
% 0.19/0.53 tff(241,plain,
% 0.19/0.53 (((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~(member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))) <=> ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[240, 238])).
% 0.19/0.53 tff(242,plain,
% 0.19/0.53 ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~(member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(243,plain,
% 0.19/0.54 ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.54 tff(244,plain,
% 0.19/0.54 (~((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[243, 71])).
% 0.19/0.54 tff(245,plain,
% 0.19/0.54 (((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), 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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | (~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(246,plain,
% 0.19/0.54 ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.19/0.54 tff(247,plain,
% 0.19/0.54 (((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(248,plain,
% 0.19/0.54 (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[247, 198])).
% 0.19/0.54 tff(249,plain,
% 0.19/0.54 ((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(250,plain,
% 0.19/0.54 ((~((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.19/0.54 tff(251,plain,
% 0.19/0.54 (![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[250, 204, 246])).
% 0.19/0.54 tff(252,plain,
% 0.19/0.54 (((~![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) | ((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) <=> ((~![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(253,plain,
% 0.19/0.54 ((~![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) | ((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(254,plain,
% 0.19/0.54 ((~![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.54 tff(255,plain,
% 0.19/0.54 (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[254, 251, 237])).
% 0.19/0.54 tff(256,plain,
% 0.19/0.54 (((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(257,plain,
% 0.19/0.54 (member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[256, 235])).
% 0.19/0.54 tff(258,plain,
% 0.19/0.54 ((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))) | (~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(259,plain,
% 0.19/0.54 ((~((~member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), A!41)) | member(tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y))))) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[258, 257, 255])).
% 0.19/0.55 tff(260,plain,
% 0.19/0.55 (![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[259, 25])).
% 0.19/0.55 tff(261,plain,
% 0.19/0.55 (((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))) <=> ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(262,plain,
% 0.19/0.55 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))) | ((~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(263,plain,
% 0.19/0.55 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), Y)))) | (~member(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), Y!39)) | (~apply(F!42, tptp_fun_E_19(tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39), A!41, F!42), tptp_fun_X_0(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.55 tff(264,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[263, 200, 237, 260])).
% 0.19/0.55 % SZS output end Proof
%------------------------------------------------------------------------------