TSTP Solution File: SET727+4 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET727+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 05:07:46 EDT 2022

% Result   : Theorem 0.20s 0.43s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET727+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Sep  3 07:35:18 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  % SZS output start Proof
% 0.20/0.43  tff(tptp_fun_Y2_12_type, type, (
% 0.20/0.43     tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.43  tff(inverse_function_type, type, (
% 0.20/0.43     inverse_function: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_B_39_type, type, (
% 0.20/0.43     tptp_fun_B_39: $i)).
% 0.20/0.43  tff(tptp_fun_A_40_type, type, (
% 0.20/0.43     tptp_fun_A_40: $i)).
% 0.20/0.43  tff(tptp_fun_F_43_type, type, (
% 0.20/0.43     tptp_fun_F_43: $i)).
% 0.20/0.43  tff(tptp_fun_H_41_type, type, (
% 0.20/0.43     tptp_fun_H_41: $i)).
% 0.20/0.43  tff(tptp_fun_Y1_13_type, type, (
% 0.20/0.43     tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_Y_3_type, type, (
% 0.20/0.43     tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_G_42_type, type, (
% 0.20/0.43     tptp_fun_G_42: $i)).
% 0.20/0.43  tff(apply_type, type, (
% 0.20/0.43     apply: ( $i * $i * $i ) > $o)).
% 0.20/0.43  tff(tptp_fun_Y_8_type, type, (
% 0.20/0.43     tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.43  tff(member_type, type, (
% 0.20/0.43     member: ( $i * $i ) > $o)).
% 0.20/0.43  tff(compose_function_type, type, (
% 0.20/0.43     compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_X_14_type, type, (
% 0.20/0.43     tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.43  tff(equal_maps_type, type, (
% 0.20/0.43     equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.43  tff(identity_type, type, (
% 0.20/0.43     identity: ( $i * $i ) > $o)).
% 0.20/0.43  tff(maps_type, type, (
% 0.20/0.43     maps: ( $i * $i * $i ) > $o)).
% 0.20/0.43  tff(tptp_fun_X_15_type, type, (
% 0.20/0.43     tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_X_4_type, type, (
% 0.20/0.43     tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_Y2_5_type, type, (
% 0.20/0.43     tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_Y1_6_type, type, (
% 0.20/0.43     tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(tptp_fun_X_7_type, type, (
% 0.20/0.43     tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(1,plain,
% 0.20/0.43      (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(2,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43  tff(3,plain,
% 0.20/0.43      (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(4,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.43  tff(5,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.43  tff(6,plain,
% 0.20/0.43      (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(7,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[6])).
% 0.20/0.43  tff(8,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(9,plain,
% 0.20/0.43      (^[F: $i, G: $i, A: $i, B: $i] : rewrite((equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(10,plain,
% 0.20/0.43      (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[9])).
% 0.20/0.44  tff(11,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.20/0.44  tff(12,plain,
% 0.20/0.44      (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.44  tff(13,plain,
% 0.20/0.44      (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.44  tff(14,plain,(
% 0.20/0.44      ![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))),
% 0.20/0.44      inference(skolemize,[status(sab)],[13])).
% 0.20/0.44  tff(15,plain,
% 0.20/0.44      (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.44  tff(16,plain,
% 0.20/0.44      (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.44  tff(17,plain,
% 0.20/0.44      (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(18,plain,
% 0.20/0.44      ((~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(19,plain,
% 0.20/0.45      (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[18])).
% 0.20/0.45  tff(20,plain,
% 0.20/0.45      (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.45  tff(21,plain,
% 0.20/0.45      ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(22,plain,
% 0.20/0.46      ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.46  tff(23,plain,
% 0.20/0.46      (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.46  tff(24,plain,
% 0.20/0.46      (((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) | (equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(25,plain,
% 0.20/0.46      (equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.46  tff(26,plain,
% 0.20/0.46      ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(27,plain,
% 0.20/0.46      ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(28,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), H, B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII18')).
% 0.20/0.46  tff(29,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.46  tff(30,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.46  tff(31,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.46  tff(32,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.46  tff(33,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.46  tff(34,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.46  tff(35,plain,
% 0.20/0.46      (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[34, 26])).
% 0.20/0.46  tff(36,plain,(
% 0.20/0.46      ~((~(maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39))) | equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40))),
% 0.20/0.46      inference(skolemize,[status(sab)],[35])).
% 0.20/0.46  tff(37,plain,
% 0.20/0.46      (~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)),
% 0.20/0.46      inference(or_elim,[status(thm)],[36])).
% 0.20/0.46  tff(38,plain,
% 0.20/0.46      ((~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(39,plain,
% 0.20/0.46      ((~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.47  tff(40,plain,
% 0.20/0.47      (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[39, 25])).
% 0.20/0.47  tff(41,plain,
% 0.20/0.47      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(42,plain,
% 0.20/0.47      (member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.47  tff(43,plain,
% 0.20/0.47      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(44,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[43])).
% 0.20/0.47  tff(45,plain,
% 0.20/0.47      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(46,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[45])).
% 0.20/0.47  tff(47,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.47  tff(48,plain,
% 0.20/0.47      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(49,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47  tff(50,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(51,plain,
% 0.20/0.47      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(52,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[51])).
% 0.20/0.47  tff(53,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.20/0.47  tff(54,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.47  tff(55,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.47  tff(56,plain,(
% 0.20/0.47      ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.47      inference(skolemize,[status(sab)],[55])).
% 0.20/0.47  tff(57,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.47  tff(58,plain,
% 0.20/0.47      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[57, 47])).
% 0.20/0.47  tff(59,plain,
% 0.20/0.47      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(60,plain,
% 0.20/0.48      (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(61,plain,
% 0.20/0.48      ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(62,plain,
% 0.20/0.48      (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.48      inference(monotonicity,[status(thm)],[61])).
% 0.20/0.48  tff(63,plain,
% 0.20/0.48      (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.49  tff(64,plain,
% 0.20/0.49      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.20/0.49      inference(monotonicity,[status(thm)],[63])).
% 0.20/0.49  tff(65,plain,
% 0.20/0.49      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[64, 59])).
% 0.20/0.49  tff(66,plain,
% 0.20/0.49      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(67,plain,
% 0.20/0.49      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.50  tff(68,plain,
% 0.20/0.50      (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[67, 58, 42])).
% 0.20/0.50  tff(69,plain,
% 0.20/0.50      (((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(70,plain,
% 0.20/0.50      ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.50  tff(71,plain,
% 0.20/0.50      (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(72,plain,
% 0.20/0.50      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[71])).
% 0.20/0.50  tff(73,plain,
% 0.20/0.50      (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(74,plain,
% 0.20/0.50      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[73])).
% 0.20/0.50  tff(75,plain,
% 0.20/0.50      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.50  tff(76,plain,
% 0.20/0.50      (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(77,plain,
% 0.20/0.50      (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[76])).
% 0.20/0.50  tff(78,plain,
% 0.20/0.50      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(79,plain,
% 0.20/0.50      (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(80,plain,
% 0.20/0.50      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[79])).
% 0.20/0.50  tff(81,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','identity')).
% 0.20/0.50  tff(82,plain,
% 0.20/0.50      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.50  tff(83,plain,
% 0.20/0.50      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.50  tff(84,plain,(
% 0.20/0.50      ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.20/0.50      inference(skolemize,[status(sab)],[83])).
% 0.20/0.50  tff(85,plain,
% 0.20/0.50      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.50  tff(86,plain,
% 0.20/0.50      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.50  tff(87,plain,
% 0.20/0.50      ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(88,plain,
% 0.20/0.50      (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40))))))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.50  tff(89,plain,
% 0.20/0.50      (((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(90,plain,
% 0.20/0.50      ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.50  tff(91,plain,
% 0.20/0.50      (maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.20/0.50      inference(or_elim,[status(thm)],[36])).
% 0.20/0.50  tff(92,plain,
% 0.20/0.50      (identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)),
% 0.20/0.50      inference(and_elim,[status(thm)],[91])).
% 0.20/0.50  tff(93,plain,
% 0.20/0.50      ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(94,plain,
% 0.20/0.50      ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.50  tff(95,plain,
% 0.20/0.50      (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[94, 90])).
% 0.20/0.50  tff(96,plain,
% 0.20/0.50      (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(97,plain,
% 0.20/0.51      ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(98,plain,
% 0.20/0.51      ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.51  tff(99,plain,
% 0.20/0.51      (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[98, 42, 95])).
% 0.20/0.51  tff(100,plain,
% 0.20/0.51      ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(101,plain,
% 0.20/0.51      ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.51  tff(102,plain,
% 0.20/0.51      (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[101, 70])).
% 0.20/0.51  tff(103,plain,
% 0.20/0.51      (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(104,plain,
% 0.20/0.51      (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.51  tff(105,plain,
% 0.20/0.51      (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(106,plain,
% 0.20/0.51      (member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[105, 102])).
% 0.20/0.51  tff(107,plain,
% 0.20/0.51      (^[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)))))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(108,plain,
% 0.20/0.51      (![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))))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[107])).
% 0.20/0.51  tff(109,plain,
% 0.20/0.51      (^[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)))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(110,plain,
% 0.20/0.51      (![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))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[109])).
% 0.20/0.51  tff(111,plain,
% 0.20/0.51      (^[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)))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(112,plain,
% 0.20/0.51      (![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))))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[111])).
% 0.20/0.51  tff(113,plain,
% 0.20/0.51      (![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))))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.51  tff(114,plain,
% 0.20/0.51      (^[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))))))))))),
% 0.38/0.51      inference(bind,[status(th)],[])).
% 0.38/0.51  tff(115,plain,
% 0.38/0.51      (![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))))))))),
% 0.38/0.52      inference(quant_intro,[status(thm)],[114])).
% 0.38/0.52  tff(116,plain,
% 0.38/0.52      (^[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)))))))),
% 0.38/0.52      inference(bind,[status(th)],[])).
% 0.38/0.52  tff(117,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(quant_intro,[status(thm)],[116])).
% 0.38/0.52  tff(118,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(rewrite,[status(thm)],[])).
% 0.38/0.52  tff(119,plain,
% 0.38/0.52      (^[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)))))))),
% 0.38/0.52      inference(bind,[status(th)],[])).
% 0.38/0.52  tff(120,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(quant_intro,[status(thm)],[119])).
% 0.38/0.52  tff(121,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/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.38/0.52  tff(122,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.38/0.52  tff(123,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[122, 118])).
% 0.38/0.52  tff(124,plain,(
% 0.38/0.52      ![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))))))))),
% 0.38/0.52      inference(skolemize,[status(sab)],[123])).
% 0.38/0.52  tff(125,plain,
% 0.38/0.52      (![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))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[124, 117])).
% 0.38/0.52  tff(126,plain,
% 0.38/0.52      (![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))))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[125, 115])).
% 0.38/0.52  tff(127,plain,
% 0.38/0.52      (![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))))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[126, 113])).
% 0.38/0.52  tff(128,plain,
% 0.38/0.52      (![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))))))))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[127, 108])).
% 0.38/0.52  tff(129,plain,
% 0.38/0.52      ((~![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!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))),
% 0.38/0.52      inference(quant_inst,[status(thm)],[])).
% 0.38/0.52  tff(130,plain,
% 0.38/0.52      (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))))))),
% 0.38/0.52      inference(unit_resolution,[status(thm)],[129, 128])).
% 0.38/0.52  tff(131,plain,
% 0.38/0.52      (((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))) | ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.38/0.52      inference(tautology,[status(thm)],[])).
% 0.38/0.52  tff(132,plain,
% 0.38/0.52      ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.38/0.52      inference(unit_resolution,[status(thm)],[131, 130])).
% 0.38/0.52  tff(133,plain,
% 0.38/0.52      (maps(F!43, A!40, B!39)),
% 0.38/0.52      inference(and_elim,[status(thm)],[91])).
% 0.38/0.52  tff(134,plain,
% 0.38/0.52      ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.38/0.52      inference(tautology,[status(thm)],[])).
% 0.38/0.52  tff(135,plain,
% 0.38/0.52      ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.38/0.52      inference(unit_resolution,[status(thm)],[134, 133])).
% 0.38/0.52  tff(136,plain,
% 0.38/0.52      (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.38/0.52      inference(unit_resolution,[status(thm)],[135, 132])).
% 0.38/0.52  tff(137,plain,
% 0.38/0.52      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.38/0.52      inference(tautology,[status(thm)],[])).
% 0.38/0.52  tff(138,plain,
% 0.38/0.52      (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.38/0.52      inference(unit_resolution,[status(thm)],[137, 136])).
% 0.38/0.52  tff(139,plain,
% 0.38/0.52      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.38/0.52      inference(rewrite,[status(thm)],[])).
% 0.38/0.52  tff(140,plain,
% 0.38/0.52      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.38/0.52      inference(quant_inst,[status(thm)],[])).
% 0.38/0.52  tff(141,plain,
% 0.38/0.52      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))))),
% 0.38/0.52      inference(modus_ponens,[status(thm)],[140, 139])).
% 0.38/0.52  tff(142,plain,
% 0.38/0.53      (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.38/0.53      inference(unit_resolution,[status(thm)],[141, 138, 42])).
% 0.38/0.53  tff(143,plain,
% 0.38/0.53      (((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.38/0.53      inference(tautology,[status(thm)],[])).
% 0.38/0.53  tff(144,plain,
% 0.38/0.53      (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.38/0.53      inference(unit_resolution,[status(thm)],[143, 142])).
% 0.38/0.53  tff(145,plain,
% 0.38/0.53      (((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.38/0.53      inference(tautology,[status(thm)],[])).
% 0.38/0.53  tff(146,plain,
% 0.38/0.53      (member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.38/0.53      inference(unit_resolution,[status(thm)],[145, 142])).
% 0.38/0.53  tff(147,plain,
% 0.38/0.53      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.38/0.53      inference(tautology,[status(thm)],[])).
% 0.38/0.53  tff(148,plain,
% 0.38/0.53      (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.38/0.53      inference(unit_resolution,[status(thm)],[147, 136])).
% 0.38/0.53  tff(149,plain,
% 0.38/0.53      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.38/0.53      inference(rewrite,[status(thm)],[])).
% 0.38/0.53  tff(150,plain,
% 0.38/0.53      (((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.38/0.53      inference(rewrite,[status(thm)],[])).
% 0.38/0.53  tff(151,plain,
% 0.38/0.53      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.40/0.53      inference(monotonicity,[status(thm)],[150])).
% 0.40/0.53  tff(152,plain,
% 0.40/0.53      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.40/0.54      inference(transitivity,[status(thm)],[151, 149])).
% 0.40/0.54  tff(153,plain,
% 0.40/0.54      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.40/0.54      inference(quant_inst,[status(thm)],[])).
% 0.40/0.54  tff(154,plain,
% 0.40/0.54      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.40/0.54      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.40/0.54  tff(155,plain,
% 0.40/0.54      (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.40/0.54      inference(unit_resolution,[status(thm)],[154, 148, 42, 146, 144, 106, 104])).
% 0.40/0.54  tff(156,plain,
% 0.40/0.54      (tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42)),
% 0.40/0.54      inference(symmetry,[status(thm)],[155])).
% 0.40/0.54  tff(157,plain,
% 0.40/0.54      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.54      inference(monotonicity,[status(thm)],[156])).
% 0.40/0.54  tff(158,plain,
% 0.40/0.54      (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.54      inference(symmetry,[status(thm)],[157])).
% 0.40/0.54  tff(159,plain,
% 0.40/0.54      (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.54      inference(tautology,[status(thm)],[])).
% 0.40/0.54  tff(160,plain,
% 0.40/0.54      (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.54      inference(unit_resolution,[status(thm)],[159, 102])).
% 0.40/0.54  tff(161,plain,
% 0.40/0.54      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.54      inference(modus_ponens,[status(thm)],[160, 158])).
% 0.40/0.54  tff(162,plain,
% 0.40/0.54      (((~![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(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))) <=> ((~![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(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.40/0.54      inference(rewrite,[status(thm)],[])).
% 0.40/0.54  tff(163,plain,
% 0.40/0.54      ((~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))))) <=> (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.40/0.54      inference(rewrite,[status(thm)],[])).
% 0.40/0.54  tff(164,plain,
% 0.40/0.54      (((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), 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) | (~((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(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.40/0.54      inference(monotonicity,[status(thm)],[163])).
% 0.40/0.54  tff(165,plain,
% 0.40/0.54      (((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), 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) | (~((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(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.40/0.55      inference(transitivity,[status(thm)],[164, 162])).
% 0.40/0.55  tff(166,plain,
% 0.40/0.55      ((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))),
% 0.40/0.55      inference(quant_inst,[status(thm)],[])).
% 0.40/0.55  tff(167,plain,
% 0.40/0.55      ((~![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(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.40/0.55      inference(modus_ponens,[status(thm)],[166, 165])).
% 0.40/0.55  tff(168,plain,
% 0.40/0.55      (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[167, 128])).
% 0.40/0.55  tff(169,plain,
% 0.40/0.55      (((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))) | ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.40/0.55      inference(tautology,[status(thm)],[])).
% 0.40/0.55  tff(170,plain,
% 0.40/0.55      ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[169, 168])).
% 0.40/0.55  tff(171,plain,
% 0.40/0.55      (maps(G!42, B!39, A!40)),
% 0.40/0.55      inference(and_elim,[status(thm)],[91])).
% 0.40/0.55  tff(172,plain,
% 0.40/0.55      ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55      inference(tautology,[status(thm)],[])).
% 0.40/0.55  tff(173,plain,
% 0.40/0.55      ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[172, 171])).
% 0.40/0.55  tff(174,plain,
% 0.40/0.55      (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[173, 170])).
% 0.40/0.55  tff(175,plain,
% 0.40/0.55      (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))),
% 0.40/0.55      inference(tautology,[status(thm)],[])).
% 0.40/0.55  tff(176,plain,
% 0.40/0.55      (![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[175, 174])).
% 0.40/0.55  tff(177,plain,
% 0.40/0.55      (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.40/0.55      inference(rewrite,[status(thm)],[])).
% 0.40/0.55  tff(178,plain,
% 0.40/0.55      ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(179,plain,
% 0.40/0.56      ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))))),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[178, 177])).
% 0.40/0.56  tff(180,plain,
% 0.40/0.56      (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[179, 176, 146])).
% 0.40/0.56  tff(181,plain,
% 0.40/0.56      (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.40/0.56      inference(tautology,[status(thm)],[])).
% 0.40/0.56  tff(182,plain,
% 0.40/0.56      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[181, 180])).
% 0.40/0.56  tff(183,plain,
% 0.40/0.56      (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.40/0.56      inference(tautology,[status(thm)],[])).
% 0.40/0.56  tff(184,plain,
% 0.40/0.56      (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[183, 180])).
% 0.40/0.56  tff(185,plain,
% 0.40/0.56      (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.40/0.56      inference(tautology,[status(thm)],[])).
% 0.40/0.56  tff(186,plain,
% 0.40/0.56      (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[185, 174])).
% 0.40/0.56  tff(187,plain,
% 0.40/0.56      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(188,plain,
% 0.40/0.56      (((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(189,plain,
% 0.40/0.56      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.56      inference(monotonicity,[status(thm)],[188])).
% 0.40/0.56  tff(190,plain,
% 0.40/0.56      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[189, 187])).
% 0.40/0.57  tff(191,plain,
% 0.40/0.57      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(192,plain,
% 0.40/0.57      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[191, 190])).
% 0.40/0.57  tff(193,plain,
% 0.40/0.57      ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[192, 186, 42, 146, 184, 182])).
% 0.40/0.57  tff(194,plain,
% 0.40/0.57      (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[193, 161])).
% 0.40/0.57  tff(195,plain,
% 0.40/0.57      (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.40/0.57      inference(symmetry,[status(thm)],[194])).
% 0.40/0.57  tff(196,plain,
% 0.40/0.57      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.40/0.57      inference(tautology,[status(thm)],[])).
% 0.40/0.57  tff(197,plain,
% 0.40/0.57      (member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[196, 40])).
% 0.40/0.57  tff(198,plain,
% 0.40/0.57      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(199,plain,
% 0.40/0.57      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(200,plain,
% 0.40/0.57      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.40/0.57  tff(201,plain,
% 0.40/0.57      (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[200, 138, 197])).
% 0.40/0.57  tff(202,plain,
% 0.40/0.57      (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.40/0.57      inference(tautology,[status(thm)],[])).
% 0.40/0.57  tff(203,plain,
% 0.40/0.57      (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[202, 201])).
% 0.40/0.57  tff(204,plain,
% 0.40/0.57      (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.40/0.57      inference(tautology,[status(thm)],[])).
% 0.40/0.57  tff(205,plain,
% 0.40/0.57      (member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[204, 201])).
% 0.40/0.57  tff(206,plain,
% 0.40/0.57      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.40/0.57      inference(tautology,[status(thm)],[])).
% 0.40/0.57  tff(207,plain,
% 0.40/0.57      (member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[206, 40])).
% 0.40/0.57  tff(208,plain,
% 0.40/0.57      (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(209,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[208])).
% 0.40/0.57  tff(210,plain,
% 0.40/0.57      (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(211,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[210])).
% 0.40/0.57  tff(212,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(213,plain,
% 0.40/0.57      (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.40/0.57      inference(bind,[status(th)],[])).
% 0.40/0.57  tff(214,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.40/0.57      inference(quant_intro,[status(thm)],[213])).
% 0.40/0.57  tff(215,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.40/0.57  tff(216,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[215, 214])).
% 0.40/0.57  tff(217,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[216, 212])).
% 0.40/0.57  tff(218,plain,(
% 0.40/0.57      ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.40/0.57      inference(skolemize,[status(sab)],[217])).
% 0.40/0.57  tff(219,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[218, 211])).
% 0.40/0.57  tff(220,plain,
% 0.40/0.57      (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[219, 209])).
% 0.40/0.57  tff(221,plain,
% 0.40/0.57      (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(222,plain,
% 0.40/0.57      (((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(223,plain,
% 0.40/0.58      (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[222])).
% 0.40/0.58  tff(224,plain,
% 0.40/0.58      (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.58      inference(transitivity,[status(thm)],[223, 221])).
% 0.40/0.58  tff(225,plain,
% 0.40/0.58      ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(226,plain,
% 0.40/0.58      ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[225, 224])).
% 0.40/0.58  tff(227,plain,
% 0.40/0.58      (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[226, 220, 207, 197])).
% 0.40/0.58  tff(228,plain,
% 0.40/0.58      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.58      inference(tautology,[status(thm)],[])).
% 0.40/0.58  tff(229,plain,
% 0.40/0.58      (apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[228, 40])).
% 0.40/0.58  tff(230,plain,
% 0.40/0.58      ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.58      inference(tautology,[status(thm)],[])).
% 0.40/0.58  tff(231,plain,
% 0.40/0.58      ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[230, 229])).
% 0.40/0.58  tff(232,plain,
% 0.40/0.58      (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[231, 227])).
% 0.40/0.58  tff(233,plain,
% 0.40/0.58      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(234,plain,
% 0.40/0.58      (((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(235,plain,
% 0.40/0.58      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[234])).
% 0.40/0.59  tff(236,plain,
% 0.40/0.59      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.40/0.59      inference(transitivity,[status(thm)],[235, 233])).
% 0.40/0.59  tff(237,plain,
% 0.40/0.59      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.40/0.59      inference(quant_inst,[status(thm)],[])).
% 0.40/0.59  tff(238,plain,
% 0.40/0.59      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.40/0.59      inference(modus_ponens,[status(thm)],[237, 236])).
% 0.40/0.59  tff(239,plain,
% 0.40/0.59      (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[238, 148, 207, 197, 232, 205, 203])).
% 0.40/0.59  tff(240,plain,
% 0.40/0.59      (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.40/0.59      inference(symmetry,[status(thm)],[239])).
% 0.40/0.59  tff(241,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[240])).
% 0.40/0.59  tff(242,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.59      inference(symmetry,[status(thm)],[241])).
% 0.40/0.59  tff(243,plain,
% 0.40/0.59      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.59      inference(tautology,[status(thm)],[])).
% 0.40/0.59  tff(244,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[243, 40])).
% 0.40/0.59  tff(245,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.59      inference(modus_ponens,[status(thm)],[244, 242])).
% 0.40/0.59  tff(246,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43)) <=> apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[240])).
% 0.40/0.59  tff(247,plain,
% 0.40/0.59      (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43)) <=> apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.40/0.59      inference(symmetry,[status(thm)],[246])).
% 0.40/0.59  tff(248,plain,
% 0.40/0.59      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(249,plain,
% 0.40/0.60      (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(250,plain,
% 0.40/0.60      ((~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(251,plain,
% 0.40/0.60      (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.60      inference(monotonicity,[status(thm)],[250])).
% 0.40/0.60  tff(252,plain,
% 0.40/0.60      (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[251, 249])).
% 0.40/0.61  tff(253,plain,
% 0.40/0.61      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[252])).
% 0.40/0.61  tff(254,plain,
% 0.40/0.61      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[253, 248])).
% 0.40/0.61  tff(255,plain,
% 0.40/0.61      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(256,plain,
% 0.40/0.61      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[255, 254])).
% 0.40/0.61  tff(257,plain,
% 0.40/0.61      (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[256, 58, 207])).
% 0.40/0.62  tff(258,plain,
% 0.40/0.62      (((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.40/0.62      inference(tautology,[status(thm)],[])).
% 0.40/0.62  tff(259,plain,
% 0.40/0.62      ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[258, 257])).
% 0.40/0.62  tff(260,plain,
% 0.40/0.62      ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(261,plain,
% 0.40/0.62      (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39))))))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[260, 86])).
% 0.40/0.62  tff(262,plain,
% 0.40/0.62      (((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))) | ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))),
% 0.40/0.62      inference(tautology,[status(thm)],[])).
% 0.40/0.62  tff(263,plain,
% 0.40/0.62      ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[262, 261])).
% 0.40/0.62  tff(264,plain,
% 0.40/0.62      (identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.40/0.62      inference(and_elim,[status(thm)],[91])).
% 0.40/0.62  tff(265,plain,
% 0.40/0.62      ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.40/0.62      inference(tautology,[status(thm)],[])).
% 0.40/0.62  tff(266,plain,
% 0.40/0.62      ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[265, 264])).
% 0.40/0.62  tff(267,plain,
% 0.40/0.62      (![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[266, 263])).
% 0.40/0.62  tff(268,plain,
% 0.40/0.62      (((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(269,plain,
% 0.40/0.62      ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(270,plain,
% 0.40/0.62      ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.62      inference(modus_ponens,[status(thm)],[269, 268])).
% 0.40/0.62  tff(271,plain,
% 0.40/0.62      (apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[270, 207, 267])).
% 0.40/0.62  tff(272,plain,
% 0.40/0.62      ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.62      inference(tautology,[status(thm)],[])).
% 0.40/0.62  tff(273,plain,
% 0.40/0.62      ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[272, 271])).
% 0.40/0.62  tff(274,plain,
% 0.40/0.62      (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[273, 259])).
% 0.40/0.62  tff(275,plain,
% 0.40/0.62      (((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.40/0.63      inference(tautology,[status(thm)],[])).
% 0.40/0.63  tff(276,plain,
% 0.40/0.63      (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.40/0.63      inference(unit_resolution,[status(thm)],[275, 274])).
% 0.40/0.63  tff(277,plain,
% 0.40/0.63      (apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.40/0.63      inference(modus_ponens,[status(thm)],[276, 247])).
% 0.40/0.63  tff(278,plain,
% 0.40/0.63      (((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)),
% 0.40/0.63      inference(tautology,[status(thm)],[])).
% 0.40/0.63  tff(279,plain,
% 0.40/0.63      (member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)),
% 0.40/0.63      inference(unit_resolution,[status(thm)],[278, 274])).
% 0.40/0.63  tff(280,plain,
% 0.40/0.63      (((~![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(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))))))) <=> ((~![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(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))))))),
% 0.40/0.63      inference(rewrite,[status(thm)],[])).
% 0.40/0.63  tff(281,plain,
% 0.40/0.63      ((~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))))) <=> (~((~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))))))),
% 0.40/0.63      inference(rewrite,[status(thm)],[])).
% 0.40/0.63  tff(282,plain,
% 0.40/0.63      (((~![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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), 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) | (~((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(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))))))),
% 0.50/0.63      inference(monotonicity,[status(thm)],[281])).
% 0.50/0.63  tff(283,plain,
% 0.50/0.63      (((~![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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), 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) | (~((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(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))))))),
% 0.50/0.63      inference(transitivity,[status(thm)],[282, 280])).
% 0.50/0.63  tff(284,plain,
% 0.50/0.63      ((~![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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y))))))))))),
% 0.50/0.63      inference(quant_inst,[status(thm)],[])).
% 0.50/0.63  tff(285,plain,
% 0.50/0.63      ((~![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(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))))))),
% 0.50/0.64      inference(modus_ponens,[status(thm)],[284, 283])).
% 0.50/0.64  tff(286,plain,
% 0.50/0.64      (~((~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))))),
% 0.50/0.64      inference(unit_resolution,[status(thm)],[285, 128])).
% 0.50/0.64  tff(287,plain,
% 0.50/0.64      (((~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))) | (~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))))) | ((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))),
% 0.50/0.64      inference(tautology,[status(thm)],[])).
% 0.50/0.64  tff(288,plain,
% 0.50/0.64      ((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.50/0.64      inference(unit_resolution,[status(thm)],[287, 286])).
% 0.50/0.64  tff(289,plain,
% 0.50/0.64      (maps(H!41, B!39, A!40)),
% 0.50/0.64      inference(and_elim,[status(thm)],[91])).
% 0.50/0.64  tff(290,plain,
% 0.50/0.64      ((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.50/0.64      inference(tautology,[status(thm)],[])).
% 0.50/0.64  tff(291,plain,
% 0.50/0.64      ((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.50/0.64      inference(unit_resolution,[status(thm)],[290, 289])).
% 0.50/0.64  tff(292,plain,
% 0.50/0.64      (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))),
% 0.50/0.64      inference(unit_resolution,[status(thm)],[291, 288])).
% 0.50/0.64  tff(293,plain,
% 0.50/0.64      (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))),
% 0.50/0.64      inference(tautology,[status(thm)],[])).
% 0.50/0.64  tff(294,plain,
% 0.50/0.64      (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))),
% 0.50/0.64      inference(unit_resolution,[status(thm)],[293, 292])).
% 0.50/0.64  tff(295,plain,
% 0.50/0.64      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.50/0.64      inference(rewrite,[status(thm)],[])).
% 0.50/0.64  tff(296,plain,
% 0.50/0.64      (((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.50/0.64      inference(rewrite,[status(thm)],[])).
% 0.50/0.64  tff(297,plain,
% 0.50/0.64      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.50/0.65      inference(monotonicity,[status(thm)],[296])).
% 0.50/0.65  tff(298,plain,
% 0.50/0.65      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.50/0.65      inference(transitivity,[status(thm)],[297, 295])).
% 0.50/0.65  tff(299,plain,
% 0.50/0.65      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.50/0.65      inference(quant_inst,[status(thm)],[])).
% 0.50/0.65  tff(300,plain,
% 0.50/0.65      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.50/0.65      inference(modus_ponens,[status(thm)],[299, 298])).
% 0.50/0.65  tff(301,plain,
% 0.50/0.65      ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.50/0.65      inference(unit_resolution,[status(thm)],[300, 294, 42, 205, 279])).
% 0.50/0.65  tff(302,plain,
% 0.50/0.65      (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.50/0.65      inference(unit_resolution,[status(thm)],[301, 277, 245])).
% 0.50/0.65  tff(303,plain,
% 0.50/0.65      (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.50/0.65      inference(monotonicity,[status(thm)],[302])).
% 0.50/0.65  tff(304,plain,
% 0.50/0.65      (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) <=> apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.50/0.65      inference(monotonicity,[status(thm)],[240])).
% 0.50/0.65  tff(305,plain,
% 0.50/0.65      (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.50/0.65      inference(symmetry,[status(thm)],[304])).
% 0.50/0.65  tff(306,plain,
% 0.50/0.65      (((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.50/0.65      inference(tautology,[status(thm)],[])).
% 0.50/0.65  tff(307,plain,
% 0.50/0.65      (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.50/0.65      inference(unit_resolution,[status(thm)],[306, 274])).
% 0.50/0.65  tff(308,plain,
% 0.50/0.65      (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.50/0.65      inference(modus_ponens,[status(thm)],[307, 305])).
% 0.50/0.65  tff(309,plain,
% 0.50/0.65      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))))))),
% 0.50/0.65      inference(rewrite,[status(thm)],[])).
% 0.50/0.65  tff(310,plain,
% 0.50/0.65      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))))))),
% 0.50/0.66      inference(quant_inst,[status(thm)],[])).
% 0.50/0.66  tff(311,plain,
% 0.50/0.66      ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43)))))),
% 0.50/0.66      inference(modus_ponens,[status(thm)],[310, 309])).
% 0.50/0.66  tff(312,plain,
% 0.50/0.66      (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))))),
% 0.50/0.66      inference(unit_resolution,[status(thm)],[311, 138, 279])).
% 0.50/0.66  tff(313,plain,
% 0.50/0.66      (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43)))) | apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))),
% 0.50/0.66      inference(tautology,[status(thm)],[])).
% 0.50/0.66  tff(314,plain,
% 0.50/0.66      (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))),
% 0.50/0.66      inference(unit_resolution,[status(thm)],[313, 312])).
% 0.50/0.66  tff(315,plain,
% 0.50/0.66      (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)),
% 0.50/0.66      inference(tautology,[status(thm)],[])).
% 0.50/0.66  tff(316,plain,
% 0.50/0.66      (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)),
% 0.50/0.66      inference(unit_resolution,[status(thm)],[315, 312])).
% 0.50/0.66  tff(317,plain,
% 0.50/0.66      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.50/0.66      inference(rewrite,[status(thm)],[])).
% 0.50/0.66  tff(318,plain,
% 0.50/0.66      (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.50/0.66      inference(rewrite,[status(thm)],[])).
% 0.50/0.66  tff(319,plain,
% 0.50/0.66      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))))),
% 0.50/0.67      inference(monotonicity,[status(thm)],[318])).
% 0.50/0.67  tff(320,plain,
% 0.50/0.67      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.50/0.67      inference(transitivity,[status(thm)],[319, 317])).
% 0.50/0.67  tff(321,plain,
% 0.50/0.67      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.50/0.67      inference(quant_inst,[status(thm)],[])).
% 0.50/0.67  tff(322,plain,
% 0.50/0.67      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.50/0.67      inference(modus_ponens,[status(thm)],[321, 320])).
% 0.50/0.67  tff(323,plain,
% 0.50/0.67      ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.50/0.67      inference(unit_resolution,[status(thm)],[322, 148, 205, 279, 316, 314])).
% 0.50/0.67  tff(324,plain,
% 0.50/0.67      (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.50/0.67      inference(unit_resolution,[status(thm)],[323, 308])).
% 0.50/0.67  tff(325,plain,
% 0.50/0.67      (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), B!39, F!43)),
% 0.50/0.67      inference(symmetry,[status(thm)],[324])).
% 0.50/0.67  tff(326,plain,
% 0.50/0.67      (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.50/0.67      inference(transitivity,[status(thm)],[325, 303])).
% 0.50/0.67  tff(327,plain,
% 0.50/0.67      (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)),
% 0.50/0.67      inference(monotonicity,[status(thm)],[326])).
% 0.50/0.67  tff(328,plain,
% 0.50/0.67      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.68      inference(rewrite,[status(thm)],[])).
% 0.50/0.68  tff(329,plain,
% 0.50/0.68      (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.68      inference(rewrite,[status(thm)],[])).
% 0.50/0.68  tff(330,plain,
% 0.50/0.68      ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.50/0.69      inference(rewrite,[status(thm)],[])).
% 0.50/0.69  tff(331,plain,
% 0.50/0.69      (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.69      inference(monotonicity,[status(thm)],[330])).
% 0.50/0.69  tff(332,plain,
% 0.50/0.69      (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.69      inference(transitivity,[status(thm)],[331, 329])).
% 0.50/0.69  tff(333,plain,
% 0.50/0.69      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.50/0.69      inference(monotonicity,[status(thm)],[332])).
% 0.50/0.69  tff(334,plain,
% 0.50/0.69      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.69      inference(transitivity,[status(thm)],[333, 328])).
% 0.50/0.69  tff(335,plain,
% 0.50/0.69      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.50/0.69      inference(quant_inst,[status(thm)],[])).
% 0.50/0.69  tff(336,plain,
% 0.50/0.69      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.56/0.70      inference(modus_ponens,[status(thm)],[335, 334])).
% 0.56/0.70  tff(337,plain,
% 0.56/0.70      (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))),
% 0.56/0.70      inference(unit_resolution,[status(thm)],[336, 58, 197])).
% 0.56/0.70  tff(338,plain,
% 0.56/0.70      (((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.56/0.70      inference(tautology,[status(thm)],[])).
% 0.56/0.70  tff(339,plain,
% 0.56/0.70      ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.56/0.70      inference(unit_resolution,[status(thm)],[338, 337])).
% 0.56/0.70  tff(340,plain,
% 0.56/0.70      (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.56/0.70      inference(rewrite,[status(thm)],[])).
% 0.56/0.70  tff(341,plain,
% 0.56/0.70      ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.56/0.70      inference(quant_inst,[status(thm)],[])).
% 0.56/0.70  tff(342,plain,
% 0.56/0.70      ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.70      inference(modus_ponens,[status(thm)],[341, 340])).
% 0.56/0.70  tff(343,plain,
% 0.56/0.70      (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.70      inference(unit_resolution,[status(thm)],[342, 197, 95])).
% 0.56/0.70  tff(344,plain,
% 0.56/0.70      ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.56/0.70      inference(tautology,[status(thm)],[])).
% 0.56/0.70  tff(345,plain,
% 0.56/0.70      ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.56/0.70      inference(unit_resolution,[status(thm)],[344, 343])).
% 0.56/0.70  tff(346,plain,
% 0.56/0.70      (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.56/0.71      inference(unit_resolution,[status(thm)],[345, 339])).
% 0.56/0.71  tff(347,plain,
% 0.56/0.71      (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.56/0.71      inference(tautology,[status(thm)],[])).
% 0.56/0.71  tff(348,plain,
% 0.56/0.71      (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.56/0.71      inference(unit_resolution,[status(thm)],[347, 346])).
% 0.56/0.71  tff(349,plain,
% 0.56/0.71      (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.56/0.71      inference(tautology,[status(thm)],[])).
% 0.56/0.71  tff(350,plain,
% 0.56/0.71      (member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.56/0.71      inference(unit_resolution,[status(thm)],[349, 346])).
% 0.56/0.71  tff(351,plain,
% 0.56/0.71      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.56/0.71      inference(rewrite,[status(thm)],[])).
% 0.56/0.71  tff(352,plain,
% 0.56/0.71      (((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.56/0.71      inference(rewrite,[status(thm)],[])).
% 0.56/0.71  tff(353,plain,
% 0.56/0.71      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.56/0.72      inference(monotonicity,[status(thm)],[352])).
% 0.56/0.72  tff(354,plain,
% 0.56/0.72      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.56/0.72      inference(transitivity,[status(thm)],[353, 351])).
% 0.56/0.72  tff(355,plain,
% 0.56/0.72      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.56/0.72      inference(quant_inst,[status(thm)],[])).
% 0.56/0.72  tff(356,plain,
% 0.56/0.72      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.56/0.72      inference(modus_ponens,[status(thm)],[355, 354])).
% 0.56/0.72  tff(357,plain,
% 0.56/0.72      (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.56/0.72      inference(unit_resolution,[status(thm)],[356, 148, 197, 205, 203, 350, 348])).
% 0.56/0.72  tff(358,plain,
% 0.56/0.72      (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42)),
% 0.56/0.72      inference(symmetry,[status(thm)],[357])).
% 0.56/0.72  tff(359,plain,
% 0.56/0.72      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.72      inference(monotonicity,[status(thm)],[358])).
% 0.56/0.72  tff(360,plain,
% 0.56/0.72      (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.72      inference(symmetry,[status(thm)],[359])).
% 0.56/0.72  tff(361,plain,
% 0.56/0.72      (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.72      inference(tautology,[status(thm)],[])).
% 0.56/0.72  tff(362,plain,
% 0.56/0.72      (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.72      inference(unit_resolution,[status(thm)],[361, 346])).
% 0.56/0.72  tff(363,plain,
% 0.56/0.72      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.72      inference(modus_ponens,[status(thm)],[362, 360])).
% 0.56/0.72  tff(364,plain,
% 0.56/0.72      (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.56/0.72      inference(rewrite,[status(thm)],[])).
% 0.56/0.72  tff(365,plain,
% 0.56/0.72      ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.56/0.72      inference(quant_inst,[status(thm)],[])).
% 0.56/0.72  tff(366,plain,
% 0.56/0.72      ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))))),
% 0.56/0.72      inference(modus_ponens,[status(thm)],[365, 364])).
% 0.56/0.72  tff(367,plain,
% 0.56/0.72      (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))),
% 0.56/0.72      inference(unit_resolution,[status(thm)],[366, 176, 205])).
% 0.56/0.72  tff(368,plain,
% 0.56/0.72      (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.56/0.72      inference(tautology,[status(thm)],[])).
% 0.56/0.72  tff(369,plain,
% 0.56/0.72      (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.56/0.72      inference(unit_resolution,[status(thm)],[368, 367])).
% 0.56/0.72  tff(370,plain,
% 0.56/0.72      (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.56/0.72      inference(tautology,[status(thm)],[])).
% 0.56/0.72  tff(371,plain,
% 0.56/0.72      (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.56/0.72      inference(unit_resolution,[status(thm)],[370, 367])).
% 0.56/0.72  tff(372,plain,
% 0.56/0.72      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.56/0.73      inference(rewrite,[status(thm)],[])).
% 0.56/0.73  tff(373,plain,
% 0.56/0.73      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.56/0.73      inference(rewrite,[status(thm)],[])).
% 0.56/0.73  tff(374,plain,
% 0.56/0.73      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.56/0.73      inference(monotonicity,[status(thm)],[373])).
% 0.56/0.73  tff(375,plain,
% 0.56/0.73      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.56/0.73      inference(transitivity,[status(thm)],[374, 372])).
% 0.56/0.73  tff(376,plain,
% 0.56/0.73      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.56/0.73      inference(quant_inst,[status(thm)],[])).
% 0.56/0.73  tff(377,plain,
% 0.56/0.73      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.56/0.73      inference(modus_ponens,[status(thm)],[376, 375])).
% 0.56/0.73  tff(378,plain,
% 0.56/0.73      ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.56/0.73      inference(unit_resolution,[status(thm)],[377, 186, 197, 205, 371, 369])).
% 0.56/0.73  tff(379,plain,
% 0.56/0.73      (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)),
% 0.56/0.73      inference(unit_resolution,[status(thm)],[378, 363])).
% 0.56/0.73  tff(380,plain,
% 0.56/0.73      (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.56/0.73      inference(transitivity,[status(thm)],[379, 327, 195])).
% 0.56/0.73  tff(381,plain,
% 0.56/0.73      (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | (~(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.56/0.74      inference(tautology,[status(thm)],[])).
% 0.56/0.74  tff(382,plain,
% 0.56/0.74      (~(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.56/0.74      inference(unit_resolution,[status(thm)],[381, 40])).
% 0.56/0.74  tff(383,plain,
% 0.56/0.74      ($false),
% 0.56/0.74      inference(unit_resolution,[status(thm)],[382, 380])).
% 0.56/0.74  % SZS output end Proof
%------------------------------------------------------------------------------