TSTP Solution File: SET720+4 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET720+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n023.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 05:07:45 EDT 2022

% Result   : Theorem 0.21s 0.43s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET720+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.13/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35  % Computer : n023.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat Sep  3 07:51:33 EDT 2022
% 0.21/0.36  % CPUTime  : 
% 0.21/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.36  Usage: tptp [options] [-file:]file
% 0.21/0.36    -h, -?       prints this message.
% 0.21/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.21/0.36    -m, -model   generate model.
% 0.21/0.36    -p, -proof   generate proof.
% 0.21/0.36    -c, -core    generate unsat core of named formulas.
% 0.21/0.36    -st, -statistics display statistics.
% 0.21/0.36    -t:timeout   set timeout (in second).
% 0.21/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.21/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.36    -<param>:<value> configuration parameter and value.
% 0.21/0.36    -o:<output-file> file to place output in.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  % SZS output start Proof
% 0.21/0.43  tff(apply_type, type, (
% 0.21/0.43     apply: ( $i * $i * $i ) > $o)).
% 0.21/0.43  tff(tptp_fun_Y1_13_type, type, (
% 0.21/0.43     tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.43  tff(inverse_function_type, type, (
% 0.21/0.43     inverse_function: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(tptp_fun_A_40_type, type, (
% 0.21/0.43     tptp_fun_A_40: $i)).
% 0.21/0.43  tff(tptp_fun_B_39_type, type, (
% 0.21/0.43     tptp_fun_B_39: $i)).
% 0.21/0.43  tff(tptp_fun_F_41_type, type, (
% 0.21/0.43     tptp_fun_F_41: $i)).
% 0.21/0.43  tff(tptp_fun_X_14_type, type, (
% 0.21/0.43     tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.43  tff(member_type, type, (
% 0.21/0.43     member: ( $i * $i ) > $o)).
% 0.21/0.43  tff(tptp_fun_Y2_12_type, type, (
% 0.21/0.43     tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.43  tff(equal_maps_type, type, (
% 0.21/0.43     equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.43  tff(one_to_one_type, type, (
% 0.21/0.43     one_to_one: ( $i * $i * $i ) > $o)).
% 0.21/0.43  tff(maps_type, type, (
% 0.21/0.43     maps: ( $i * $i * $i ) > $o)).
% 0.21/0.43  tff(tptp_fun_Y_3_type, type, (
% 0.21/0.43     tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(tptp_fun_X_4_type, type, (
% 0.21/0.43     tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(tptp_fun_Y2_5_type, type, (
% 0.21/0.43     tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(tptp_fun_Y1_6_type, type, (
% 0.21/0.43     tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(tptp_fun_X_7_type, type, (
% 0.21/0.43     tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.21/0.43  tff(1,plain,
% 0.21/0.43      (^[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))))))))))),
% 0.21/0.43      inference(bind,[status(th)],[])).
% 0.21/0.43  tff(2,plain,
% 0.21/0.43      (![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)))))))))),
% 0.21/0.43      inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43  tff(3,plain,
% 0.21/0.43      (^[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))))))))))),
% 0.21/0.43      inference(bind,[status(th)],[])).
% 0.21/0.43  tff(4,plain,
% 0.21/0.43      (![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)))))))))),
% 0.21/0.43      inference(quant_intro,[status(thm)],[3])).
% 0.21/0.43  tff(5,plain,
% 0.21/0.43      (![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)))))))))),
% 0.21/0.43      inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.43  tff(6,plain,
% 0.21/0.43      (^[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)))))))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(7,plain,
% 0.21/0.44      (![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)))))))) <=> ![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)))))))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[6])).
% 0.21/0.44  tff(8,plain,
% 0.21/0.44      (![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))))) <=> ![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)))))),
% 0.21/0.44      inference(rewrite,[status(thm)],[])).
% 0.21/0.44  tff(9,plain,
% 0.21/0.44      (^[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))))))),
% 0.21/0.44      inference(bind,[status(th)],[])).
% 0.21/0.44  tff(10,plain,
% 0.21/0.44      (![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)))))),
% 0.21/0.44      inference(quant_intro,[status(thm)],[9])).
% 0.21/0.44  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/sandbox2/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.23/0.44  tff(12,plain,
% 0.23/0.44      (![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)))))),
% 0.23/0.44      inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.44  tff(13,plain,
% 0.23/0.44      (![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)))))),
% 0.23/0.44      inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.44  tff(14,plain,(
% 0.23/0.44      ![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))))))))),
% 0.23/0.44      inference(skolemize,[status(sab)],[13])).
% 0.23/0.44  tff(15,plain,
% 0.23/0.44      (![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)))))))))),
% 0.23/0.44      inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.44  tff(16,plain,
% 0.23/0.44      (![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)))))))))),
% 0.23/0.44      inference(modus_ponens,[status(thm)],[15, 5])).
% 0.23/0.44  tff(17,plain,
% 0.23/0.44      ((~![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(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), X, Y1))))) | (~(equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))))))),
% 0.23/0.44      inference(quant_inst,[status(thm)],[])).
% 0.23/0.44  tff(18,plain,
% 0.23/0.44      (~((~((~equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), X, Y1))))) | (~(equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))))))),
% 0.23/0.44      inference(unit_resolution,[status(thm)],[17, 16])).
% 0.23/0.44  tff(19,plain,
% 0.23/0.44      (((~((~equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), X, Y1))))) | (~(equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))))) | (equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))))),
% 0.23/0.45      inference(tautology,[status(thm)],[])).
% 0.23/0.45  tff(20,plain,
% 0.23/0.45      (equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.45      inference(unit_resolution,[status(thm)],[19, 18])).
% 0.23/0.45  tff(21,plain,
% 0.23/0.45      ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B)))),
% 0.23/0.45      inference(rewrite,[status(thm)],[])).
% 0.23/0.45  tff(22,plain,
% 0.23/0.45      ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B)))),
% 0.23/0.45      inference(rewrite,[status(thm)],[])).
% 0.23/0.45  tff(23,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII11')).
% 0.23/0.45  tff(24,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[23, 22])).
% 0.23/0.45  tff(25,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[24, 21])).
% 0.23/0.45  tff(26,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.45  tff(27,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[26, 21])).
% 0.23/0.45  tff(28,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[27, 21])).
% 0.23/0.45  tff(29,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[28, 21])).
% 0.23/0.45  tff(30,plain,
% 0.23/0.45      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | equal_maps(inverse_function(inverse_function(F, A, B), B, A), F, A, B))),
% 0.23/0.45      inference(modus_ponens,[status(thm)],[29, 21])).
% 0.23/0.45  tff(31,plain,(
% 0.23/0.45      ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39))),
% 0.23/0.45      inference(skolemize,[status(sab)],[30])).
% 0.23/0.45  tff(32,plain,
% 0.23/0.45      (~equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39)),
% 0.23/0.45      inference(or_elim,[status(thm)],[31])).
% 0.23/0.45  tff(33,plain,
% 0.23/0.45      ((~(equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))))) | equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.45      inference(tautology,[status(thm)],[])).
% 0.23/0.45  tff(34,plain,
% 0.23/0.45      ((~(equal_maps(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), F!41, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))))) | (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.46      inference(unit_resolution,[status(thm)],[33, 32])).
% 0.23/0.46  tff(35,plain,
% 0.23/0.46      (~((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.46      inference(unit_resolution,[status(thm)],[34, 20])).
% 0.23/0.46  tff(36,plain,
% 0.23/0.46      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)),
% 0.23/0.46      inference(tautology,[status(thm)],[])).
% 0.23/0.46  tff(37,plain,
% 0.23/0.46      (member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)),
% 0.23/0.46      inference(unit_resolution,[status(thm)],[36, 35])).
% 0.23/0.46  tff(38,plain,
% 0.23/0.46      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)),
% 0.23/0.46      inference(tautology,[status(thm)],[])).
% 0.23/0.46  tff(39,plain,
% 0.23/0.46      (member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)),
% 0.23/0.46      inference(unit_resolution,[status(thm)],[38, 35])).
% 0.23/0.46  tff(40,plain,
% 0.23/0.46      (^[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))))),
% 0.23/0.46      inference(bind,[status(th)],[])).
% 0.23/0.46  tff(41,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(quant_intro,[status(thm)],[40])).
% 0.23/0.46  tff(42,plain,
% 0.23/0.46      (^[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)))))),
% 0.23/0.46      inference(bind,[status(th)],[])).
% 0.23/0.46  tff(43,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(quant_intro,[status(thm)],[42])).
% 0.23/0.46  tff(44,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(rewrite,[status(thm)],[])).
% 0.23/0.46  tff(45,plain,
% 0.23/0.46      (^[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))))),
% 0.23/0.46      inference(bind,[status(th)],[])).
% 0.23/0.46  tff(46,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(quant_intro,[status(thm)],[45])).
% 0.23/0.46  tff(47,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/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.23/0.46  tff(48,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.46  tff(49,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(modus_ponens,[status(thm)],[48, 44])).
% 0.23/0.46  tff(50,plain,(
% 0.23/0.46      ![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)))),
% 0.23/0.46      inference(skolemize,[status(sab)],[49])).
% 0.23/0.46  tff(51,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(modus_ponens,[status(thm)],[50, 43])).
% 0.23/0.46  tff(52,plain,
% 0.23/0.46      (![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)))),
% 0.23/0.46      inference(modus_ponens,[status(thm)],[51, 41])).
% 0.23/0.46  tff(53,plain,
% 0.23/0.46      (((~![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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.46      inference(rewrite,[status(thm)],[])).
% 0.23/0.46  tff(54,plain,
% 0.23/0.46      (((apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.47      inference(rewrite,[status(thm)],[])).
% 0.23/0.47  tff(55,plain,
% 0.23/0.47      (((~![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!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.47      inference(monotonicity,[status(thm)],[54])).
% 0.23/0.47  tff(56,plain,
% 0.23/0.47      (((~![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!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.47      inference(transitivity,[status(thm)],[55, 53])).
% 0.23/0.47  tff(57,plain,
% 0.23/0.47      ((~![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!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)))),
% 0.23/0.47      inference(quant_inst,[status(thm)],[])).
% 0.23/0.47  tff(58,plain,
% 0.23/0.47      ((~![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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.47      inference(modus_ponens,[status(thm)],[57, 56])).
% 0.23/0.47  tff(59,plain,
% 0.23/0.47      (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.47      inference(unit_resolution,[status(thm)],[58, 52, 39, 37])).
% 0.23/0.47  tff(60,plain,
% 0.23/0.47      (((~![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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.47      inference(rewrite,[status(thm)],[])).
% 0.23/0.47  tff(61,plain,
% 0.23/0.47      (((apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.48      inference(rewrite,[status(thm)],[])).
% 0.23/0.48  tff(62,plain,
% 0.23/0.48      (((~![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(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.48      inference(monotonicity,[status(thm)],[61])).
% 0.23/0.48  tff(63,plain,
% 0.23/0.48      (((~![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(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, 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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.48      inference(transitivity,[status(thm)],[62, 60])).
% 0.23/0.48  tff(64,plain,
% 0.23/0.48      ((~![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(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)))),
% 0.23/0.48      inference(quant_inst,[status(thm)],[])).
% 0.23/0.48  tff(65,plain,
% 0.23/0.48      ((~![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(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.48      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.23/0.48  tff(66,plain,
% 0.23/0.48      (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.48      inference(unit_resolution,[status(thm)],[65, 52, 39, 37])).
% 0.23/0.48  tff(67,plain,
% 0.23/0.48      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(68,plain,
% 0.23/0.49      (apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[67, 35])).
% 0.23/0.49  tff(69,plain,
% 0.23/0.49      ((~(apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(70,plain,
% 0.23/0.49      ((~(apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[69, 68])).
% 0.23/0.49  tff(71,plain,
% 0.23/0.49      (apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[70, 66])).
% 0.23/0.49  tff(72,plain,
% 0.23/0.49      ((~(apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(73,plain,
% 0.23/0.49      ((~(apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[72, 71])).
% 0.23/0.49  tff(74,plain,
% 0.23/0.49      (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[73, 59])).
% 0.23/0.49  tff(75,plain,
% 0.23/0.49      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(76,plain,
% 0.23/0.49      (apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[75, 35])).
% 0.23/0.49  tff(77,plain,
% 0.23/0.49      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(78,plain,
% 0.23/0.49      (member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[77, 35])).
% 0.23/0.49  tff(79,plain,
% 0.23/0.49      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40), tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))) | (~(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.49      inference(tautology,[status(thm)],[])).
% 0.23/0.49  tff(80,plain,
% 0.23/0.49      (~(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))),
% 0.23/0.49      inference(unit_resolution,[status(thm)],[79, 35])).
% 0.23/0.49  tff(81,plain,
% 0.23/0.49      (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.23/0.49      inference(bind,[status(th)],[])).
% 0.23/0.49  tff(82,plain,
% 0.23/0.49      (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[81])).
% 0.23/0.50  tff(83,plain,
% 0.23/0.50      (^[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)))))))))),
% 0.23/0.50      inference(bind,[status(th)],[])).
% 0.23/0.50  tff(84,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[83])).
% 0.23/0.50  tff(85,plain,
% 0.23/0.50      (^[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)))))))))),
% 0.23/0.50      inference(bind,[status(th)],[])).
% 0.23/0.50  tff(86,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[85])).
% 0.23/0.50  tff(87,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(transitivity,[status(thm)],[86, 84])).
% 0.23/0.50  tff(88,plain,
% 0.23/0.50      (^[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))))))))))),
% 0.23/0.50      inference(bind,[status(th)],[])).
% 0.23/0.50  tff(89,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[88])).
% 0.23/0.50  tff(90,plain,
% 0.23/0.50      (^[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)))))))),
% 0.23/0.50      inference(bind,[status(th)],[])).
% 0.23/0.50  tff(91,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[90])).
% 0.23/0.50  tff(92,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(rewrite,[status(thm)],[])).
% 0.23/0.50  tff(93,plain,
% 0.23/0.50      (^[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)))))))),
% 0.23/0.50      inference(bind,[status(th)],[])).
% 0.23/0.50  tff(94,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(quant_intro,[status(thm)],[93])).
% 0.23/0.50  tff(95,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.23/0.50  tff(96,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.50  tff(97,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[96, 92])).
% 0.23/0.50  tff(98,plain,(
% 0.23/0.50      ![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))))))))),
% 0.23/0.50      inference(skolemize,[status(sab)],[97])).
% 0.23/0.50  tff(99,plain,
% 0.23/0.50      (![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))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[98, 91])).
% 0.23/0.50  tff(100,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[99, 89])).
% 0.23/0.50  tff(101,plain,
% 0.23/0.50      (![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))))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[100, 87])).
% 0.23/0.50  tff(102,plain,
% 0.23/0.50      (![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))))))))))),
% 0.23/0.50      inference(modus_ponens,[status(thm)],[101, 82])).
% 0.23/0.50  tff(103,plain,
% 0.23/0.50      ((~![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!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))))),
% 0.23/0.50      inference(quant_inst,[status(thm)],[])).
% 0.23/0.50  tff(104,plain,
% 0.23/0.50      (~((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y)))))))))),
% 0.23/0.50      inference(unit_resolution,[status(thm)],[103, 102])).
% 0.23/0.50  tff(105,plain,
% 0.23/0.50      (((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!41, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!41) = tptp_fun_Y2_5(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y1_6(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X_7(B!39, A!40, F!41), tptp_fun_Y2_5(B!39, A!40, F!41))) | (~member(tptp_fun_X_7(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!41), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!41), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!41, tptp_fun_X_4(B!39, A!40, F!41), Y))))))))) | ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.23/0.51      inference(tautology,[status(thm)],[])).
% 0.23/0.51  tff(106,plain,
% 0.23/0.51      ((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.23/0.51      inference(unit_resolution,[status(thm)],[105, 104])).
% 0.23/0.51  tff(107,plain,
% 0.23/0.51      (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.23/0.51      inference(or_elim,[status(thm)],[31])).
% 0.23/0.51  tff(108,plain,
% 0.23/0.51      (maps(F!41, A!40, B!39)),
% 0.23/0.51      inference(and_elim,[status(thm)],[107])).
% 0.23/0.51  tff(109,plain,
% 0.23/0.51      ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.23/0.51      inference(tautology,[status(thm)],[])).
% 0.23/0.51  tff(110,plain,
% 0.23/0.51      ((~((~maps(F!41, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, 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!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.23/0.51      inference(unit_resolution,[status(thm)],[109, 108])).
% 0.23/0.51  tff(111,plain,
% 0.23/0.51      (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.23/0.51      inference(unit_resolution,[status(thm)],[110, 106])).
% 0.23/0.51  tff(112,plain,
% 0.23/0.51      (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!41), B!39)) | (~apply(F!41, X, tptp_fun_Y_3(X, B!39, F!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.23/0.51      inference(tautology,[status(thm)],[])).
% 0.23/0.51  tff(113,plain,
% 0.23/0.51      (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.23/0.51      inference(unit_resolution,[status(thm)],[112, 111])).
% 0.23/0.51  tff(114,plain,
% 0.23/0.51      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.51      inference(rewrite,[status(thm)],[])).
% 0.23/0.51  tff(115,plain,
% 0.23/0.51      (((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39))) <=> ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.51      inference(rewrite,[status(thm)],[])).
% 0.23/0.51  tff(116,plain,
% 0.23/0.51      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))))),
% 0.23/0.51      inference(monotonicity,[status(thm)],[115])).
% 0.23/0.51  tff(117,plain,
% 0.23/0.51      (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))))),
% 0.23/0.52      inference(transitivity,[status(thm)],[116, 114])).
% 0.23/0.52  tff(118,plain,
% 0.23/0.52      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)))),
% 0.23/0.52      inference(quant_inst,[status(thm)],[])).
% 0.23/0.52  tff(119,plain,
% 0.23/0.52      ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!41, X, Y1)) | (~apply(F!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)) = tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))) | (~member(tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), B!39)) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y2_12(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)))) | (~apply(F!41, tptp_fun_X_14(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40)), tptp_fun_Y1_13(B!39, A!40, F!41, inverse_function(inverse_function(F!41, A!40, B!39), B!39, A!40))))),
% 0.23/0.52      inference(modus_ponens,[status(thm)],[118, 117])).
% 0.23/0.52  tff(120,plain,
% 0.23/0.52      ($false),
% 0.23/0.52      inference(unit_resolution,[status(thm)],[119, 113, 80, 39, 37, 78, 76, 74])).
% 0.23/0.52  % SZS output end Proof
%------------------------------------------------------------------------------