TSTP Solution File: SET726+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:46 EDT 2022
% Result : Theorem 0.17s 0.41s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 07:41:18 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.17/0.41 % SZS status Theorem
% 0.17/0.41 % SZS output start Proof
% 0.17/0.41 tff(apply_type, type, (
% 0.17/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.17/0.41 tff(tptp_fun_Y1_13_type, type, (
% 0.17/0.41 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.17/0.41 tff(inverse_function_type, type, (
% 0.17/0.41 inverse_function: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_B_39_type, type, (
% 0.17/0.41 tptp_fun_B_39: $i)).
% 0.17/0.41 tff(tptp_fun_A_40_type, type, (
% 0.17/0.41 tptp_fun_A_40: $i)).
% 0.17/0.41 tff(tptp_fun_F_43_type, type, (
% 0.17/0.41 tptp_fun_F_43: $i)).
% 0.17/0.41 tff(tptp_fun_G_42_type, type, (
% 0.17/0.41 tptp_fun_G_42: $i)).
% 0.17/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.17/0.41 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.17/0.41 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.17/0.41 tff(member_type, type, (
% 0.17/0.41 member: ( $i * $i ) > $o)).
% 0.17/0.41 tff(compose_function_type, type, (
% 0.17/0.41 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_Y2_12_type, type, (
% 0.17/0.41 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_X_14_type, type, (
% 0.17/0.41 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.17/0.41 tff(equal_maps_type, type, (
% 0.17/0.41 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.17/0.41 tff(identity_type, type, (
% 0.17/0.41 identity: ( $i * $i ) > $o)).
% 0.17/0.41 tff(tptp_fun_H_41_type, type, (
% 0.17/0.41 tptp_fun_H_41: $i)).
% 0.17/0.41 tff(maps_type, type, (
% 0.17/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.17/0.41 tff(tptp_fun_X_15_type, type, (
% 0.17/0.41 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_X_4_type, type, (
% 0.17/0.41 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_Y2_5_type, type, (
% 0.17/0.41 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_Y1_6_type, type, (
% 0.17/0.41 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(tptp_fun_X_7_type, type, (
% 0.17/0.41 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.17/0.41 tff(1,plain,
% 0.17/0.41 (^[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))))))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(2,plain,
% 0.17/0.41 (![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)))))))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.41 tff(3,plain,
% 0.17/0.41 (^[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))))))))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(4,plain,
% 0.17/0.41 (![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)))))))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.41 tff(5,plain,
% 0.17/0.41 (![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)))))))))),
% 0.17/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.17/0.41 tff(6,plain,
% 0.17/0.41 (^[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)))))))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(7,plain,
% 0.17/0.42 (![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)))))))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.42 tff(8,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(9,plain,
% 0.17/0.42 (^[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))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(10,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.17/0.42 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')).
% 0.17/0.42 tff(12,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.17/0.42 tff(13,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.17/0.42 tff(14,plain,(
% 0.17/0.42 ![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))))))))),
% 0.17/0.42 inference(skolemize,[status(sab)],[13])).
% 0.17/0.42 tff(15,plain,
% 0.17/0.42 (![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)))))))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.17/0.42 tff(16,plain,
% 0.17/0.42 (![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)))))))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.17/0.42 tff(17,plain,
% 0.17/0.42 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(18,plain,
% 0.17/0.42 ((~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))) <=> (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(19,plain,
% 0.17/0.43 (((~![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)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.17/0.43 tff(20,plain,
% 0.17/0.43 (((~![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)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.17/0.43 inference(transitivity,[status(thm)],[19, 17])).
% 0.17/0.43 tff(21,plain,
% 0.17/0.43 ((~![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)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(22,plain,
% 0.17/0.44 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.17/0.44 tff(23,plain,
% 0.17/0.44 (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.17/0.44 tff(24,plain,
% 0.17/0.44 (((~((~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))) | (equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(25,plain,
% 0.17/0.44 (equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.17/0.44 tff(26,plain,
% 0.17/0.44 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(27,plain,
% 0.17/0.44 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), G, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(28,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), G, B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII17')).
% 0.17/0.44 tff(29,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.17/0.44 tff(30,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.17/0.44 tff(31,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.17/0.44 tff(32,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.17/0.44 tff(33,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.17/0.44 tff(34,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.17/0.44 tff(35,plain,
% 0.17/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), G, B, A))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.17/0.44 tff(36,plain,(
% 0.17/0.44 ~((~(maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39))) | equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40))),
% 0.17/0.44 inference(skolemize,[status(sab)],[35])).
% 0.17/0.44 tff(37,plain,
% 0.17/0.44 (~equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40)),
% 0.17/0.44 inference(or_elim,[status(thm)],[36])).
% 0.17/0.44 tff(38,plain,
% 0.17/0.44 ((~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.44 inference(tautology,[status(thm)],[])).
% 0.17/0.44 tff(39,plain,
% 0.17/0.44 ((~(equal_maps(inverse_function(F!43, A!40, B!39), G!42, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.17/0.45 tff(40,plain,
% 0.17/0.45 (~((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.17/0.45 tff(41,plain,
% 0.17/0.45 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.17/0.45 inference(tautology,[status(thm)],[])).
% 0.17/0.45 tff(42,plain,
% 0.17/0.45 (member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.17/0.45 tff(43,plain,
% 0.17/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(44,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.17/0.45 tff(45,plain,
% 0.17/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(46,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[45])).
% 0.17/0.45 tff(47,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.45 inference(transitivity,[status(thm)],[46, 44])).
% 0.17/0.45 tff(48,plain,
% 0.17/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(49,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.17/0.45 tff(50,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(51,plain,
% 0.17/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(52,plain,
% 0.17/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.17/0.45 tff(53,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.17/0.46 tff(54,plain,
% 0.17/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.17/0.46 tff(55,plain,
% 0.17/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.17/0.46 tff(56,plain,(
% 0.17/0.46 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.17/0.46 inference(skolemize,[status(sab)],[55])).
% 0.17/0.46 tff(57,plain,
% 0.17/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.17/0.46 tff(58,plain,
% 0.17/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.17/0.46 tff(59,plain,
% 0.17/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(60,plain,
% 0.17/0.46 (((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(61,plain,
% 0.17/0.47 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(62,plain,
% 0.17/0.47 (((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.17/0.47 tff(63,plain,
% 0.17/0.47 (((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.47 inference(transitivity,[status(thm)],[62, 60])).
% 0.17/0.47 tff(64,plain,
% 0.17/0.47 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.17/0.48 inference(monotonicity,[status(thm)],[63])).
% 0.17/0.48 tff(65,plain,
% 0.17/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[64, 59])).
% 0.17/0.48 tff(66,plain,
% 0.17/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(67,plain,
% 0.17/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.17/0.48 tff(68,plain,
% 0.17/0.48 (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[67, 58, 42])).
% 0.17/0.48 tff(69,plain,
% 0.17/0.48 (((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(70,plain,
% 0.17/0.48 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.17/0.48 tff(71,plain,
% 0.17/0.48 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(72,plain,
% 0.17/0.48 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[71])).
% 0.17/0.48 tff(73,plain,
% 0.17/0.48 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(74,plain,
% 0.17/0.48 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[73])).
% 0.17/0.48 tff(75,plain,
% 0.17/0.48 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[74, 72])).
% 0.17/0.48 tff(76,plain,
% 0.17/0.48 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(77,plain,
% 0.17/0.49 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.17/0.49 tff(78,plain,
% 0.17/0.49 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(79,plain,
% 0.17/0.49 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(80,plain,
% 0.17/0.49 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[79])).
% 0.17/0.49 tff(81,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','identity')).
% 0.17/0.49 tff(82,plain,
% 0.17/0.49 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.17/0.49 tff(83,plain,
% 0.17/0.49 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.17/0.49 tff(84,plain,(
% 0.17/0.49 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.17/0.49 inference(skolemize,[status(sab)],[83])).
% 0.17/0.49 tff(85,plain,
% 0.17/0.49 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.17/0.49 tff(86,plain,
% 0.17/0.49 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.17/0.49 tff(87,plain,
% 0.17/0.49 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(88,plain,
% 0.17/0.49 (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40))))))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.17/0.49 tff(89,plain,
% 0.17/0.49 (((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(90,plain,
% 0.17/0.49 ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.17/0.49 tff(91,plain,
% 0.17/0.49 (maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.17/0.49 inference(or_elim,[status(thm)],[36])).
% 0.17/0.49 tff(92,plain,
% 0.17/0.49 (identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)),
% 0.17/0.49 inference(and_elim,[status(thm)],[91])).
% 0.17/0.49 tff(93,plain,
% 0.17/0.49 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(94,plain,
% 0.17/0.49 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.17/0.49 tff(95,plain,
% 0.17/0.49 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.17/0.49 tff(96,plain,
% 0.17/0.49 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(97,plain,
% 0.17/0.49 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(98,plain,
% 0.17/0.49 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.17/0.49 tff(99,plain,
% 0.17/0.49 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[98, 42, 95])).
% 0.17/0.49 tff(100,plain,
% 0.17/0.49 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(101,plain,
% 0.17/0.49 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.17/0.50 tff(102,plain,
% 0.17/0.50 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[101, 70])).
% 0.17/0.50 tff(103,plain,
% 0.17/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.17/0.50 inference(tautology,[status(thm)],[])).
% 0.17/0.50 tff(104,plain,
% 0.17/0.50 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.17/0.50 tff(105,plain,
% 0.17/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.17/0.50 inference(tautology,[status(thm)],[])).
% 0.17/0.50 tff(106,plain,
% 0.17/0.50 (member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.17/0.50 tff(107,plain,
% 0.17/0.50 (^[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)))))))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(108,plain,
% 0.17/0.50 (![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))))))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.50 tff(109,plain,
% 0.17/0.50 (^[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)))))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(110,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.17/0.50 tff(111,plain,
% 0.17/0.50 (^[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)))))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(112,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[111])).
% 0.17/0.50 tff(113,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(transitivity,[status(thm)],[112, 110])).
% 0.17/0.50 tff(114,plain,
% 0.17/0.50 (^[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))))))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(115,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[114])).
% 0.17/0.50 tff(116,plain,
% 0.17/0.50 (^[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)))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(117,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[116])).
% 0.17/0.50 tff(118,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(119,plain,
% 0.17/0.50 (^[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)))))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(120,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[119])).
% 0.17/0.50 tff(121,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.17/0.50 tff(122,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.17/0.50 tff(123,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.17/0.50 tff(124,plain,(
% 0.17/0.50 ![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))))))))),
% 0.17/0.50 inference(skolemize,[status(sab)],[123])).
% 0.17/0.50 tff(125,plain,
% 0.17/0.50 (![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))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.17/0.50 tff(126,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.17/0.50 tff(127,plain,
% 0.17/0.50 (![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))))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[126, 113])).
% 0.17/0.50 tff(128,plain,
% 0.17/0.50 (![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))))))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[127, 108])).
% 0.17/0.50 tff(129,plain,
% 0.17/0.50 ((~![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!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))),
% 0.17/0.51 inference(quant_inst,[status(thm)],[])).
% 0.17/0.51 tff(130,plain,
% 0.17/0.51 (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.17/0.51 tff(131,plain,
% 0.17/0.51 (((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))) | ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(132,plain,
% 0.17/0.51 ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.17/0.51 tff(133,plain,
% 0.17/0.51 (maps(F!43, A!40, B!39)),
% 0.17/0.51 inference(and_elim,[status(thm)],[91])).
% 0.17/0.51 tff(134,plain,
% 0.17/0.51 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(135,plain,
% 0.17/0.51 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.17/0.51 tff(136,plain,
% 0.17/0.51 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.17/0.51 tff(137,plain,
% 0.17/0.51 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(138,plain,
% 0.17/0.51 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.17/0.51 tff(139,plain,
% 0.17/0.51 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.17/0.51 inference(rewrite,[status(thm)],[])).
% 0.17/0.51 tff(140,plain,
% 0.17/0.51 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.17/0.51 inference(quant_inst,[status(thm)],[])).
% 0.17/0.51 tff(141,plain,
% 0.17/0.51 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))))),
% 0.17/0.51 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.17/0.51 tff(142,plain,
% 0.17/0.51 (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[141, 138, 42])).
% 0.17/0.51 tff(143,plain,
% 0.17/0.51 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(144,plain,
% 0.17/0.51 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.17/0.51 tff(145,plain,
% 0.17/0.51 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(146,plain,
% 0.17/0.51 (member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.17/0.51 tff(147,plain,
% 0.17/0.51 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(148,plain,
% 0.17/0.51 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[147, 136])).
% 0.17/0.51 tff(149,plain,
% 0.17/0.51 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.51 inference(rewrite,[status(thm)],[])).
% 0.17/0.51 tff(150,plain,
% 0.17/0.51 (((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.51 inference(rewrite,[status(thm)],[])).
% 0.17/0.51 tff(151,plain,
% 0.17/0.51 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.17/0.52 inference(monotonicity,[status(thm)],[150])).
% 0.17/0.52 tff(152,plain,
% 0.17/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.52 inference(transitivity,[status(thm)],[151, 149])).
% 0.17/0.52 tff(153,plain,
% 0.17/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.17/0.52 inference(quant_inst,[status(thm)],[])).
% 0.17/0.52 tff(154,plain,
% 0.17/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.17/0.52 tff(155,plain,
% 0.17/0.52 (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.17/0.52 inference(unit_resolution,[status(thm)],[154, 148, 42, 146, 144, 106, 104])).
% 0.17/0.52 tff(156,plain,
% 0.17/0.52 (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42)),
% 0.17/0.52 inference(symmetry,[status(thm)],[155])).
% 0.17/0.52 tff(157,plain,
% 0.17/0.52 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.52 inference(monotonicity,[status(thm)],[156])).
% 0.17/0.52 tff(158,plain,
% 0.17/0.52 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.52 inference(symmetry,[status(thm)],[157])).
% 0.17/0.52 tff(159,plain,
% 0.17/0.52 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.52 inference(tautology,[status(thm)],[])).
% 0.17/0.52 tff(160,plain,
% 0.17/0.52 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.52 inference(unit_resolution,[status(thm)],[159, 102])).
% 0.17/0.52 tff(161,plain,
% 0.17/0.52 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.17/0.52 tff(162,plain,
% 0.17/0.52 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.17/0.52 inference(tautology,[status(thm)],[])).
% 0.17/0.52 tff(163,plain,
% 0.17/0.52 (member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.17/0.52 inference(unit_resolution,[status(thm)],[162, 40])).
% 0.17/0.52 tff(164,plain,
% 0.17/0.52 (^[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))))),
% 0.17/0.52 inference(bind,[status(th)],[])).
% 0.17/0.52 tff(165,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(quant_intro,[status(thm)],[164])).
% 0.17/0.52 tff(166,plain,
% 0.17/0.52 (^[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)))))),
% 0.17/0.52 inference(bind,[status(th)],[])).
% 0.17/0.52 tff(167,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(quant_intro,[status(thm)],[166])).
% 0.17/0.52 tff(168,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(rewrite,[status(thm)],[])).
% 0.17/0.52 tff(169,plain,
% 0.17/0.52 (^[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))))),
% 0.17/0.52 inference(bind,[status(th)],[])).
% 0.17/0.52 tff(170,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(quant_intro,[status(thm)],[169])).
% 0.17/0.52 tff(171,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')).
% 0.17/0.52 tff(172,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.17/0.52 tff(173,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.17/0.52 tff(174,plain,(
% 0.17/0.52 ![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)))),
% 0.17/0.52 inference(skolemize,[status(sab)],[173])).
% 0.17/0.52 tff(175,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.17/0.52 tff(176,plain,
% 0.17/0.52 (![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)))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.17/0.52 tff(177,plain,
% 0.17/0.52 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.17/0.53 inference(rewrite,[status(thm)],[])).
% 0.17/0.53 tff(178,plain,
% 0.17/0.53 (((apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.17/0.53 inference(rewrite,[status(thm)],[])).
% 0.17/0.53 tff(179,plain,
% 0.17/0.53 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.17/0.53 inference(monotonicity,[status(thm)],[178])).
% 0.17/0.53 tff(180,plain,
% 0.17/0.53 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.17/0.53 inference(transitivity,[status(thm)],[179, 177])).
% 0.17/0.53 tff(181,plain,
% 0.17/0.53 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.17/0.53 inference(quant_inst,[status(thm)],[])).
% 0.17/0.53 tff(182,plain,
% 0.17/0.53 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.17/0.53 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.17/0.53 tff(183,plain,
% 0.17/0.53 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.53 inference(unit_resolution,[status(thm)],[182, 176, 163, 42])).
% 0.17/0.53 tff(184,plain,
% 0.17/0.53 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.53 inference(tautology,[status(thm)],[])).
% 0.17/0.53 tff(185,plain,
% 0.17/0.53 (apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.53 inference(unit_resolution,[status(thm)],[184, 40])).
% 0.17/0.53 tff(186,plain,
% 0.17/0.53 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.17/0.53 inference(tautology,[status(thm)],[])).
% 0.17/0.53 tff(187,plain,
% 0.17/0.53 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.53 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.17/0.53 tff(188,plain,
% 0.17/0.53 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.53 inference(unit_resolution,[status(thm)],[187, 183])).
% 0.17/0.53 tff(189,plain,
% 0.17/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.53 inference(rewrite,[status(thm)],[])).
% 0.17/0.53 tff(190,plain,
% 0.17/0.53 (((tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39))) <=> ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.54 inference(rewrite,[status(thm)],[])).
% 0.17/0.54 tff(191,plain,
% 0.17/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.17/0.54 inference(monotonicity,[status(thm)],[190])).
% 0.17/0.54 tff(192,plain,
% 0.17/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.17/0.54 inference(transitivity,[status(thm)],[191, 189])).
% 0.17/0.54 tff(193,plain,
% 0.17/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)))),
% 0.17/0.54 inference(quant_inst,[status(thm)],[])).
% 0.17/0.54 tff(194,plain,
% 0.17/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.17/0.54 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.17/0.54 tff(195,plain,
% 0.17/0.54 (tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.17/0.54 inference(unit_resolution,[status(thm)],[194, 148, 163, 42, 188, 146, 144])).
% 0.17/0.54 tff(196,plain,
% 0.17/0.54 (tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))),
% 0.17/0.54 inference(symmetry,[status(thm)],[195])).
% 0.17/0.54 tff(197,plain,
% 0.17/0.54 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(monotonicity,[status(thm)],[196])).
% 0.17/0.54 tff(198,plain,
% 0.17/0.54 (apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(symmetry,[status(thm)],[197])).
% 0.17/0.54 tff(199,plain,
% 0.17/0.54 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(tautology,[status(thm)],[])).
% 0.17/0.54 tff(200,plain,
% 0.17/0.54 (apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(unit_resolution,[status(thm)],[199, 40])).
% 0.17/0.54 tff(201,plain,
% 0.17/0.54 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(modus_ponens,[status(thm)],[200, 198])).
% 0.17/0.54 tff(202,plain,
% 0.17/0.54 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.17/0.54 inference(tautology,[status(thm)],[])).
% 0.17/0.54 tff(203,plain,
% 0.17/0.54 (member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.17/0.54 inference(unit_resolution,[status(thm)],[202, 40])).
% 0.17/0.54 tff(204,plain,
% 0.17/0.54 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))) | (~(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.17/0.54 inference(tautology,[status(thm)],[])).
% 0.17/0.54 tff(205,plain,
% 0.17/0.54 (~(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))),
% 0.17/0.54 inference(unit_resolution,[status(thm)],[204, 40])).
% 0.17/0.54 tff(206,plain,
% 0.17/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.17/0.55 inference(rewrite,[status(thm)],[])).
% 0.17/0.55 tff(207,plain,
% 0.17/0.55 ((~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))))) <=> (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(208,plain,
% 0.40/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[207])).
% 0.40/0.55 tff(209,plain,
% 0.40/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.40/0.55 inference(transitivity,[status(thm)],[208, 206])).
% 0.40/0.55 tff(210,plain,
% 0.40/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(211,plain,
% 0.40/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.40/0.55 tff(212,plain,
% 0.40/0.55 (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[211, 128])).
% 0.40/0.55 tff(213,plain,
% 0.40/0.55 (((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))) | ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(214,plain,
% 0.40/0.55 ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.40/0.55 tff(215,plain,
% 0.40/0.55 (maps(G!42, B!39, A!40)),
% 0.40/0.55 inference(and_elim,[status(thm)],[91])).
% 0.40/0.55 tff(216,plain,
% 0.40/0.55 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(217,plain,
% 0.40/0.55 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.40/0.55 tff(218,plain,
% 0.40/0.55 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[217, 214])).
% 0.40/0.55 tff(219,plain,
% 0.40/0.55 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(220,plain,
% 0.40/0.55 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.40/0.55 tff(221,plain,
% 0.40/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(222,plain,
% 0.40/0.56 (((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(223,plain,
% 0.40/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[222])).
% 0.40/0.56 tff(224,plain,
% 0.40/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))))),
% 0.40/0.56 inference(transitivity,[status(thm)],[223, 221])).
% 0.40/0.56 tff(225,plain,
% 0.40/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.42/0.56 inference(quant_inst,[status(thm)],[])).
% 0.42/0.56 tff(226,plain,
% 0.42/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.42/0.56 tff(227,plain,
% 0.42/0.56 ((~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y1_13(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, G!42, inverse_function(F!43, A!40, B!39))))),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[226, 220, 205, 42, 203, 146])).
% 0.42/0.56 tff(228,plain,
% 0.42/0.56 ($false),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[227, 201, 161])).
% 0.42/0.56 % SZS output end Proof
%------------------------------------------------------------------------------