TSTP Solution File: SET735+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET735+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 05:07:48 EDT 2022
% Result : Theorem 0.50s 0.54s
% Output : Proof 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET735+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:34:54 EDT 2022
% 0.12/0.33 % 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.
% 0.50/0.54 % SZS status Theorem
% 0.50/0.54 % SZS output start Proof
% 0.50/0.54 tff(tptp_fun_Y2_12_type, type, (
% 0.50/0.54 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_F1_43_type, type, (
% 0.50/0.54 tptp_fun_F1_43: $i)).
% 0.50/0.54 tff(tptp_fun_F2_42_type, type, (
% 0.50/0.54 tptp_fun_F2_42: $i)).
% 0.50/0.54 tff(tptp_fun_A_40_type, type, (
% 0.50/0.54 tptp_fun_A_40: $i)).
% 0.50/0.54 tff(tptp_fun_B_39_type, type, (
% 0.50/0.54 tptp_fun_B_39: $i)).
% 0.50/0.54 tff(tptp_fun_Y1_13_type, type, (
% 0.50/0.54 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_Y_3_type, type, (
% 0.50/0.54 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_X_14_type, type, (
% 0.50/0.54 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.50/0.54 tff(apply_type, type, (
% 0.50/0.54 apply: ( $i * $i * $i ) > $o)).
% 0.50/0.54 tff(member_type, type, (
% 0.50/0.54 member: ( $i * $i ) > $o)).
% 0.50/0.54 tff(equal_maps_type, type, (
% 0.50/0.54 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.50/0.54 tff(equal_set_type, type, (
% 0.50/0.54 equal_set: ( $i * $i ) > $o)).
% 0.50/0.54 tff(image3_type, type, (
% 0.50/0.54 image3: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(identity_type, type, (
% 0.50/0.54 identity: ( $i * $i ) > $o)).
% 0.50/0.54 tff(compose_function_type, type, (
% 0.50/0.54 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_G_41_type, type, (
% 0.50/0.54 tptp_fun_G_41: $i)).
% 0.50/0.54 tff(maps_type, type, (
% 0.50/0.54 maps: ( $i * $i * $i ) > $o)).
% 0.50/0.54 tff(tptp_fun_X_4_type, type, (
% 0.50/0.54 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_Y2_5_type, type, (
% 0.50/0.54 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_Y1_6_type, type, (
% 0.50/0.54 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_X_7_type, type, (
% 0.50/0.54 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_Y_8_type, type, (
% 0.50/0.54 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_X_15_type, type, (
% 0.50/0.54 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_X_24_type, type, (
% 0.50/0.54 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(tptp_fun_Y_26_type, type, (
% 0.50/0.54 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(inverse_image3_type, type, (
% 0.50/0.54 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.50/0.54 tff(subset_type, type, (
% 0.50/0.54 subset: ( $i * $i ) > $o)).
% 0.50/0.54 tff(tptp_fun_X_0_type, type, (
% 0.50/0.54 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.50/0.54 tff(1,plain,
% 0.50/0.54 (^[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))))))))))),
% 0.50/0.54 inference(bind,[status(th)],[])).
% 0.50/0.54 tff(2,plain,
% 0.50/0.54 (![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)))))))))),
% 0.50/0.54 inference(quant_intro,[status(thm)],[1])).
% 0.50/0.54 tff(3,plain,
% 0.50/0.54 (^[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))))))))))),
% 0.50/0.54 inference(bind,[status(th)],[])).
% 0.50/0.54 tff(4,plain,
% 0.50/0.54 (![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)))))))))),
% 0.50/0.54 inference(quant_intro,[status(thm)],[3])).
% 0.50/0.54 tff(5,plain,
% 0.50/0.54 (![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)))))))))),
% 0.50/0.54 inference(transitivity,[status(thm)],[4, 2])).
% 0.50/0.54 tff(6,plain,
% 0.50/0.54 (^[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)))))))))))),
% 0.50/0.55 inference(bind,[status(th)],[])).
% 0.50/0.55 tff(7,plain,
% 0.50/0.55 (![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)))))))))),
% 0.50/0.55 inference(quant_intro,[status(thm)],[6])).
% 0.50/0.55 tff(8,plain,
% 0.50/0.55 (![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)))))),
% 0.50/0.55 inference(rewrite,[status(thm)],[])).
% 0.50/0.55 tff(9,plain,
% 0.50/0.55 (^[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))))))),
% 0.50/0.55 inference(bind,[status(th)],[])).
% 0.50/0.55 tff(10,plain,
% 0.50/0.55 (![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)))))),
% 0.50/0.55 inference(quant_intro,[status(thm)],[9])).
% 0.50/0.55 tff(11,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.50/0.55 tff(12,plain,
% 0.50/0.55 (![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)))))),
% 0.50/0.55 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.50/0.55 tff(13,plain,
% 0.50/0.55 (![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)))))),
% 0.50/0.55 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.50/0.55 tff(14,plain,(
% 0.50/0.55 ![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))))))))),
% 0.50/0.55 inference(skolemize,[status(sab)],[13])).
% 0.50/0.55 tff(15,plain,
% 0.50/0.55 (![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)))))))))),
% 0.50/0.55 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.50/0.55 tff(16,plain,
% 0.50/0.55 (![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)))))))))),
% 0.50/0.55 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.50/0.55 tff(17,plain,
% 0.50/0.55 (((~![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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))))),
% 0.50/0.55 inference(rewrite,[status(thm)],[])).
% 0.50/0.55 tff(18,plain,
% 0.50/0.55 ((~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))) <=> (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.55 inference(rewrite,[status(thm)],[])).
% 0.50/0.55 tff(19,plain,
% 0.50/0.55 (((~![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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))))),
% 0.50/0.55 inference(monotonicity,[status(thm)],[18])).
% 0.50/0.55 tff(20,plain,
% 0.50/0.55 (((~![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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))))),
% 0.50/0.56 inference(transitivity,[status(thm)],[19, 17])).
% 0.50/0.56 tff(21,plain,
% 0.50/0.56 ((~![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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.56 inference(quant_inst,[status(thm)],[])).
% 0.50/0.56 tff(22,plain,
% 0.50/0.56 ((~![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(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.50/0.56 tff(23,plain,
% 0.50/0.56 (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))),
% 0.50/0.56 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.50/0.56 tff(24,plain,
% 0.50/0.56 (((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))) | (equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))),
% 0.50/0.56 inference(tautology,[status(thm)],[])).
% 0.50/0.56 tff(25,plain,
% 0.50/0.56 (equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.56 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.50/0.56 tff(26,plain,
% 0.50/0.56 ((~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))) <=> (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B)))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(27,plain,
% 0.50/0.56 ((~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((((((maps(F1, A, B) & maps(F2, A, B)) & maps(G, B, A)) & identity(compose_function(G, F1, A, B, A), A)) & identity(compose_function(G, F2, A, B, A), A)) & equal_set(image3(F1, A, B), image3(F2, A, B))) => equal_maps(F1, F2, A, B))) <=> (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B)))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(28,axiom,(~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((((((maps(F1, A, B) & maps(F2, A, B)) & maps(G, B, A)) & identity(compose_function(G, F1, A, B, A), A)) & identity(compose_function(G, F2, A, B, A), A)) & equal_set(image3(F1, A, B), image3(F2, A, B))) => equal_maps(F1, F2, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII26')).
% 0.50/0.56 tff(29,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.50/0.56 tff(30,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.50/0.56 tff(31,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.50/0.56 tff(32,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.50/0.56 tff(33,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.50/0.56 tff(34,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.50/0.56 tff(35,plain,
% 0.50/0.56 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.50/0.56 tff(36,plain,(
% 0.50/0.56 ~((~(maps(F1!43, A!40, B!39) & maps(F2!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) & identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) & equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)))) | equal_maps(F1!43, F2!42, A!40, B!39))),
% 0.50/0.56 inference(skolemize,[status(sab)],[35])).
% 0.50/0.56 tff(37,plain,
% 0.50/0.56 (~equal_maps(F1!43, F2!42, A!40, B!39)),
% 0.50/0.56 inference(or_elim,[status(thm)],[36])).
% 0.50/0.56 tff(38,plain,
% 0.50/0.56 ((~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))) | equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.56 inference(tautology,[status(thm)],[])).
% 0.50/0.56 tff(39,plain,
% 0.50/0.56 ((~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.56 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.50/0.56 tff(40,plain,
% 0.50/0.56 (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 0.50/0.56 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.50/0.56 tff(41,plain,
% 0.50/0.56 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)),
% 0.50/0.56 inference(tautology,[status(thm)],[])).
% 0.50/0.56 tff(42,plain,
% 0.50/0.56 (member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)),
% 0.50/0.56 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.50/0.56 tff(43,plain,
% 0.50/0.56 (^[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)))))))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(44,plain,
% 0.50/0.56 (![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))))))))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[43])).
% 0.50/0.56 tff(45,plain,
% 0.50/0.56 (^[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)))))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(46,plain,
% 0.50/0.56 (![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))))))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[45])).
% 0.50/0.56 tff(47,plain,
% 0.50/0.56 (^[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)))))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(48,plain,
% 0.50/0.56 (![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))))))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[47])).
% 0.50/0.56 tff(49,plain,
% 0.50/0.56 (![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))))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[48, 46])).
% 0.50/0.57 tff(50,plain,
% 0.50/0.57 (^[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))))))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(51,plain,
% 0.50/0.57 (![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))))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[50])).
% 0.50/0.57 tff(52,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(53,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[52])).
% 0.50/0.57 tff(54,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(55,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(56,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[55])).
% 0.50/0.57 tff(57,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.50/0.57 tff(58,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.50/0.57 tff(59,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.50/0.57 tff(60,plain,(
% 0.50/0.57 ![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))))))))),
% 0.50/0.57 inference(skolemize,[status(sab)],[59])).
% 0.50/0.57 tff(61,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.50/0.57 tff(62,plain,
% 0.50/0.57 (![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))))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.50/0.57 tff(63,plain,
% 0.50/0.57 (![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))))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.50/0.57 tff(64,plain,
% 0.50/0.57 (![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))))))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[63, 44])).
% 0.50/0.57 tff(65,plain,
% 0.50/0.57 (((~![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(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(66,plain,
% 0.50/0.57 ((~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))))) <=> (~((~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(67,plain,
% 0.50/0.57 (((~![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(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!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(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[66])).
% 0.50/0.58 tff(68,plain,
% 0.50/0.58 (((~![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(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!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(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[67, 65])).
% 0.50/0.58 tff(69,plain,
% 0.50/0.58 ((~![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(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y))))))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(70,plain,
% 0.50/0.58 ((~![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(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.50/0.58 tff(71,plain,
% 0.50/0.58 (~((~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.50/0.58 tff(72,plain,
% 0.50/0.58 (((~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))) | (~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))))) | ((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(73,plain,
% 0.50/0.58 ((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.50/0.58 tff(74,plain,
% 0.50/0.58 (maps(F1!43, A!40, B!39) & maps(F2!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) & identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) & equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 0.50/0.58 inference(or_elim,[status(thm)],[36])).
% 0.50/0.58 tff(75,plain,
% 0.50/0.58 (maps(F2!42, A!40, B!39)),
% 0.50/0.58 inference(and_elim,[status(thm)],[74])).
% 0.50/0.58 tff(76,plain,
% 0.50/0.58 ((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(77,plain,
% 0.50/0.58 ((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.50/0.58 tff(78,plain,
% 0.50/0.58 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.50/0.58 tff(79,plain,
% 0.50/0.58 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(80,plain,
% 0.50/0.58 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.50/0.58 tff(81,plain,
% 0.50/0.58 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(82,plain,
% 0.50/0.58 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(83,plain,
% 0.50/0.58 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.50/0.58 tff(84,plain,
% 0.50/0.58 (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[83, 80, 42])).
% 0.50/0.58 tff(85,plain,
% 0.50/0.58 (((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))) | apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(86,plain,
% 0.50/0.58 (apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.50/0.58 tff(87,plain,
% 0.50/0.58 (((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))) | member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(88,plain,
% 0.50/0.59 (member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.50/0.59 tff(89,plain,
% 0.50/0.59 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(90,plain,
% 0.50/0.59 (apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[89, 40])).
% 0.50/0.59 tff(91,plain,
% 0.50/0.59 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(92,plain,
% 0.50/0.59 (member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[91, 40])).
% 0.50/0.59 tff(93,plain,
% 0.50/0.59 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(94,plain,
% 0.50/0.59 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[93, 78])).
% 0.50/0.59 tff(95,plain,
% 0.50/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(96,plain,
% 0.50/0.59 (((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(97,plain,
% 0.50/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[96])).
% 0.50/0.59 tff(98,plain,
% 0.50/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[97, 95])).
% 0.50/0.59 tff(99,plain,
% 0.50/0.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(100,plain,
% 0.50/0.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.50/0.59 tff(101,plain,
% 0.50/0.59 (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[100, 94, 42, 92, 90, 88, 86])).
% 0.50/0.59 tff(102,plain,
% 0.50/0.59 (^[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)))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(103,plain,
% 0.50/0.59 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[102])).
% 0.50/0.59 tff(104,plain,
% 0.50/0.59 (^[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)))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(105,plain,
% 0.50/0.59 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[104])).
% 0.50/0.59 tff(106,plain,
% 0.50/0.59 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[105, 103])).
% 0.50/0.59 tff(107,plain,
% 0.50/0.59 (^[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))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(108,plain,
% 0.50/0.59 (![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))))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[107])).
% 0.50/0.60 tff(109,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(110,plain,
% 0.50/0.60 (^[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))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(111,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[110])).
% 0.50/0.60 tff(112,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.50/0.60 tff(113,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.50/0.60 tff(114,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.50/0.60 tff(115,plain,(
% 0.50/0.60 ![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))))))),
% 0.50/0.60 inference(skolemize,[status(sab)],[114])).
% 0.50/0.60 tff(116,plain,
% 0.50/0.60 (![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))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.50/0.60 tff(117,plain,
% 0.50/0.60 (![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))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.50/0.60 tff(118,plain,
% 0.50/0.60 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(119,plain,
% 0.50/0.60 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(120,plain,
% 0.50/0.60 ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))) <=> (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(121,plain,
% 0.50/0.60 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[120])).
% 0.50/0.61 tff(122,plain,
% 0.50/0.61 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[121, 119])).
% 0.50/0.61 tff(123,plain,
% 0.50/0.61 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[122])).
% 0.50/0.61 tff(124,plain,
% 0.50/0.61 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.61 inference(transitivity,[status(thm)],[123, 118])).
% 0.50/0.61 tff(125,plain,
% 0.50/0.61 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(126,plain,
% 0.50/0.61 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.50/0.61 tff(127,plain,
% 0.50/0.61 (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[126, 117, 42])).
% 0.50/0.61 tff(128,plain,
% 0.50/0.61 (((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))),
% 0.50/0.61 inference(tautology,[status(thm)],[])).
% 0.50/0.61 tff(129,plain,
% 0.50/0.61 ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.50/0.61 tff(130,plain,
% 0.50/0.61 (^[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)))))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(131,plain,
% 0.50/0.62 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![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))))))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[130])).
% 0.50/0.62 tff(132,plain,
% 0.50/0.62 (^[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)))))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(133,plain,
% 0.50/0.62 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![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))))))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[132])).
% 0.50/0.62 tff(134,plain,
% 0.50/0.62 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![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))))))))),
% 0.50/0.62 inference(transitivity,[status(thm)],[133, 131])).
% 0.50/0.62 tff(135,plain,
% 0.50/0.62 (^[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))))))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(136,plain,
% 0.50/0.62 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![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))))))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[135])).
% 0.50/0.62 tff(137,plain,
% 0.50/0.62 (![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)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(138,plain,
% 0.50/0.62 (^[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))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(139,plain,
% 0.50/0.62 (![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)))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[138])).
% 0.50/0.62 tff(140,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','identity')).
% 0.50/0.62 tff(141,plain,
% 0.50/0.62 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.50/0.62 tff(142,plain,
% 0.50/0.62 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.50/0.62 tff(143,plain,(
% 0.50/0.62 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.50/0.62 inference(skolemize,[status(sab)],[142])).
% 0.50/0.62 tff(144,plain,
% 0.50/0.62 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.50/0.62 tff(145,plain,
% 0.50/0.62 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.50/0.62 tff(146,plain,
% 0.50/0.62 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)))))))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(147,plain,
% 0.50/0.62 (~((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40))))))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.50/0.62 tff(148,plain,
% 0.50/0.62 (((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(149,plain,
% 0.50/0.62 ((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.50/0.62 tff(150,plain,
% 0.50/0.62 (identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)),
% 0.50/0.62 inference(and_elim,[status(thm)],[74])).
% 0.50/0.62 tff(151,plain,
% 0.50/0.62 ((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(152,plain,
% 0.50/0.62 ((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.50/0.62 tff(153,plain,
% 0.50/0.62 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.50/0.62 tff(154,plain,
% 0.50/0.62 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(155,plain,
% 0.50/0.62 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(156,plain,
% 0.50/0.62 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.50/0.62 tff(157,plain,
% 0.50/0.62 (apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[156, 42, 153])).
% 0.50/0.62 tff(158,plain,
% 0.50/0.62 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(159,plain,
% 0.50/0.62 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.50/0.62 tff(160,plain,
% 0.50/0.62 (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[159, 129])).
% 0.50/0.62 tff(161,plain,
% 0.50/0.62 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(162,plain,
% 0.50/0.62 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.50/0.62 tff(163,plain,
% 0.50/0.62 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(164,plain,
% 0.50/0.62 (member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[163, 160])).
% 0.50/0.62 tff(165,plain,
% 0.50/0.62 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(166,plain,
% 0.59/0.63 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[165, 40])).
% 0.59/0.63 tff(167,plain,
% 0.59/0.63 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(168,plain,
% 0.59/0.63 (member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[167, 40])).
% 0.59/0.63 tff(169,plain,
% 0.59/0.63 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y))))))))))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(170,plain,
% 0.59/0.63 (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[169, 64])).
% 0.59/0.63 tff(171,plain,
% 0.59/0.63 (((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y))))))))) | ((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(172,plain,
% 0.59/0.63 ((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.59/0.63 tff(173,plain,
% 0.59/0.63 (maps(F1!43, A!40, B!39)),
% 0.59/0.63 inference(and_elim,[status(thm)],[74])).
% 0.59/0.63 tff(174,plain,
% 0.59/0.63 ((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(175,plain,
% 0.59/0.63 ((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!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, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.59/0.63 tff(176,plain,
% 0.59/0.63 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.59/0.63 tff(177,plain,
% 0.59/0.63 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.59/0.63 inference(tautology,[status(thm)],[])).
% 0.59/0.63 tff(178,plain,
% 0.59/0.63 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.59/0.63 tff(179,plain,
% 0.59/0.63 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(180,plain,
% 0.59/0.63 (((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(181,plain,
% 0.59/0.63 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[180])).
% 0.59/0.64 tff(182,plain,
% 0.59/0.64 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.64 inference(transitivity,[status(thm)],[181, 179])).
% 0.59/0.64 tff(183,plain,
% 0.59/0.64 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(184,plain,
% 0.59/0.64 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.59/0.64 tff(185,plain,
% 0.59/0.64 (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[184, 178, 42, 168, 166, 164, 162])).
% 0.59/0.64 tff(186,plain,
% 0.59/0.64 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41)),
% 0.59/0.64 inference(symmetry,[status(thm)],[185])).
% 0.59/0.64 tff(187,plain,
% 0.59/0.64 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[186])).
% 0.59/0.64 tff(188,plain,
% 0.59/0.64 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) <=> apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(symmetry,[status(thm)],[187])).
% 0.59/0.64 tff(189,plain,
% 0.59/0.64 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(tautology,[status(thm)],[])).
% 0.59/0.64 tff(190,plain,
% 0.59/0.64 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[189, 160])).
% 0.59/0.64 tff(191,plain,
% 0.59/0.64 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[190, 188])).
% 0.59/0.64 tff(192,plain,
% 0.59/0.64 (((~![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!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, 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!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(193,plain,
% 0.59/0.64 ((~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))))) <=> (~((~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(194,plain,
% 0.59/0.64 (((~![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!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[193])).
% 0.59/0.64 tff(195,plain,
% 0.59/0.64 (((~![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!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.59/0.65 inference(transitivity,[status(thm)],[194, 192])).
% 0.59/0.65 tff(196,plain,
% 0.59/0.65 ((~![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!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(197,plain,
% 0.59/0.65 ((~![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!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.59/0.65 tff(198,plain,
% 0.59/0.65 (~((~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[197, 64])).
% 0.59/0.65 tff(199,plain,
% 0.59/0.65 (((~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))) | (~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))) | ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(200,plain,
% 0.59/0.65 ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.59/0.65 tff(201,plain,
% 0.59/0.65 (maps(G!41, B!39, A!40)),
% 0.59/0.65 inference(and_elim,[status(thm)],[74])).
% 0.59/0.65 tff(202,plain,
% 0.59/0.65 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(203,plain,
% 0.59/0.65 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, 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!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.59/0.65 tff(204,plain,
% 0.59/0.65 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.59/0.65 tff(205,plain,
% 0.59/0.65 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, 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!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(206,plain,
% 0.59/0.65 (![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.59/0.65 tff(207,plain,
% 0.59/0.65 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(208,plain,
% 0.59/0.65 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(209,plain,
% 0.59/0.65 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.59/0.65 tff(210,plain,
% 0.59/0.65 (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[209, 206, 168])).
% 0.59/0.65 tff(211,plain,
% 0.59/0.65 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))) | apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(212,plain,
% 0.59/0.65 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.59/0.65 tff(213,plain,
% 0.59/0.65 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(214,plain,
% 0.59/0.65 (member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[213, 210])).
% 0.59/0.65 tff(215,plain,
% 0.59/0.65 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(216,plain,
% 0.59/0.65 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[215, 204])).
% 0.59/0.65 tff(217,plain,
% 0.59/0.65 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(218,plain,
% 0.59/0.66 (((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(219,plain,
% 0.59/0.66 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[218])).
% 0.59/0.66 tff(220,plain,
% 0.59/0.66 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.66 inference(transitivity,[status(thm)],[219, 217])).
% 0.59/0.66 tff(221,plain,
% 0.59/0.66 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(222,plain,
% 0.59/0.66 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.59/0.66 tff(223,plain,
% 0.59/0.66 ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[222, 216, 42, 168, 214, 212])).
% 0.59/0.66 tff(224,plain,
% 0.59/0.66 (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[223, 191])).
% 0.59/0.66 tff(225,plain,
% 0.59/0.66 (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42)),
% 0.59/0.66 inference(monotonicity,[status(thm)],[224])).
% 0.59/0.66 tff(226,plain,
% 0.59/0.66 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)),
% 0.59/0.66 inference(symmetry,[status(thm)],[225])).
% 0.59/0.66 tff(227,plain,
% 0.59/0.66 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(228,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[227])).
% 0.59/0.66 tff(229,plain,
% 0.59/0.66 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(230,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[229])).
% 0.59/0.66 tff(231,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(transitivity,[status(thm)],[230, 228])).
% 0.59/0.66 tff(232,plain,
% 0.59/0.66 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(233,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[232])).
% 0.59/0.66 tff(234,plain,
% 0.59/0.66 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(235,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[234])).
% 0.59/0.66 tff(236,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(237,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','image3')).
% 0.59/0.66 tff(238,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.59/0.66 tff(239,plain,(
% 0.59/0.66 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.59/0.66 inference(skolemize,[status(sab)],[238])).
% 0.59/0.66 tff(240,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.59/0.66 tff(241,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[240, 233])).
% 0.59/0.66 tff(242,plain,
% 0.59/0.66 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[241, 231])).
% 0.59/0.66 tff(243,plain,
% 0.59/0.66 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(244,plain,
% 0.59/0.66 (~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.59/0.66 tff(245,plain,
% 0.59/0.66 (((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))),
% 0.59/0.67 inference(tautology,[status(thm)],[])).
% 0.59/0.67 tff(246,plain,
% 0.59/0.67 ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.59/0.67 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.59/0.67 tff(247,plain,
% 0.59/0.67 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 0.59/0.67 inference(rewrite,[status(thm)],[])).
% 0.59/0.67 tff(248,plain,
% 0.59/0.67 ((~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))) <=> (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 0.59/0.67 inference(rewrite,[status(thm)],[])).
% 0.59/0.67 tff(249,plain,
% 0.59/0.67 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 0.59/0.67 inference(monotonicity,[status(thm)],[248])).
% 0.59/0.67 tff(250,plain,
% 0.59/0.67 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 0.59/0.67 inference(transitivity,[status(thm)],[249, 247])).
% 0.59/0.67 tff(251,plain,
% 0.59/0.67 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 0.59/0.67 inference(quant_inst,[status(thm)],[])).
% 0.59/0.67 tff(252,plain,
% 0.59/0.67 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 0.59/0.67 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.59/0.67 tff(253,plain,
% 0.59/0.67 (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))),
% 0.59/0.67 inference(unit_resolution,[status(thm)],[252, 242])).
% 0.59/0.67 tff(254,plain,
% 0.59/0.67 (((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 0.59/0.68 inference(tautology,[status(thm)],[])).
% 0.59/0.68 tff(255,plain,
% 0.59/0.68 ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.59/0.68 tff(256,plain,
% 0.59/0.68 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_X_14(B!39, A!40, F2!42, F1!43)),
% 0.59/0.68 inference(symmetry,[status(thm)],[224])).
% 0.59/0.68 tff(257,plain,
% 0.59/0.68 (apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) <=> apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.68 inference(monotonicity,[status(thm)],[256])).
% 0.59/0.68 tff(258,plain,
% 0.59/0.68 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) <=> apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.68 inference(symmetry,[status(thm)],[257])).
% 0.59/0.68 tff(259,plain,
% 0.59/0.68 (apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[166, 258])).
% 0.59/0.68 tff(260,assumption,(![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))), introduced(assumption)).
% 0.59/0.68 tff(261,plain,
% 0.59/0.68 (((~![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(rewrite,[status(thm)],[])).
% 0.59/0.68 tff(262,plain,
% 0.59/0.68 ((~![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(quant_inst,[status(thm)],[])).
% 0.59/0.68 tff(263,plain,
% 0.59/0.68 ((~![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.59/0.68 tff(264,plain,
% 0.59/0.68 ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[263, 260])).
% 0.59/0.68 tff(265,plain,
% 0.59/0.68 (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[264, 259])).
% 0.59/0.68 tff(266,plain,
% 0.59/0.68 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(tautology,[status(thm)],[])).
% 0.59/0.68 tff(267,plain,
% 0.59/0.68 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[266, 168, 265])).
% 0.59/0.68 tff(268,plain,
% 0.59/0.68 (![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[267, 255])).
% 0.59/0.68 tff(269,plain,
% 0.59/0.68 (((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(rewrite,[status(thm)],[])).
% 0.59/0.68 tff(270,plain,
% 0.59/0.68 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.59/0.68 inference(quant_inst,[status(thm)],[])).
% 0.59/0.68 tff(271,plain,
% 0.59/0.68 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.59/0.68 tff(272,plain,
% 0.59/0.68 ($false),
% 0.59/0.68 inference(unit_resolution,[status(thm)],[271, 214, 259, 268])).
% 0.59/0.68 tff(273,plain,(~![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.68 tff(274,plain,
% 0.59/0.68 (^[F: $i, B: $i, A: $i, X: $i] : refl((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.59/0.68 inference(bind,[status(th)],[])).
% 0.59/0.68 tff(275,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(quant_intro,[status(thm)],[274])).
% 0.59/0.68 tff(276,plain,
% 0.59/0.68 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.59/0.68 inference(bind,[status(th)],[])).
% 0.59/0.68 tff(277,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(quant_intro,[status(thm)],[276])).
% 0.59/0.68 tff(278,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(transitivity,[status(thm)],[277, 275])).
% 0.59/0.68 tff(279,plain,
% 0.59/0.68 (^[F: $i, B: $i, A: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) <=> ((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, X, Y)) <=> (~((~member(Y, B)) | (~apply(F, X, Y))))), ((~(member(Y, B) & apply(F, X, Y))) <=> (~(~((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, X, Y))))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))), ((~(member(Y, B) & apply(F, X, Y))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, X, Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), rewrite((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.59/0.68 inference(bind,[status(th)],[])).
% 0.59/0.68 tff(280,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(quant_intro,[status(thm)],[279])).
% 0.59/0.68 tff(281,plain,
% 0.59/0.68 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.59/0.68 inference(bind,[status(th)],[])).
% 0.59/0.68 tff(282,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.59/0.68 inference(quant_intro,[status(thm)],[281])).
% 0.59/0.68 tff(283,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))) <=> ![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.59/0.68 inference(rewrite,[status(thm)],[])).
% 0.59/0.68 tff(284,axiom,(![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_image3')).
% 0.59/0.68 tff(285,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.59/0.68 tff(286,plain,(
% 0.59/0.68 ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.59/0.68 inference(skolemize,[status(sab)],[285])).
% 0.59/0.68 tff(287,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.59/0.68 tff(288,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[287, 280])).
% 0.59/0.68 tff(289,plain,
% 0.59/0.68 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.59/0.68 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.59/0.68 tff(290,plain,
% 0.59/0.68 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))))))),
% 0.59/0.68 inference(rewrite,[status(thm)],[])).
% 0.59/0.68 tff(291,plain,
% 0.59/0.68 ((~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))))) <=> (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(292,plain,
% 0.65/0.69 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))))))),
% 0.65/0.69 inference(monotonicity,[status(thm)],[291])).
% 0.65/0.69 tff(293,plain,
% 0.65/0.69 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))))))),
% 0.65/0.69 inference(transitivity,[status(thm)],[292, 290])).
% 0.65/0.69 tff(294,plain,
% 0.65/0.69 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))),
% 0.65/0.69 inference(quant_inst,[status(thm)],[])).
% 0.65/0.69 tff(295,plain,
% 0.65/0.69 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.65/0.69 tff(296,plain,
% 0.65/0.69 (~((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))))),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[295, 289])).
% 0.65/0.69 tff(297,plain,
% 0.65/0.69 (((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))),
% 0.65/0.69 inference(tautology,[status(thm)],[])).
% 0.65/0.69 tff(298,plain,
% 0.65/0.69 ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.65/0.69 tff(299,plain,
% 0.65/0.69 ((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))),
% 0.65/0.69 inference(tautology,[status(thm)],[])).
% 0.65/0.69 tff(300,plain,
% 0.65/0.69 ((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y))))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[299, 214])).
% 0.65/0.69 tff(301,plain,
% 0.65/0.69 (member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[300, 298])).
% 0.65/0.69 tff(302,plain,
% 0.65/0.69 (member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[301, 273])).
% 0.65/0.69 tff(303,plain,
% 0.65/0.69 (((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40)) | ![Y: $i] : ((~member(Y, image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))),
% 0.65/0.69 inference(tautology,[status(thm)],[])).
% 0.65/0.69 tff(304,plain,
% 0.65/0.69 ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[303, 296])).
% 0.65/0.70 tff(305,plain,
% 0.65/0.70 ((~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(306,plain,
% 0.65/0.70 ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), inverse_image3(F1!43, image3(F1!43, A!40, B!39), A!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.65/0.70 tff(307,plain,
% 0.65/0.70 (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[306, 302])).
% 0.65/0.70 tff(308,plain,
% 0.65/0.70 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(309,plain,
% 0.65/0.70 (member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[308, 307])).
% 0.65/0.70 tff(310,plain,
% 0.65/0.70 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(311,plain,
% 0.65/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[310])).
% 0.65/0.70 tff(312,plain,
% 0.65/0.70 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(313,plain,
% 0.65/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[312])).
% 0.65/0.70 tff(314,plain,
% 0.65/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(transitivity,[status(thm)],[313, 311])).
% 0.65/0.70 tff(315,plain,
% 0.65/0.70 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(316,plain,
% 0.65/0.70 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[315])).
% 0.65/0.70 tff(317,plain,
% 0.65/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(318,plain,
% 0.65/0.70 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(319,plain,
% 0.65/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[318])).
% 0.65/0.70 tff(320,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.65/0.70 tff(321,plain,
% 0.65/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.65/0.70 tff(322,plain,
% 0.65/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[321, 317])).
% 0.65/0.70 tff(323,plain,(
% 0.65/0.70 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.65/0.70 inference(skolemize,[status(sab)],[322])).
% 0.65/0.70 tff(324,plain,
% 0.65/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[323, 316])).
% 0.65/0.70 tff(325,plain,
% 0.65/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[324, 314])).
% 0.65/0.70 tff(326,plain,
% 0.65/0.70 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39))))))))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(327,plain,
% 0.65/0.70 (~((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39)))))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[326, 325])).
% 0.65/0.70 tff(328,plain,
% 0.65/0.70 (((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39))))))) | ((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(329,plain,
% 0.65/0.70 ((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.65/0.70 tff(330,plain,
% 0.65/0.70 (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(331,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[330])).
% 0.65/0.70 tff(332,plain,
% 0.65/0.70 (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(333,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[332])).
% 0.65/0.70 tff(334,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(335,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.65/0.70 tff(336,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.65/0.70 tff(337,plain,(
% 0.65/0.70 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.65/0.70 inference(skolemize,[status(sab)],[336])).
% 0.65/0.70 tff(338,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.65/0.70 tff(339,plain,
% 0.65/0.70 (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[338, 331])).
% 0.65/0.70 tff(340,plain,
% 0.65/0.70 ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) <=> (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(341,plain,
% 0.65/0.70 (equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) <=> (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[340, 339])).
% 0.65/0.70 tff(342,plain,
% 0.65/0.70 (equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 0.65/0.70 inference(and_elim,[status(thm)],[74])).
% 0.65/0.70 tff(343,plain,
% 0.65/0.70 ((~(equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) <=> (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))))) | (~equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(344,plain,
% 0.65/0.70 ((~(equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) <=> (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))))) | (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[343, 342])).
% 0.65/0.70 tff(345,plain,
% 0.65/0.70 (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[344, 341])).
% 0.65/0.70 tff(346,plain,
% 0.65/0.70 (((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) | subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(347,plain,
% 0.65/0.70 (subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[346, 345])).
% 0.65/0.70 tff(348,plain,
% 0.65/0.70 ((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 0.65/0.70 inference(tautology,[status(thm)],[])).
% 0.65/0.70 tff(349,plain,
% 0.65/0.70 ((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[348, 347])).
% 0.65/0.71 tff(350,plain,
% 0.65/0.71 (![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[349, 329])).
% 0.65/0.71 tff(351,plain,
% 0.65/0.71 (((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)))) <=> ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(352,plain,
% 0.65/0.71 ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39)))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(353,plain,
% 0.65/0.71 ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.65/0.71 tff(354,plain,
% 0.65/0.71 (member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[353, 350, 309])).
% 0.65/0.71 tff(355,plain,
% 0.65/0.71 ((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.65/0.71 inference(tautology,[status(thm)],[])).
% 0.65/0.71 tff(356,plain,
% 0.65/0.71 ((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[355, 354])).
% 0.65/0.71 tff(357,plain,
% 0.65/0.71 (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[356, 246])).
% 0.65/0.71 tff(358,plain,
% 0.65/0.71 (((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)),
% 0.65/0.71 inference(tautology,[status(thm)],[])).
% 0.65/0.71 tff(359,plain,
% 0.65/0.71 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.65/0.71 tff(360,plain,
% 0.65/0.71 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(361,plain,
% 0.65/0.72 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(362,plain,
% 0.65/0.72 ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))) <=> (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(363,plain,
% 0.65/0.72 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[362])).
% 0.65/0.73 tff(364,plain,
% 0.65/0.73 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.65/0.73 inference(transitivity,[status(thm)],[363, 361])).
% 0.65/0.73 tff(365,plain,
% 0.65/0.73 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[364])).
% 0.65/0.73 tff(366,plain,
% 0.65/0.73 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.65/0.74 inference(transitivity,[status(thm)],[365, 360])).
% 0.65/0.74 tff(367,plain,
% 0.65/0.74 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.65/0.74 inference(quant_inst,[status(thm)],[])).
% 0.65/0.74 tff(368,plain,
% 0.65/0.74 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.65/0.74 tff(369,plain,
% 0.65/0.74 (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))),
% 0.65/0.75 inference(unit_resolution,[status(thm)],[368, 117, 359])).
% 0.65/0.75 tff(370,plain,
% 0.65/0.75 (((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))) | ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))),
% 0.65/0.75 inference(tautology,[status(thm)],[])).
% 0.65/0.75 tff(371,plain,
% 0.65/0.75 ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.65/0.75 inference(unit_resolution,[status(thm)],[370, 369])).
% 0.65/0.75 tff(372,plain,
% 0.65/0.75 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.72/0.75 inference(rewrite,[status(thm)],[])).
% 0.72/0.75 tff(373,plain,
% 0.72/0.75 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.72/0.75 inference(quant_inst,[status(thm)],[])).
% 0.72/0.75 tff(374,plain,
% 0.72/0.75 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.72/0.75 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.72/0.75 tff(375,plain,
% 0.72/0.75 (apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.72/0.75 inference(unit_resolution,[status(thm)],[374, 153, 359])).
% 0.72/0.75 tff(376,plain,
% 0.72/0.75 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.72/0.76 inference(tautology,[status(thm)],[])).
% 0.72/0.76 tff(377,plain,
% 0.72/0.76 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.72/0.76 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.72/0.76 tff(378,plain,
% 0.72/0.76 (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))),
% 0.72/0.76 inference(unit_resolution,[status(thm)],[377, 371])).
% 0.72/0.76 tff(379,plain,
% 0.72/0.76 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))),
% 0.72/0.76 inference(tautology,[status(thm)],[])).
% 0.72/0.76 tff(380,plain,
% 0.72/0.76 (apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))),
% 0.72/0.76 inference(unit_resolution,[status(thm)],[379, 378])).
% 0.72/0.76 tff(381,plain,
% 0.72/0.76 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)),
% 0.72/0.76 inference(tautology,[status(thm)],[])).
% 0.72/0.76 tff(382,plain,
% 0.72/0.76 (member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)),
% 0.72/0.76 inference(unit_resolution,[status(thm)],[381, 378])).
% 0.72/0.76 tff(383,plain,
% 0.72/0.76 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!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, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))),
% 0.72/0.76 inference(tautology,[status(thm)],[])).
% 0.72/0.76 tff(384,plain,
% 0.72/0.76 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))),
% 0.72/0.76 inference(unit_resolution,[status(thm)],[383, 176])).
% 0.72/0.76 tff(385,plain,
% 0.72/0.76 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))))))),
% 0.73/0.77 inference(rewrite,[status(thm)],[])).
% 0.73/0.77 tff(386,plain,
% 0.73/0.77 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))))))),
% 0.73/0.77 inference(quant_inst,[status(thm)],[])).
% 0.73/0.77 tff(387,plain,
% 0.73/0.77 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.73/0.77 tff(388,plain,
% 0.73/0.77 (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[387, 384, 359])).
% 0.73/0.77 tff(389,plain,
% 0.73/0.77 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))) | apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(390,plain,
% 0.73/0.77 (apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[389, 388])).
% 0.73/0.77 tff(391,plain,
% 0.73/0.77 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(392,plain,
% 0.73/0.77 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[391, 388])).
% 0.73/0.77 tff(393,plain,
% 0.73/0.77 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))),
% 0.73/0.77 inference(rewrite,[status(thm)],[])).
% 0.73/0.77 tff(394,plain,
% 0.73/0.77 (((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))),
% 0.73/0.78 inference(rewrite,[status(thm)],[])).
% 0.73/0.78 tff(395,plain,
% 0.73/0.78 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))))),
% 0.73/0.78 inference(monotonicity,[status(thm)],[394])).
% 0.73/0.78 tff(396,plain,
% 0.73/0.78 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)))),
% 0.73/0.78 inference(transitivity,[status(thm)],[395, 393])).
% 0.73/0.78 tff(397,plain,
% 0.73/0.78 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)))),
% 0.73/0.79 inference(quant_inst,[status(thm)],[])).
% 0.73/0.79 tff(398,plain,
% 0.73/0.79 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43))),
% 0.73/0.79 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.73/0.79 tff(399,plain,
% 0.73/0.79 (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43)),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[398, 178, 359, 392, 390, 382, 380])).
% 0.73/0.79 tff(400,plain,
% 0.73/0.79 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43) = tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41)),
% 0.73/0.79 inference(symmetry,[status(thm)],[399])).
% 0.73/0.79 tff(401,plain,
% 0.73/0.79 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.73/0.79 inference(monotonicity,[status(thm)],[400])).
% 0.73/0.79 tff(402,plain,
% 0.73/0.79 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.73/0.79 inference(symmetry,[status(thm)],[401])).
% 0.73/0.79 tff(403,plain,
% 0.73/0.79 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.73/0.79 inference(tautology,[status(thm)],[])).
% 0.73/0.79 tff(404,plain,
% 0.73/0.79 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[403, 378])).
% 0.73/0.79 tff(405,plain,
% 0.73/0.79 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.73/0.79 inference(modus_ponens,[status(thm)],[404, 402])).
% 0.73/0.79 tff(406,plain,
% 0.73/0.79 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))),
% 0.73/0.79 inference(rewrite,[status(thm)],[])).
% 0.73/0.79 tff(407,plain,
% 0.73/0.79 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))),
% 0.73/0.79 inference(quant_inst,[status(thm)],[])).
% 0.73/0.79 tff(408,plain,
% 0.73/0.79 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))))),
% 0.73/0.80 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.73/0.80 tff(409,plain,
% 0.73/0.80 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))),
% 0.73/0.80 inference(unit_resolution,[status(thm)],[408, 206, 392])).
% 0.73/0.80 tff(410,plain,
% 0.73/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))) | apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))),
% 0.73/0.80 inference(tautology,[status(thm)],[])).
% 0.73/0.80 tff(411,plain,
% 0.73/0.80 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))),
% 0.73/0.80 inference(unit_resolution,[status(thm)],[410, 409])).
% 0.73/0.80 tff(412,plain,
% 0.73/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)),
% 0.73/0.80 inference(tautology,[status(thm)],[])).
% 0.73/0.80 tff(413,plain,
% 0.73/0.80 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)),
% 0.73/0.80 inference(unit_resolution,[status(thm)],[412, 409])).
% 0.73/0.80 tff(414,plain,
% 0.73/0.80 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))),
% 0.73/0.80 inference(rewrite,[status(thm)],[])).
% 0.73/0.80 tff(415,plain,
% 0.73/0.80 (((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))),
% 0.73/0.80 inference(rewrite,[status(thm)],[])).
% 0.73/0.80 tff(416,plain,
% 0.73/0.80 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.73/0.81 inference(monotonicity,[status(thm)],[415])).
% 0.73/0.81 tff(417,plain,
% 0.73/0.81 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))),
% 0.77/0.81 inference(transitivity,[status(thm)],[416, 414])).
% 0.77/0.81 tff(418,plain,
% 0.77/0.81 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))),
% 0.77/0.81 inference(quant_inst,[status(thm)],[])).
% 0.77/0.81 tff(419,plain,
% 0.77/0.81 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.77/0.81 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.77/0.81 tff(420,plain,
% 0.77/0.81 ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.77/0.81 inference(unit_resolution,[status(thm)],[419, 216, 359, 392, 413, 411])).
% 0.77/0.81 tff(421,plain,
% 0.77/0.81 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)),
% 0.77/0.81 inference(unit_resolution,[status(thm)],[420, 405])).
% 0.77/0.81 tff(422,plain,
% 0.77/0.81 (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)),
% 0.77/0.81 inference(symmetry,[status(thm)],[421])).
% 0.77/0.81 tff(423,plain,
% 0.77/0.81 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.82 inference(rewrite,[status(thm)],[])).
% 0.77/0.82 tff(424,plain,
% 0.77/0.82 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.82 inference(rewrite,[status(thm)],[])).
% 0.77/0.82 tff(425,plain,
% 0.77/0.82 ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))) <=> (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))),
% 0.77/0.82 inference(rewrite,[status(thm)],[])).
% 0.77/0.82 tff(426,plain,
% 0.77/0.82 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.83 inference(monotonicity,[status(thm)],[425])).
% 0.77/0.83 tff(427,plain,
% 0.77/0.83 (((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.83 inference(transitivity,[status(thm)],[426, 424])).
% 0.77/0.83 tff(428,plain,
% 0.77/0.83 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))))),
% 0.77/0.83 inference(monotonicity,[status(thm)],[427])).
% 0.77/0.83 tff(429,plain,
% 0.77/0.83 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.84 inference(transitivity,[status(thm)],[428, 423])).
% 0.77/0.84 tff(430,plain,
% 0.77/0.84 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))))),
% 0.77/0.84 inference(quant_inst,[status(thm)],[])).
% 0.77/0.84 tff(431,plain,
% 0.77/0.84 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))))),
% 0.77/0.84 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.77/0.84 tff(432,plain,
% 0.77/0.84 (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[431, 117, 359])).
% 0.80/0.84 tff(433,plain,
% 0.80/0.84 (((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | ((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))),
% 0.80/0.84 inference(tautology,[status(thm)],[])).
% 0.80/0.84 tff(434,plain,
% 0.80/0.84 ((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[433, 432])).
% 0.80/0.84 tff(435,plain,
% 0.80/0.84 ((~![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!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)))))))))),
% 0.80/0.84 inference(quant_inst,[status(thm)],[])).
% 0.80/0.84 tff(436,plain,
% 0.80/0.84 (~((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40))))))))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[435, 145])).
% 0.80/0.84 tff(437,plain,
% 0.80/0.84 (((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))),
% 0.80/0.84 inference(tautology,[status(thm)],[])).
% 0.80/0.84 tff(438,plain,
% 0.80/0.84 ((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[437, 436])).
% 0.80/0.84 tff(439,plain,
% 0.80/0.84 (identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)),
% 0.80/0.84 inference(and_elim,[status(thm)],[74])).
% 0.80/0.84 tff(440,plain,
% 0.80/0.84 ((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 0.80/0.84 inference(tautology,[status(thm)],[])).
% 0.80/0.84 tff(441,plain,
% 0.80/0.84 ((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[440, 439])).
% 0.80/0.84 tff(442,plain,
% 0.80/0.84 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 0.80/0.84 inference(unit_resolution,[status(thm)],[441, 438])).
% 0.80/0.84 tff(443,plain,
% 0.80/0.84 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.80/0.85 inference(rewrite,[status(thm)],[])).
% 0.80/0.85 tff(444,plain,
% 0.80/0.85 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))),
% 0.80/0.85 inference(quant_inst,[status(thm)],[])).
% 0.80/0.85 tff(445,plain,
% 0.80/0.85 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.85 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.80/0.85 tff(446,plain,
% 0.80/0.85 (apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.85 inference(unit_resolution,[status(thm)],[445, 442, 359])).
% 0.80/0.85 tff(447,plain,
% 0.80/0.85 ((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.80/0.85 inference(tautology,[status(thm)],[])).
% 0.80/0.85 tff(448,plain,
% 0.80/0.85 ((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))))),
% 0.80/0.85 inference(unit_resolution,[status(thm)],[447, 446])).
% 0.80/0.85 tff(449,plain,
% 0.80/0.85 (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))))),
% 0.80/0.85 inference(unit_resolution,[status(thm)],[448, 434])).
% 0.80/0.85 tff(450,plain,
% 0.80/0.85 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))),
% 0.80/0.85 inference(tautology,[status(thm)],[])).
% 0.80/0.85 tff(451,plain,
% 0.80/0.85 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))),
% 0.80/0.85 inference(unit_resolution,[status(thm)],[450, 449])).
% 0.80/0.85 tff(452,plain,
% 0.80/0.85 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)),
% 0.80/0.85 inference(tautology,[status(thm)],[])).
% 0.80/0.85 tff(453,plain,
% 0.80/0.85 (member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)),
% 0.80/0.85 inference(unit_resolution,[status(thm)],[452, 449])).
% 0.80/0.85 tff(454,plain,
% 0.80/0.85 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))))),
% 0.80/0.86 inference(rewrite,[status(thm)],[])).
% 0.80/0.86 tff(455,plain,
% 0.80/0.86 ((~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))) <=> (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))))),
% 0.80/0.86 inference(rewrite,[status(thm)],[])).
% 0.80/0.86 tff(456,plain,
% 0.80/0.86 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))))),
% 0.80/0.86 inference(monotonicity,[status(thm)],[455])).
% 0.80/0.86 tff(457,plain,
% 0.80/0.86 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))))),
% 0.80/0.86 inference(transitivity,[status(thm)],[456, 454])).
% 0.80/0.86 tff(458,plain,
% 0.80/0.86 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))),
% 0.80/0.86 inference(quant_inst,[status(thm)],[])).
% 0.80/0.86 tff(459,plain,
% 0.80/0.86 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))))),
% 0.80/0.86 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.80/0.86 tff(460,plain,
% 0.80/0.86 (~((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))))),
% 0.80/0.86 inference(unit_resolution,[status(thm)],[459, 242])).
% 0.80/0.86 tff(461,plain,
% 0.80/0.86 (((~(member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))))) | ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))),
% 0.80/0.87 inference(tautology,[status(thm)],[])).
% 0.80/0.87 tff(462,plain,
% 0.80/0.87 ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.80/0.87 inference(unit_resolution,[status(thm)],[461, 460])).
% 0.80/0.87 tff(463,plain,
% 0.80/0.87 ((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.80/0.87 inference(tautology,[status(thm)],[])).
% 0.80/0.87 tff(464,plain,
% 0.80/0.87 ((~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))))) | (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))))),
% 0.80/0.87 inference(unit_resolution,[status(thm)],[463, 309])).
% 0.80/0.87 tff(465,plain,
% 0.80/0.87 (~((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))))),
% 0.80/0.87 inference(unit_resolution,[status(thm)],[464, 462])).
% 0.80/0.87 tff(466,plain,
% 0.80/0.87 (((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F1!43), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))) | member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)),
% 0.80/0.87 inference(tautology,[status(thm)],[])).
% 0.80/0.87 tff(467,plain,
% 0.80/0.87 (member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)),
% 0.80/0.87 inference(unit_resolution,[status(thm)],[466, 465])).
% 0.80/0.87 tff(468,plain,
% 0.80/0.87 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), image3(F1!43, A!40, B!39))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))) | apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))),
% 0.80/0.87 inference(tautology,[status(thm)],[])).
% 0.80/0.87 tff(469,plain,
% 0.80/0.87 (apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))),
% 0.80/0.87 inference(unit_resolution,[status(thm)],[468, 307])).
% 0.80/0.87 tff(470,plain,
% 0.80/0.87 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.80/0.87 inference(rewrite,[status(thm)],[])).
% 0.80/0.87 tff(471,plain,
% 0.80/0.87 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.80/0.87 inference(rewrite,[status(thm)],[])).
% 0.80/0.87 tff(472,plain,
% 0.80/0.87 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 0.80/0.87 inference(monotonicity,[status(thm)],[471])).
% 0.80/0.87 tff(473,plain,
% 0.80/0.87 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.80/0.87 inference(transitivity,[status(thm)],[472, 470])).
% 0.80/0.87 tff(474,plain,
% 0.80/0.87 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)))),
% 0.80/0.87 inference(quant_inst,[status(thm)],[])).
% 0.80/0.87 tff(475,plain,
% 0.80/0.87 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))) | (~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.87 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.80/0.87 tff(476,plain,
% 0.80/0.87 ((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.88 inference(unit_resolution,[status(thm)],[475, 178, 168, 214, 469])).
% 0.80/0.88 tff(477,plain,
% 0.80/0.88 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)),
% 0.80/0.88 inference(unit_resolution,[status(thm)],[476, 259, 467])).
% 0.80/0.88 tff(478,plain,
% 0.80/0.88 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) <=> apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))),
% 0.80/0.88 inference(monotonicity,[status(thm)],[477])).
% 0.80/0.88 tff(479,plain,
% 0.80/0.88 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)) <=> apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.80/0.88 inference(symmetry,[status(thm)],[478])).
% 0.80/0.88 tff(480,plain,
% 0.80/0.88 (((~member(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))),
% 0.80/0.88 inference(tautology,[status(thm)],[])).
% 0.80/0.88 tff(481,plain,
% 0.80/0.88 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43))),
% 0.80/0.88 inference(unit_resolution,[status(thm)],[480, 357])).
% 0.80/0.88 tff(482,plain,
% 0.80/0.88 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.80/0.88 inference(modus_ponens,[status(thm)],[481, 479])).
% 0.80/0.88 tff(483,plain,
% 0.80/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.88 inference(rewrite,[status(thm)],[])).
% 0.80/0.88 tff(484,plain,
% 0.80/0.88 (((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.88 inference(rewrite,[status(thm)],[])).
% 0.80/0.88 tff(485,plain,
% 0.80/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.80/0.88 inference(monotonicity,[status(thm)],[484])).
% 0.80/0.88 tff(486,plain,
% 0.80/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.89 inference(transitivity,[status(thm)],[485, 483])).
% 0.80/0.89 tff(487,plain,
% 0.80/0.89 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 0.80/0.89 inference(quant_inst,[status(thm)],[])).
% 0.80/0.89 tff(488,plain,
% 0.80/0.89 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 0.80/0.89 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.80/0.89 tff(489,plain,
% 0.80/0.89 (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)),
% 0.80/0.89 inference(unit_resolution,[status(thm)],[488, 94, 168, 359, 482, 453, 451])).
% 0.80/0.89 tff(490,plain,
% 0.80/0.89 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41)),
% 0.80/0.89 inference(symmetry,[status(thm)],[489])).
% 0.80/0.89 tff(491,plain,
% 0.80/0.89 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.89 inference(monotonicity,[status(thm)],[490])).
% 0.80/0.89 tff(492,plain,
% 0.80/0.89 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.89 inference(symmetry,[status(thm)],[491])).
% 0.80/0.89 tff(493,plain,
% 0.80/0.89 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.89 inference(tautology,[status(thm)],[])).
% 0.80/0.89 tff(494,plain,
% 0.80/0.89 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.89 inference(unit_resolution,[status(thm)],[493, 449])).
% 0.80/0.89 tff(495,plain,
% 0.80/0.89 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))),
% 0.80/0.89 inference(modus_ponens,[status(thm)],[494, 492])).
% 0.80/0.89 tff(496,plain,
% 0.80/0.89 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))),
% 0.80/0.89 inference(rewrite,[status(thm)],[])).
% 0.80/0.89 tff(497,plain,
% 0.80/0.89 (((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))),
% 0.80/0.89 inference(rewrite,[status(thm)],[])).
% 0.80/0.89 tff(498,plain,
% 0.80/0.89 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))),
% 0.80/0.89 inference(monotonicity,[status(thm)],[497])).
% 0.80/0.89 tff(499,plain,
% 0.80/0.89 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))),
% 0.80/0.89 inference(transitivity,[status(thm)],[498, 496])).
% 0.80/0.89 tff(500,plain,
% 0.80/0.89 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)))),
% 0.80/0.89 inference(quant_inst,[status(thm)],[])).
% 0.80/0.89 tff(501,plain,
% 0.80/0.89 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 0.80/0.89 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.80/0.89 tff(502,plain,
% 0.80/0.89 ((~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 0.80/0.90 inference(unit_resolution,[status(thm)],[501, 216, 168, 214, 212, 359])).
% 0.80/0.90 tff(503,plain,
% 0.80/0.90 (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)),
% 0.80/0.90 inference(unit_resolution,[status(thm)],[502, 495])).
% 0.80/0.90 tff(504,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42)),
% 0.80/0.90 inference(symmetry,[status(thm)],[503])).
% 0.80/0.90 tff(505,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)),
% 0.80/0.90 inference(transitivity,[status(thm)],[504, 422])).
% 0.80/0.90 tff(506,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42)),
% 0.80/0.90 inference(monotonicity,[status(thm)],[505])).
% 0.80/0.90 tff(507,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42)),
% 0.80/0.90 inference(symmetry,[status(thm)],[506])).
% 0.80/0.90 tff(508,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)),
% 0.80/0.90 inference(monotonicity,[status(thm)],[421])).
% 0.80/0.90 tff(509,plain,
% 0.80/0.90 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42)),
% 0.80/0.90 inference(symmetry,[status(thm)],[508])).
% 0.80/0.90 tff(510,plain,
% 0.80/0.90 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))))),
% 0.80/0.90 inference(rewrite,[status(thm)],[])).
% 0.80/0.90 tff(511,plain,
% 0.80/0.90 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))))),
% 0.80/0.90 inference(quant_inst,[status(thm)],[])).
% 0.80/0.90 tff(512,plain,
% 0.80/0.90 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))))),
% 0.80/0.90 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.80/0.90 tff(513,plain,
% 0.80/0.90 (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))),
% 0.80/0.90 inference(unit_resolution,[status(thm)],[512, 80, 359])).
% 0.80/0.90 tff(514,plain,
% 0.80/0.90 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))),
% 0.80/0.90 inference(tautology,[status(thm)],[])).
% 0.80/0.90 tff(515,plain,
% 0.80/0.90 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))),
% 0.80/0.90 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.80/0.90 tff(516,plain,
% 0.80/0.90 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)),
% 0.80/0.90 inference(tautology,[status(thm)],[])).
% 0.80/0.90 tff(517,plain,
% 0.80/0.90 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)),
% 0.80/0.90 inference(unit_resolution,[status(thm)],[516, 513])).
% 0.80/0.90 tff(518,plain,
% 0.80/0.90 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))),
% 0.80/0.90 inference(rewrite,[status(thm)],[])).
% 0.80/0.90 tff(519,plain,
% 0.80/0.90 (((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))),
% 0.80/0.91 inference(rewrite,[status(thm)],[])).
% 0.80/0.91 tff(520,plain,
% 0.80/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))),
% 0.80/0.91 inference(monotonicity,[status(thm)],[519])).
% 0.80/0.91 tff(521,plain,
% 0.80/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)))),
% 0.80/0.91 inference(transitivity,[status(thm)],[520, 518])).
% 0.80/0.91 tff(522,plain,
% 0.80/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))))),
% 0.80/0.91 inference(quant_inst,[status(thm)],[])).
% 0.80/0.91 tff(523,plain,
% 0.80/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42))),
% 0.80/0.91 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.80/0.91 tff(524,plain,
% 0.80/0.91 (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), image3(F1!43, A!40, B!39), F1!43), A!40, F2!42), B!39, F2!42)),
% 0.80/0.91 inference(unit_resolution,[status(thm)],[523, 94, 359, 517, 515, 453, 451])).
% 0.80/0.91 tff(525,plain,
% 0.80/0.91 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)),
% 0.80/0.91 inference(transitivity,[status(thm)],[490, 524, 509, 507, 226, 101])).
% 0.80/0.91 tff(526,plain,
% 0.80/0.91 (((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) | (~(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 0.80/0.91 inference(tautology,[status(thm)],[])).
% 0.80/0.91 tff(527,plain,
% 0.80/0.91 (~(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 0.80/0.91 inference(unit_resolution,[status(thm)],[526, 40])).
% 0.80/0.92 tff(528,plain,
% 0.80/0.92 ($false),
% 0.80/0.92 inference(unit_resolution,[status(thm)],[527, 525])).
% 0.80/0.92 % SZS output end Proof
%------------------------------------------------------------------------------