TSTP Solution File: SET710+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET710+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 05:07:42 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET710+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 07:22:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(tptp_fun_Y2_12_type, type, (
% 0.19/0.41 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.41 tff(compose_function_type, type, (
% 0.19/0.41 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_D_39_type, type, (
% 0.19/0.41 tptp_fun_D_39: $i)).
% 0.19/0.41 tff(tptp_fun_C_40_type, type, (
% 0.19/0.41 tptp_fun_C_40: $i)).
% 0.19/0.41 tff(tptp_fun_A_42_type, type, (
% 0.19/0.41 tptp_fun_A_42: $i)).
% 0.19/0.41 tff(tptp_fun_B_41_type, type, (
% 0.19/0.41 tptp_fun_B_41: $i)).
% 0.19/0.41 tff(tptp_fun_F_45_type, type, (
% 0.19/0.41 tptp_fun_F_45: $i)).
% 0.19/0.41 tff(tptp_fun_G_44_type, type, (
% 0.19/0.41 tptp_fun_G_44: $i)).
% 0.19/0.41 tff(tptp_fun_H_43_type, type, (
% 0.19/0.41 tptp_fun_H_43: $i)).
% 0.19/0.41 tff(tptp_fun_Y1_13_type, type, (
% 0.19/0.41 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.41 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.41 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X_14_type, type, (
% 0.19/0.41 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.41 tff(apply_type, type, (
% 0.19/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(member_type, type, (
% 0.19/0.41 member: ( $i * $i ) > $o)).
% 0.19/0.41 tff(equal_maps_type, type, (
% 0.19/0.41 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.41 tff(maps_type, type, (
% 0.19/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X_4_type, type, (
% 0.19/0.41 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.41 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.41 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X_7_type, type, (
% 0.19/0.41 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![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)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.41 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')).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![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)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.41 tff(14,plain,(
% 0.19/0.41 ![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))))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[13])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!42)) | (~member(Y1, D!39)) | (~member(Y2, D!39)) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), X, Y2)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), X, Y1))))) | (~(equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39) | (~((tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | 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% 0.19/0.43 inference(rewrite,[status(thm)],[])).
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% 0.19/0.43 inference(rewrite,[status(thm)],[])).
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% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[22, 16])).
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% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39) | (~((tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 ((~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 ((~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : (((maps(F, A, B) & maps(G, B, C)) & maps(H, C, D)) => equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(28,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : (((maps(F, A, B) & maps(G, B, C)) & maps(H, C, D)) => equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII02')).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i, D: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, D))) | equal_maps(compose_function(H, compose_function(G, F, A, B, C), A, C, D), compose_function(compose_function(H, G, B, C, D), F, A, B, D), A, D))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.19/0.46 tff(36,plain,(
% 0.19/0.46 ~((~(maps(F!45, A!42, B!41) & maps(G!44, B!41, C!40) & maps(H!43, C!40, D!39))) | equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39))),
% 0.19/0.46 inference(skolemize,[status(sab)],[35])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (~equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39)),
% 0.19/0.46 inference(or_elim,[status(thm)],[36])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((~(equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39) | (~((tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))))))) | equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39) | (~((tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(39,plain,
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% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (^[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))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 (![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))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.48 tff(55,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')).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.48 tff(58,plain,(
% 0.19/0.48 ![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))))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[57])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~((~((~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), 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% 0.41/0.57 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.41/0.57 tff(80,plain,
% 0.41/0.57 (^[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)))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(81,plain,
% 0.41/0.57 (![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))))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[80])).
% 0.41/0.57 tff(82,plain,
% 0.41/0.57 (^[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)))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(83,plain,
% 0.41/0.57 (![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) | (~((~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))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[82])).
% 0.41/0.57 tff(84,plain,
% 0.41/0.57 (^[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) | (~((~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)))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(85,plain,
% 0.41/0.57 (![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) | (~((~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))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[84])).
% 0.41/0.57 tff(86,plain,
% 0.41/0.57 (![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) | (~((~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))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[85, 83])).
% 0.41/0.57 tff(87,plain,
% 0.41/0.57 (^[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))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(88,plain,
% 0.41/0.57 (![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))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[87])).
% 0.41/0.57 tff(89,plain,
% 0.41/0.57 (^[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)))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(90,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[89])).
% 0.41/0.57 tff(91,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(92,plain,
% 0.41/0.57 (^[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)))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(93,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[92])).
% 0.41/0.57 tff(94,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')).
% 0.41/0.57 tff(95,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.41/0.57 tff(96,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.41/0.57 tff(97,plain,(
% 0.41/0.57 ![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))))))))),
% 0.41/0.57 inference(skolemize,[status(sab)],[96])).
% 0.41/0.57 tff(98,plain,
% 0.41/0.57 (![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))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.41/0.57 tff(99,plain,
% 0.41/0.57 (![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))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.41/0.57 tff(100,plain,
% 0.41/0.57 (![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))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[99, 86])).
% 0.41/0.57 tff(101,plain,
% 0.41/0.57 (![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))))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[100, 81])).
% 0.41/0.57 tff(102,plain,
% 0.41/0.57 ((~![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(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y))))))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(103,plain,
% 0.41/0.58 (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.41/0.58 tff(104,plain,
% 0.41/0.58 (((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y))))))))) | ((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(105,plain,
% 0.41/0.58 ((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.41/0.58 tff(106,plain,
% 0.41/0.58 (maps(F!45, A!42, B!41) & maps(G!44, B!41, C!40) & maps(H!43, C!40, D!39)),
% 0.41/0.58 inference(or_elim,[status(thm)],[36])).
% 0.41/0.58 tff(107,plain,
% 0.41/0.58 (maps(G!44, B!41, C!40)),
% 0.41/0.58 inference(and_elim,[status(thm)],[106])).
% 0.41/0.58 tff(108,plain,
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% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(109,plain,
% 0.41/0.58 ((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.41/0.58 tff(110,plain,
% 0.41/0.58 (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.41/0.58 tff(111,plain,
% 0.41/0.58 (((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40))))) | ![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(112,plain,
% 0.41/0.58 (![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.41/0.58 tff(113,plain,
% 0.41/0.58 (((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44))))))) <=> ((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(114,plain,
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% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(115,plain,
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% 0.41/0.59 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.41/0.59 tff(116,plain,
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% 0.41/0.59 inference(unit_resolution,[status(thm)],[115, 112, 79])).
% 0.41/0.59 tff(117,plain,
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% 0.41/0.59 inference(tautology,[status(thm)],[])).
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% 0.41/0.59 inference(tautology,[status(thm)],[])).
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% 0.55/0.71 inference(modus_ponens,[status(thm)],[142, 141])).
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% 0.55/0.71 inference(unit_resolution,[status(thm)],[143, 137, 79, 135, 133, 120, 118])).
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% 0.55/0.71 inference(monotonicity,[status(thm)],[144])).
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% 0.55/0.71 inference(symmetry,[status(thm)],[145])).
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% 0.55/0.72 inference(tautology,[status(thm)],[])).
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% 0.55/0.72 inference(unit_resolution,[status(thm)],[147, 131])).
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% 0.55/0.72 inference(modus_ponens,[status(thm)],[148, 146])).
% 0.55/0.72 tff(150,plain,
% 0.55/0.72 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y))))))))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(151,plain,
% 0.55/0.72 (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[150, 101])).
% 0.55/0.72 tff(152,plain,
% 0.55/0.72 (((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y))))))))) | ((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))),
% 0.55/0.72 inference(tautology,[status(thm)],[])).
% 0.55/0.72 tff(153,plain,
% 0.55/0.72 ((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39))))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.55/0.72 tff(154,plain,
% 0.55/0.72 (maps(H!43, C!40, D!39)),
% 0.55/0.72 inference(and_elim,[status(thm)],[106])).
% 0.55/0.72 tff(155,plain,
% 0.55/0.72 ((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39))))))),
% 0.55/0.72 inference(tautology,[status(thm)],[])).
% 0.55/0.72 tff(156,plain,
% 0.55/0.72 ((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39))))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.55/0.72 tff(157,plain,
% 0.55/0.72 (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[156, 153])).
% 0.55/0.72 tff(158,plain,
% 0.55/0.72 (((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39))))) | ![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))),
% 0.55/0.72 inference(tautology,[status(thm)],[])).
% 0.55/0.72 tff(159,plain,
% 0.55/0.72 (![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.55/0.72 tff(160,plain,
% 0.55/0.72 (((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43))))))) <=> ((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(161,plain,
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% 0.63/0.78 inference(modus_ponens,[status(thm)],[174, 173])).
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% 0.63/0.78 inference(unit_resolution,[status(thm)],[176, 149])).
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% 0.63/0.78 inference(tautology,[status(thm)],[])).
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% 0.63/0.78 inference(unit_resolution,[status(thm)],[178, 40])).
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% 0.80/0.94 inference(tautology,[status(thm)],[])).
% 0.80/0.94 tff(221,plain,
% 0.80/0.94 (apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[220, 77])).
% 0.80/0.95 tff(222,plain,
% 0.80/0.95 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y))))))))))),
% 0.80/0.95 inference(quant_inst,[status(thm)],[])).
% 0.80/0.95 tff(223,plain,
% 0.80/0.95 (~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))))))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[222, 101])).
% 0.80/0.95 tff(224,plain,
% 0.80/0.95 (((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y))))))))) | ((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))),
% 0.80/0.95 inference(tautology,[status(thm)],[])).
% 0.80/0.95 tff(225,plain,
% 0.80/0.95 ((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41))))))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.80/0.95 tff(226,plain,
% 0.80/0.95 (maps(F!45, A!42, B!41)),
% 0.80/0.95 inference(and_elim,[status(thm)],[106])).
% 0.80/0.95 tff(227,plain,
% 0.80/0.95 ((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41))))))),
% 0.80/0.95 inference(tautology,[status(thm)],[])).
% 0.80/0.95 tff(228,plain,
% 0.80/0.95 ((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41))))))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.80/0.95 tff(229,plain,
% 0.80/0.95 (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.80/0.95 tff(230,plain,
% 0.80/0.95 (((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))),
% 0.80/0.95 inference(tautology,[status(thm)],[])).
% 0.80/0.95 tff(231,plain,
% 0.80/0.95 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))),
% 0.80/0.95 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.80/0.95 tff(232,plain,
% 0.80/0.95 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))) | ((~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, 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% 0.85/0.98 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.85/0.98 tff(238,plain,
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% 0.85/0.98 inference(unit_resolution,[status(thm)],[237, 231, 44, 79, 221, 219, 217])).
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% 0.85/0.98 (tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)) = tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44)),
% 0.85/0.98 inference(symmetry,[status(thm)],[238])).
% 0.85/0.98 tff(240,plain,
% 0.85/0.98 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43)) <=> apply(G!44, tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43))),
% 0.85/0.98 inference(monotonicity,[status(thm)],[239])).
% 0.85/0.98 tff(241,plain,
% 0.85/0.98 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43)) <=> apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43))),
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% 0.85/1.02 inference(modus_ponens,[status(thm)],[249, 248])).
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% 0.85/1.02 inference(unit_resolution,[status(thm)],[250, 137, 79, 198, 120, 118])).
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% 0.85/1.02 inference(unit_resolution,[status(thm)],[251, 244])).
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% 0.85/1.02 inference(monotonicity,[status(thm)],[252])).
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% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(255,plain,
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% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(256,plain,
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% 0.85/1.03 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.85/1.03 tff(257,plain,
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% 0.85/1.03 inference(unit_resolution,[status(thm)],[256, 159, 198])).
% 0.85/1.03 tff(258,plain,
% 0.85/1.03 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)))) | apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(259,plain,
% 0.85/1.03 (apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.85/1.03 tff(260,plain,
% 0.85/1.03 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)),
% 0.85/1.03 inference(tautology,[status(thm)],[])).
% 0.85/1.03 tff(261,plain,
% 0.85/1.03 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[260, 257])).
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% 0.91/1.06 inference(transitivity,[status(thm)],[266, 264])).
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% 0.91/1.06 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43) = tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), C!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)))),
% 0.91/1.06 inference(quant_inst,[status(thm)],[])).
% 0.91/1.06 tff(269,plain,
% 0.91/1.06 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), C!40)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43) = tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))),
% 0.91/1.06 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.91/1.06 tff(270,plain,
% 0.91/1.06 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43) = tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))),
% 0.91/1.06 inference(unit_resolution,[status(thm)],[269, 169, 179, 198, 263, 261, 259])).
% 0.91/1.06 tff(271,plain,
% 0.91/1.06 (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)),
% 0.91/1.06 inference(symmetry,[status(thm)],[270])).
% 0.91/1.06 tff(272,plain,
% 0.91/1.06 (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))),
% 0.91/1.06 inference(transitivity,[status(thm)],[271, 253, 177])).
% 0.91/1.06 tff(273,plain,
% 0.91/1.06 (((tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))) | (~(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))),
% 0.91/1.07 inference(tautology,[status(thm)],[])).
% 0.91/1.07 tff(274,plain,
% 0.91/1.07 (~(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[273, 40])).
% 0.91/1.07 tff(275,plain,
% 0.91/1.07 ($false),
% 0.91/1.07 inference(unit_resolution,[status(thm)],[274, 272])).
% 0.91/1.07 % SZS output end Proof
%------------------------------------------------------------------------------