TSTP Solution File: SET725+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET725+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:46 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET725+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n011.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat Sep 3 07:29:28 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % SZS output start Proof
% 0.14/0.36 tff(apply_type, type, (
% 0.14/0.36 apply: ( $i * $i * $i ) > $o)).
% 0.14/0.36 tff(tptp_fun_X1_18_type, type, (
% 0.14/0.36 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_F_43_type, type, (
% 0.14/0.36 tptp_fun_F_43: $i)).
% 0.14/0.36 tff(tptp_fun_A_40_type, type, (
% 0.14/0.36 tptp_fun_A_40: $i)).
% 0.14/0.36 tff(tptp_fun_B_39_type, type, (
% 0.14/0.36 tptp_fun_B_39: $i)).
% 0.14/0.36 tff(tptp_fun_Y_16_type, type, (
% 0.14/0.36 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_G_42_type, type, (
% 0.14/0.36 tptp_fun_G_42: $i)).
% 0.14/0.36 tff(tptp_fun_Y_8_type, type, (
% 0.14/0.36 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.14/0.36 tff(member_type, type, (
% 0.14/0.36 member: ( $i * $i ) > $o)).
% 0.14/0.36 tff(compose_function_type, type, (
% 0.14/0.36 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_X2_17_type, type, (
% 0.14/0.36 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(injective_type, type, (
% 0.14/0.36 injective: ( $i * $i * $i ) > $o)).
% 0.14/0.36 tff(surjective_type, type, (
% 0.14/0.36 surjective: ( $i * $i * $i ) > $o)).
% 0.14/0.36 tff(tptp_fun_Y_20_type, type, (
% 0.14/0.36 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_E_19_type, type, (
% 0.14/0.36 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_H_41_type, type, (
% 0.14/0.36 tptp_fun_H_41: $i)).
% 0.14/0.36 tff(identity_type, type, (
% 0.14/0.36 identity: ( $i * $i ) > $o)).
% 0.14/0.36 tff(tptp_fun_X_15_type, type, (
% 0.14/0.36 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.14/0.36 tff(maps_type, type, (
% 0.14/0.36 maps: ( $i * $i * $i ) > $o)).
% 0.14/0.36 tff(one_to_one_type, type, (
% 0.14/0.36 one_to_one: ( $i * $i * $i ) > $o)).
% 0.14/0.36 tff(tptp_fun_Y_3_type, type, (
% 0.14/0.36 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_X_4_type, type, (
% 0.14/0.36 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_Y2_5_type, type, (
% 0.14/0.36 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_Y1_6_type, type, (
% 0.14/0.36 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_X_7_type, type, (
% 0.14/0.36 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(1,plain,
% 0.14/0.36 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(2,plain,
% 0.14/0.36 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.36 tff(3,plain,
% 0.14/0.36 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(4,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.37 tff(5,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.37 tff(6,plain,
% 0.14/0.37 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(7,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.37 tff(8,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(9,plain,
% 0.14/0.37 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(10,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.37 tff(11,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.14/0.37 tff(12,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.14/0.37 tff(13,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.14/0.37 tff(14,plain,(
% 0.14/0.37 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.14/0.37 inference(skolemize,[status(sab)],[13])).
% 0.14/0.37 tff(15,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.14/0.37 tff(16,plain,
% 0.14/0.37 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.14/0.37 tff(17,plain,
% 0.14/0.37 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(18,plain,
% 0.14/0.37 ((~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))) <=> (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(19,plain,
% 0.14/0.37 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))))),
% 0.14/0.37 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.37 tff(20,plain,
% 0.14/0.37 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[19, 17])).
% 0.14/0.38 tff(21,plain,
% 0.14/0.38 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(22,plain,
% 0.14/0.38 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.38 tff(23,plain,
% 0.14/0.38 (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.14/0.38 tff(24,plain,
% 0.14/0.38 (((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))) | (injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(25,plain,
% 0.14/0.38 (injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.14/0.38 tff(26,assumption,((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))), introduced(assumption)).
% 0.14/0.38 tff(27,plain,
% 0.14/0.38 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(28,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.38 tff(29,plain,
% 0.14/0.38 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(30,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.38 tff(31,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.14/0.38 tff(32,plain,
% 0.14/0.38 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(33,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.38 tff(34,plain,
% 0.14/0.38 (^[F: $i, A: $i, B: $i] : rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(35,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.38 tff(36,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(37,plain,
% 0.14/0.38 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.38 tff(39,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.14/0.38 tff(40,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.38 tff(41,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.14/0.38 tff(42,plain,(
% 0.14/0.38 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[41])).
% 0.14/0.38 tff(43,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.14/0.38 tff(44,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.14/0.38 tff(45,plain,
% 0.14/0.38 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.14/0.38 tff(46,plain,
% 0.14/0.38 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[46, 45, 26])).
% 0.14/0.39 tff(48,plain,(~((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.39 tff(49,plain,
% 0.14/0.39 (((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) | (surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(50,plain,
% 0.14/0.39 (surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.14/0.39 tff(51,assumption,(~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))), introduced(assumption)).
% 0.14/0.39 tff(52,plain,
% 0.14/0.39 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))) | member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(53,plain,
% 0.14/0.39 (member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.14/0.39 tff(54,plain,
% 0.14/0.39 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(55,plain,
% 0.14/0.39 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.14/0.39 tff(56,plain,
% 0.14/0.39 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(57,plain,
% 0.14/0.39 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.14/0.39 tff(58,plain,
% 0.14/0.39 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[57, 55])).
% 0.14/0.39 tff(59,plain,
% 0.14/0.39 (^[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))))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(60,plain,
% 0.14/0.39 (![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))))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.14/0.39 tff(61,plain,
% 0.14/0.39 (![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))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(62,plain,
% 0.14/0.39 (^[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))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(63,plain,
% 0.14/0.39 (![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))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.14/0.39 tff(64,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.14/0.39 tff(65,plain,
% 0.14/0.39 (![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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.14/0.39 tff(66,plain,
% 0.14/0.39 (![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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.14/0.39 tff(67,plain,(
% 0.14/0.39 ![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))))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[66])).
% 0.14/0.39 tff(68,plain,
% 0.14/0.39 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.14/0.39 tff(69,plain,
% 0.14/0.39 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.14/0.39 tff(70,plain,
% 0.14/0.39 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))) <=> ((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(71,plain,
% 0.14/0.39 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(72,plain,
% 0.14/0.39 ((~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))) <=> (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(73,plain,
% 0.14/0.39 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 (((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[75, 70])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 ((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 ((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[78, 69, 53])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 (((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))) | ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.14/0.40 tff(82,plain,
% 0.14/0.40 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[82])).
% 0.14/0.40 tff(84,plain,
% 0.14/0.40 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.14/0.40 tff(86,plain,
% 0.14/0.40 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(88,plain,
% 0.14/0.41 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(90,plain,
% 0.14/0.41 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(91,plain,
% 0.14/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.14/0.41 tff(92,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','identity')).
% 0.14/0.41 tff(93,plain,
% 0.14/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.14/0.41 tff(94,plain,
% 0.14/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.14/0.41 tff(95,plain,(
% 0.14/0.41 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[94])).
% 0.14/0.41 tff(96,plain,
% 0.14/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.14/0.41 tff(97,plain,
% 0.14/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.14/0.41 tff(98,plain,
% 0.14/0.41 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(99,plain,
% 0.14/0.41 (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39))))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 (((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))) | ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(101,plain,
% 0.14/0.41 ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.14/0.41 tff(102,plain,
% 0.14/0.41 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(103,plain,
% 0.14/0.41 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => one_to_one(F, A, B))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(104,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => one_to_one(F, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII16')).
% 0.14/0.41 tff(105,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.14/0.41 tff(106,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.14/0.41 tff(107,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.14/0.41 tff(108,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[107, 102])).
% 0.14/0.41 tff(109,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[108, 102])).
% 0.14/0.41 tff(110,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.14/0.41 tff(111,plain,
% 0.14/0.41 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[110, 102])).
% 0.14/0.41 tff(112,plain,(
% 0.14/0.41 ~((~(maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39))) | one_to_one(F!43, A!40, B!39))),
% 0.14/0.41 inference(skolemize,[status(sab)],[111])).
% 0.14/0.41 tff(113,plain,
% 0.14/0.41 (maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.14/0.41 inference(or_elim,[status(thm)],[112])).
% 0.14/0.41 tff(114,plain,
% 0.14/0.41 (identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.14/0.41 inference(and_elim,[status(thm)],[113])).
% 0.14/0.41 tff(115,plain,
% 0.14/0.41 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(116,plain,
% 0.14/0.41 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.14/0.41 tff(117,plain,
% 0.14/0.41 (![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[116, 101])).
% 0.14/0.41 tff(118,plain,
% 0.14/0.41 (((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(119,plain,
% 0.14/0.41 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(120,plain,
% 0.14/0.41 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.14/0.41 tff(121,plain,
% 0.14/0.41 (apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[120, 117, 53])).
% 0.14/0.41 tff(122,plain,
% 0.14/0.41 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(123,plain,
% 0.14/0.41 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.14/0.41 tff(124,plain,
% 0.14/0.41 (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[123, 81])).
% 0.14/0.41 tff(125,plain,
% 0.14/0.41 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))) | apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(126,plain,
% 0.14/0.41 (apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.14/0.42 tff(127,plain,
% 0.14/0.42 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))) | member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(128,plain,
% 0.14/0.42 (member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.14/0.42 tff(129,plain,
% 0.14/0.42 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))) | ![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(130,plain,
% 0.14/0.42 (![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[129, 51])).
% 0.14/0.42 tff(131,plain,
% 0.14/0.42 (((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))) <=> ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(132,plain,
% 0.14/0.42 ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(133,plain,
% 0.14/0.42 ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.14/0.42 tff(134,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[133, 130, 128, 126])).
% 0.14/0.42 tff(135,plain,((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(136,plain,
% 0.14/0.42 ((~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))) | surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(137,plain,
% 0.14/0.42 ((~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))) | surjective(F!43, A!40, B!39)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.14/0.42 tff(138,plain,
% 0.14/0.42 (surjective(F!43, A!40, B!39)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[137, 50])).
% 0.14/0.42 tff(139,plain,
% 0.14/0.42 (^[F: $i, A: $i, B: $i] : refl((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(140,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.14/0.42 tff(141,plain,
% 0.14/0.42 (^[F: $i, A: $i, B: $i] : rewrite((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(142,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[141])).
% 0.14/0.42 tff(143,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(144,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.14/0.42 tff(145,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.14/0.42 tff(146,plain,(
% 0.14/0.42 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[145])).
% 0.14/0.42 tff(147,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.14/0.42 tff(148,plain,
% 0.14/0.42 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.14/0.42 tff(149,plain,
% 0.14/0.42 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(F!43, A!40, B!39) <=> (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(150,plain,
% 0.14/0.42 (one_to_one(F!43, A!40, B!39) <=> (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.14/0.42 tff(151,plain,
% 0.14/0.42 (~one_to_one(F!43, A!40, B!39)),
% 0.14/0.42 inference(or_elim,[status(thm)],[112])).
% 0.14/0.42 tff(152,plain,
% 0.14/0.42 ((~(one_to_one(F!43, A!40, B!39) <=> (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))))) | one_to_one(F!43, A!40, B!39) | ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(153,plain,
% 0.14/0.42 ((~(one_to_one(F!43, A!40, B!39) <=> (~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))))) | ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.14/0.42 tff(154,plain,
% 0.14/0.42 ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.14/0.42 tff(155,plain,
% 0.14/0.42 ((~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))) | (~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(156,plain,
% 0.14/0.42 ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.14/0.42 tff(157,plain,
% 0.14/0.42 (~injective(F!43, A!40, B!39)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[156, 138])).
% 0.14/0.42 tff(158,plain,
% 0.14/0.42 ((~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))) | injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(159,plain,
% 0.14/0.42 ((~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.14/0.42 tff(160,plain,
% 0.14/0.42 (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[159, 25])).
% 0.14/0.42 tff(161,plain,
% 0.14/0.42 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(162,plain,
% 0.14/0.42 (member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.14/0.42 tff(163,plain,
% 0.14/0.42 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(164,plain,
% 0.14/0.42 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(165,plain,
% 0.14/0.42 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(166,plain,
% 0.14/0.43 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[165])).
% 0.14/0.43 tff(167,plain,
% 0.14/0.43 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[166, 164])).
% 0.14/0.43 tff(168,plain,
% 0.14/0.43 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[167])).
% 0.14/0.43 tff(169,plain,
% 0.14/0.43 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[168, 163])).
% 0.14/0.43 tff(170,plain,
% 0.14/0.43 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(171,plain,
% 0.14/0.43 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.14/0.43 tff(172,plain,
% 0.14/0.43 (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[171, 69, 162])).
% 0.14/0.43 tff(173,plain,
% 0.14/0.43 (((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(174,plain,
% 0.14/0.43 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.14/0.43 tff(175,plain,
% 0.14/0.43 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(176,plain,
% 0.14/0.44 (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40))))))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[175, 97])).
% 0.14/0.44 tff(177,plain,
% 0.14/0.44 (((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(178,plain,
% 0.14/0.44 ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.14/0.44 tff(179,plain,
% 0.14/0.44 (identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)),
% 0.14/0.44 inference(and_elim,[status(thm)],[113])).
% 0.14/0.44 tff(180,plain,
% 0.14/0.44 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(181,plain,
% 0.14/0.44 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.14/0.44 tff(182,plain,
% 0.14/0.44 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.14/0.44 tff(183,plain,
% 0.14/0.44 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(184,plain,
% 0.14/0.44 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(185,plain,
% 0.14/0.44 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.14/0.44 tff(186,plain,
% 0.14/0.44 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[185, 182, 162])).
% 0.14/0.44 tff(187,plain,
% 0.14/0.44 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(188,plain,
% 0.14/0.44 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.14/0.44 tff(189,plain,
% 0.14/0.44 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[188, 174])).
% 0.14/0.44 tff(190,plain,
% 0.14/0.44 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(191,plain,
% 0.14/0.44 (apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.14/0.44 tff(192,plain,
% 0.14/0.44 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(193,plain,
% 0.14/0.44 (member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.14/0.44 tff(194,plain,
% 0.14/0.44 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(195,plain,
% 0.14/0.44 (member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[194, 160])).
% 0.14/0.44 tff(196,plain,
% 0.14/0.44 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(197,plain,
% 0.14/0.44 (apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[196, 160])).
% 0.14/0.44 tff(198,plain,
% 0.14/0.44 (^[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)))))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(199,plain,
% 0.14/0.44 (![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))))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[198])).
% 0.14/0.44 tff(200,plain,
% 0.14/0.44 (^[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)))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(201,plain,
% 0.14/0.44 (![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))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[200])).
% 0.14/0.44 tff(202,plain,
% 0.14/0.44 (^[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)))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(203,plain,
% 0.14/0.44 (![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))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[202])).
% 0.14/0.44 tff(204,plain,
% 0.14/0.44 (![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))))))))),
% 0.14/0.44 inference(transitivity,[status(thm)],[203, 201])).
% 0.14/0.44 tff(205,plain,
% 0.14/0.44 (^[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))))))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(206,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[205])).
% 0.14/0.45 tff(207,plain,
% 0.14/0.45 (^[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)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(208,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[207])).
% 0.14/0.45 tff(209,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(210,plain,
% 0.14/0.45 (^[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)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(211,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[210])).
% 0.14/0.45 tff(212,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.14/0.45 tff(213,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.14/0.45 tff(214,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.14/0.45 tff(215,plain,(
% 0.14/0.45 ![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))))))))),
% 0.14/0.45 inference(skolemize,[status(sab)],[214])).
% 0.14/0.45 tff(216,plain,
% 0.14/0.45 (![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))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.14/0.45 tff(217,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.14/0.45 tff(218,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[217, 204])).
% 0.14/0.45 tff(219,plain,
% 0.14/0.45 (![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))))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[218, 199])).
% 0.14/0.45 tff(220,plain,
% 0.14/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(221,plain,
% 0.14/0.45 (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))))))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.14/0.45 tff(222,plain,
% 0.14/0.45 (((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))) | ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))),
% 0.14/0.45 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(223,plain,
% 0.14/0.45 ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.14/0.45 tff(224,plain,
% 0.14/0.45 (maps(F!43, A!40, B!39)),
% 0.14/0.45 inference(and_elim,[status(thm)],[113])).
% 0.14/0.45 tff(225,plain,
% 0.14/0.45 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.14/0.45 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(226,plain,
% 0.14/0.45 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.14/0.45 tff(227,plain,
% 0.14/0.45 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[226, 223])).
% 0.14/0.45 tff(228,plain,
% 0.14/0.45 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.14/0.45 inference(tautology,[status(thm)],[])).
% 0.14/0.45 tff(229,plain,
% 0.14/0.45 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.14/0.45 tff(230,plain,
% 0.14/0.45 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(231,plain,
% 0.14/0.45 (((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) <=> ((~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(232,plain,
% 0.14/0.45 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[231])).
% 0.14/0.46 tff(233,plain,
% 0.14/0.46 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.46 inference(transitivity,[status(thm)],[232, 230])).
% 0.14/0.46 tff(234,plain,
% 0.14/0.46 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(235,plain,
% 0.14/0.46 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.14/0.46 tff(236,plain,
% 0.14/0.46 (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[235, 229, 197, 162, 195, 193, 191])).
% 0.14/0.46 tff(237,plain,
% 0.14/0.46 (tptp_fun_Y_16(B!39, A!40, F!43) = tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42)),
% 0.14/0.46 inference(symmetry,[status(thm)],[236])).
% 0.14/0.46 tff(238,plain,
% 0.14/0.46 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[237])).
% 0.14/0.46 tff(239,plain,
% 0.14/0.46 (apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.46 inference(symmetry,[status(thm)],[238])).
% 0.14/0.46 tff(240,plain,
% 0.14/0.46 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.46 inference(tautology,[status(thm)],[])).
% 0.14/0.46 tff(241,plain,
% 0.14/0.46 (apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[240, 189])).
% 0.14/0.46 tff(242,plain,
% 0.14/0.46 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[241, 239])).
% 0.14/0.46 tff(243,plain,
% 0.14/0.46 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)),
% 0.14/0.46 inference(tautology,[status(thm)],[])).
% 0.14/0.46 tff(244,plain,
% 0.14/0.46 (member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[243, 160])).
% 0.14/0.46 tff(245,plain,
% 0.14/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(246,plain,
% 0.14/0.46 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(247,plain,
% 0.14/0.46 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(248,plain,
% 0.14/0.47 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.47 inference(monotonicity,[status(thm)],[247])).
% 0.14/0.47 tff(249,plain,
% 0.14/0.47 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.47 inference(transitivity,[status(thm)],[248, 246])).
% 0.14/0.47 tff(250,plain,
% 0.14/0.47 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.14/0.47 inference(monotonicity,[status(thm)],[249])).
% 0.14/0.47 tff(251,plain,
% 0.14/0.47 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.47 inference(transitivity,[status(thm)],[250, 245])).
% 0.14/0.47 tff(252,plain,
% 0.14/0.47 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(253,plain,
% 0.14/0.47 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))),
% 0.14/0.47 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.14/0.47 tff(254,plain,
% 0.14/0.47 (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[253, 69, 244])).
% 0.14/0.47 tff(255,plain,
% 0.14/0.47 (((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))),
% 0.14/0.47 inference(tautology,[status(thm)],[])).
% 0.14/0.47 tff(256,plain,
% 0.14/0.47 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.14/0.47 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.14/0.47 tff(257,plain,
% 0.14/0.47 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.14/0.47 inference(rewrite,[status(thm)],[])).
% 0.14/0.47 tff(258,plain,
% 0.14/0.47 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.14/0.47 inference(quant_inst,[status(thm)],[])).
% 0.14/0.47 tff(259,plain,
% 0.14/0.47 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.14/0.48 tff(260,plain,
% 0.14/0.48 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[259, 182, 244])).
% 0.14/0.48 tff(261,plain,
% 0.14/0.48 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.14/0.48 inference(tautology,[status(thm)],[])).
% 0.14/0.48 tff(262,plain,
% 0.14/0.48 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.14/0.48 tff(263,plain,
% 0.14/0.48 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[262, 256])).
% 0.14/0.48 tff(264,plain,
% 0.14/0.48 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.14/0.48 inference(tautology,[status(thm)],[])).
% 0.14/0.48 tff(265,plain,
% 0.14/0.48 (apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.14/0.48 tff(266,plain,
% 0.14/0.48 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.14/0.48 inference(tautology,[status(thm)],[])).
% 0.14/0.48 tff(267,plain,
% 0.14/0.48 (member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[266, 263])).
% 0.14/0.48 tff(268,plain,
% 0.14/0.48 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.48 inference(tautology,[status(thm)],[])).
% 0.14/0.48 tff(269,plain,
% 0.14/0.48 (apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[268, 160])).
% 0.14/0.48 tff(270,plain,
% 0.14/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(271,plain,
% 0.14/0.48 (((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) <=> ((~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(272,plain,
% 0.14/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))))),
% 0.14/0.48 inference(monotonicity,[status(thm)],[271])).
% 0.14/0.48 tff(273,plain,
% 0.14/0.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.14/0.48 inference(transitivity,[status(thm)],[272, 270])).
% 0.14/0.48 tff(274,plain,
% 0.14/0.48 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.49 tff(275,plain,
% 0.14/0.49 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.14/0.49 tff(276,plain,
% 0.14/0.49 (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[275, 229, 269, 244, 195, 267, 265])).
% 0.14/0.49 tff(277,plain,
% 0.14/0.49 (tptp_fun_Y_16(B!39, A!40, F!43) = tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42)),
% 0.14/0.49 inference(symmetry,[status(thm)],[276])).
% 0.14/0.49 tff(278,plain,
% 0.14/0.49 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(monotonicity,[status(thm)],[277])).
% 0.14/0.49 tff(279,plain,
% 0.14/0.49 (apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(symmetry,[status(thm)],[278])).
% 0.14/0.49 tff(280,plain,
% 0.14/0.49 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(tautology,[status(thm)],[])).
% 0.14/0.49 tff(281,plain,
% 0.14/0.49 (apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[280, 263])).
% 0.14/0.49 tff(282,plain,
% 0.14/0.49 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[281, 279])).
% 0.14/0.49 tff(283,plain,
% 0.14/0.49 ((tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) <=> (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(commutativity,[status(thm)],[])).
% 0.14/0.49 tff(284,plain,
% 0.14/0.49 ((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) <=> (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.49 inference(symmetry,[status(thm)],[283])).
% 0.14/0.49 tff(285,plain,
% 0.14/0.49 ((~(tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))) <=> (~(tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.14/0.49 inference(monotonicity,[status(thm)],[284])).
% 0.14/0.49 tff(286,plain,
% 0.14/0.49 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))) | (~(tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.14/0.49 inference(tautology,[status(thm)],[])).
% 0.14/0.49 tff(287,plain,
% 0.14/0.49 (~(tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.14/0.49 inference(unit_resolution,[status(thm)],[286, 160])).
% 0.14/0.49 tff(288,plain,
% 0.14/0.49 (~(tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[287, 285])).
% 0.14/0.49 tff(289,plain,
% 0.14/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(290,plain,
% 0.14/0.49 ((~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))))) <=> (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.14/0.49 inference(rewrite,[status(thm)],[])).
% 0.14/0.49 tff(291,plain,
% 0.14/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.14/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.14/0.49 tff(292,plain,
% 0.14/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))))),
% 0.14/0.49 inference(transitivity,[status(thm)],[291, 289])).
% 0.14/0.49 tff(293,plain,
% 0.14/0.49 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))),
% 0.14/0.49 inference(quant_inst,[status(thm)],[])).
% 0.14/0.49 tff(294,plain,
% 0.14/0.49 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))))),
% 0.14/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.14/0.49 tff(295,plain,
% 0.14/0.49 (~((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[294, 219])).
% 0.14/0.50 tff(296,plain,
% 0.14/0.50 (((~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))) | (~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))))) | ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.14/0.50 inference(tautology,[status(thm)],[])).
% 0.14/0.50 tff(297,plain,
% 0.14/0.50 ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.14/0.50 tff(298,plain,
% 0.14/0.50 (maps(G!42, B!39, A!40)),
% 0.14/0.50 inference(and_elim,[status(thm)],[113])).
% 0.14/0.50 tff(299,plain,
% 0.14/0.50 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.14/0.50 inference(tautology,[status(thm)],[])).
% 0.14/0.50 tff(300,plain,
% 0.14/0.50 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.14/0.50 tff(301,plain,
% 0.14/0.50 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[300, 297])).
% 0.14/0.50 tff(302,plain,
% 0.14/0.50 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.14/0.50 inference(tautology,[status(thm)],[])).
% 0.14/0.50 tff(303,plain,
% 0.14/0.50 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.14/0.50 tff(304,plain,
% 0.14/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(305,plain,
% 0.14/0.50 (((tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))))),
% 0.14/0.50 inference(rewrite,[status(thm)],[])).
% 0.14/0.50 tff(306,plain,
% 0.14/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.14/0.50 inference(monotonicity,[status(thm)],[305])).
% 0.14/0.50 tff(307,plain,
% 0.14/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))))),
% 0.14/0.50 inference(transitivity,[status(thm)],[306, 304])).
% 0.14/0.50 tff(308,plain,
% 0.14/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)))),
% 0.14/0.50 inference(quant_inst,[status(thm)],[])).
% 0.14/0.50 tff(309,plain,
% 0.14/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.14/0.50 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.14/0.50 tff(310,plain,
% 0.14/0.50 ((~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (tptp_fun_X2_17(B!39, A!40, F!43) = tptp_fun_X1_18(B!39, A!40, F!43)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[309, 303, 162, 244, 195])).
% 0.14/0.50 tff(311,plain,
% 0.14/0.50 ($false),
% 0.14/0.50 inference(unit_resolution,[status(thm)],[310, 288, 282, 242])).
% 0.14/0.50 % SZS output end Proof
%------------------------------------------------------------------------------