TSTP Solution File: SET729+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET729+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 05:07:47 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET729+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 07:55:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(apply_type, type, (
% 0.21/0.44 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_X1_18_type, type, (
% 0.21/0.44 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_F_40_type, type, (
% 0.21/0.44 tptp_fun_F_40: $i)).
% 0.21/0.44 tff(tptp_fun_A_39_type, type, (
% 0.21/0.44 tptp_fun_A_39: $i)).
% 0.21/0.44 tff(tptp_fun_Y_16_type, type, (
% 0.21/0.44 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.44 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.44 tff(member_type, type, (
% 0.21/0.44 member: ( $i * $i ) > $o)).
% 0.21/0.44 tff(compose_function_type, type, (
% 0.21/0.44 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_X2_17_type, type, (
% 0.21/0.44 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(injective_type, type, (
% 0.21/0.44 injective: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(surjective_type, type, (
% 0.21/0.44 surjective: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(one_to_one_type, type, (
% 0.21/0.44 one_to_one: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(inverse_predicate_type, type, (
% 0.21/0.44 inverse_predicate: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_Y_21_type, type, (
% 0.21/0.44 tptp_fun_Y_21: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_X_22_type, type, (
% 0.21/0.44 tptp_fun_X_22: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.44 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(maps_type, type, (
% 0.21/0.44 maps: ( $i * $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_X_4_type, type, (
% 0.21/0.44 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y2_5_type, type, (
% 0.21/0.44 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y1_6_type, type, (
% 0.21/0.44 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_X_7_type, type, (
% 0.21/0.44 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(identity_type, type, (
% 0.21/0.44 identity: ( $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_X_15_type, type, (
% 0.21/0.44 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_Y_20_type, type, (
% 0.21/0.44 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_E_19_type, type, (
% 0.21/0.44 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (^[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))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (^[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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.44 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')).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.45 tff(14,plain,(
% 0.21/0.45 ![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)))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (![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))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (![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))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (((~![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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 ((~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))) <=> (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (((~![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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (((~![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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ((~![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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 ((~![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!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))) | (injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (^[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))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (![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)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (^[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))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (![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)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(31,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')).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.46 tff(33,plain,(
% 0.21/0.46 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[32])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(F!40, A!39, A!39) <=> (~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (one_to_one(F!40, A!39, A!39) <=> (~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.46 tff(38,assumption,((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))), introduced(assumption)).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (^[G: $i, F: $i, A: $i, B: $i] : refl((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 (^[G: $i, F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))) <=> (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), rewrite((inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))), rewrite((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.47 tff(49,axiom,(![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_predicate')).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.47 tff(52,plain,(
% 0.21/0.47 ![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[51])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 ((~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))) <=> (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[60, 54, 38])).
% 0.21/0.48 tff(62,plain,(~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))) | (inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.48 tff(65,assumption,(~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))), introduced(assumption)).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))) | member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (^[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)))))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![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))))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (^[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)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 (^[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)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (^[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))))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (![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))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (^[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)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.49 tff(82,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')).
% 0.21/0.49 tff(83,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.49 tff(84,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.49 tff(85,plain,(
% 0.21/0.49 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[84])).
% 0.21/0.49 tff(86,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.49 tff(87,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.21/0.49 tff(88,plain,
% 0.21/0.49 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.21/0.49 tff(89,plain,
% 0.21/0.49 (![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))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[88, 69])).
% 0.21/0.49 tff(90,plain,
% 0.21/0.49 (((~![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(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))))))) <=> ((~![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!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ((~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))))) <=> (~((~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 (((~![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(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), 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(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), 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(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[92, 90])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y))))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (~((~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (((~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))) | (~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))))) | ((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 ((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 ((~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))) <=> (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 ((~![F: $i, A: $i] : (maps(F, A, A) => ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))) <=> (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(101,axiom,(~![F: $i, A: $i] : (maps(F, A, A) => ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII20')).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[105, 99])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[107, 99])).
% 0.21/0.50 tff(109,plain,(
% 0.21/0.50 ~((~maps(F!40, A!39, A!39)) | ((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[108])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (maps(F!40, A!39, A!39)),
% 0.21/0.50 inference(or_elim,[status(thm)],[109])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 ((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 ((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[112, 98])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))) | ![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.50 tff(116,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[118, 115, 67])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(121,plain,
% 0.21/0.50 (member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (^[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)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (^[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)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (^[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))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (^[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))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.51 tff(132,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')).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.51 tff(135,plain,(
% 0.21/0.51 ![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))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[134])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.21/0.51 tff(137,plain,
% 0.21/0.51 (![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))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.21/0.51 tff(138,plain,
% 0.21/0.51 (((~![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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(139,plain,
% 0.21/0.51 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[141, 139])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (((~![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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 (((~![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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[143, 138])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 ((~![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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(146,plain,
% 0.21/0.53 ((~![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_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.53 tff(147,plain,
% 0.21/0.53 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[146, 137, 121])).
% 0.21/0.53 tff(148,plain,
% 0.21/0.53 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(149,plain,
% 0.21/0.53 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.53 tff(150,assumption,(~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)), introduced(assumption)).
% 0.21/0.53 tff(151,plain,
% 0.21/0.53 (^[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)))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(152,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[151])).
% 0.21/0.53 tff(153,plain,
% 0.21/0.53 (^[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)))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(154,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.53 tff(155,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[154, 152])).
% 0.21/0.53 tff(156,plain,
% 0.21/0.53 (^[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))))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(157,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[156])).
% 0.21/0.53 tff(158,plain,
% 0.21/0.53 (![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)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(159,plain,
% 0.21/0.53 (^[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))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(160,plain,
% 0.21/0.53 (![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)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[159])).
% 0.21/0.53 tff(161,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')).
% 0.21/0.53 tff(162,plain,
% 0.21/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.53 tff(163,plain,
% 0.21/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.21/0.53 tff(164,plain,(
% 0.21/0.53 ![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))))))),
% 0.21/0.53 inference(skolemize,[status(sab)],[163])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.21/0.53 tff(166,plain,
% 0.21/0.53 (![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))))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.21/0.53 tff(167,plain,
% 0.21/0.53 ((~![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!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(168,plain,
% 0.21/0.53 (~((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.53 tff(169,plain,
% 0.21/0.53 (((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(170,plain,
% 0.21/0.54 (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.54 tff(171,plain,
% 0.21/0.54 ((~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(172,plain,
% 0.21/0.54 (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.54 tff(173,plain,
% 0.21/0.54 (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[172, 150])).
% 0.21/0.54 tff(174,plain,
% 0.21/0.54 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(175,plain,
% 0.21/0.54 (member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.21/0.54 tff(176,plain,
% 0.21/0.54 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(177,plain,
% 0.21/0.54 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(178,plain,
% 0.21/0.54 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.54 tff(179,plain,
% 0.21/0.54 (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[178, 115, 175])).
% 0.21/0.54 tff(180,plain,
% 0.21/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(181,plain,
% 0.21/0.54 (apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.54 tff(182,plain,
% 0.21/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(183,plain,
% 0.21/0.54 (member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.21/0.54 tff(184,plain,
% 0.21/0.54 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!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_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(185,plain,
% 0.21/0.54 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(186,plain,
% 0.21/0.55 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(187,plain,
% 0.21/0.55 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[186])).
% 0.21/0.55 tff(188,plain,
% 0.21/0.55 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[187, 185])).
% 0.21/0.55 tff(189,plain,
% 0.21/0.55 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!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_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.56 tff(190,plain,
% 0.21/0.56 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!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_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[189, 184])).
% 0.21/0.56 tff(191,plain,
% 0.21/0.56 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(192,plain,
% 0.21/0.56 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.56 tff(193,plain,
% 0.21/0.56 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[192, 137, 175])).
% 0.21/0.56 tff(194,plain,
% 0.21/0.56 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(195,plain,
% 0.21/0.56 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.21/0.56 tff(196,plain,
% 0.21/0.56 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(197,plain,
% 0.21/0.56 (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[196, 173])).
% 0.21/0.56 tff(198,plain,
% 0.21/0.56 ((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(199,plain,
% 0.21/0.56 ((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.21/0.56 tff(200,plain,
% 0.21/0.56 (![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[199, 195])).
% 0.21/0.56 tff(201,plain,
% 0.21/0.56 (((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(202,plain,
% 0.21/0.57 ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(203,plain,
% 0.21/0.57 ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.57 tff(204,plain,
% 0.21/0.57 (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[203, 200, 183, 181])).
% 0.21/0.57 tff(205,plain,
% 0.21/0.57 ((~(apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(206,plain,
% 0.21/0.57 (~(apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[205, 181, 204])).
% 0.21/0.57 tff(207,plain,
% 0.21/0.57 (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[60, 54])).
% 0.21/0.57 tff(208,plain,
% 0.21/0.57 (((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))) | ((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(209,plain,
% 0.21/0.57 ((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.21/0.57 tff(210,plain,
% 0.21/0.57 ((~((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(211,plain,
% 0.21/0.57 (((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) <=> ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(212,plain,
% 0.21/0.57 ((~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (~((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.57 tff(213,plain,
% 0.21/0.57 ((~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.21/0.57 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.57 tff(214,plain,
% 0.21/0.57 (~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.21/0.57 inference(or_elim,[status(thm)],[109])).
% 0.21/0.57 tff(215,plain,
% 0.21/0.57 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.57 tff(216,plain,
% 0.21/0.57 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(217,plain,
% 0.21/0.57 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.21/0.57 tff(218,plain,
% 0.21/0.57 (~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[217, 150])).
% 0.21/0.57 tff(219,plain,
% 0.21/0.57 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(220,plain,
% 0.21/0.57 (inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.21/0.57 tff(221,plain,
% 0.21/0.57 ((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(222,plain,
% 0.21/0.57 ((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.21/0.57 tff(223,plain,
% 0.21/0.57 (![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[222, 209])).
% 0.21/0.57 tff(224,plain,
% 0.21/0.57 (((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(225,plain,
% 0.21/0.57 ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(226,plain,
% 0.21/0.57 ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.58 tff(227,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[226, 175, 223, 183, 206])).
% 0.21/0.58 tff(228,plain,(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(229,plain,
% 0.21/0.58 (((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(230,plain,
% 0.21/0.58 ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[229, 168])).
% 0.21/0.58 tff(231,plain,
% 0.21/0.58 ((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(232,plain,
% 0.21/0.58 ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.21/0.58 tff(233,plain,
% 0.21/0.58 (![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[232, 228])).
% 0.21/0.58 tff(234,plain,
% 0.21/0.58 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(235,plain,
% 0.21/0.58 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(236,plain,
% 0.21/0.58 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.21/0.58 tff(237,plain,
% 0.21/0.58 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[236, 233, 121])).
% 0.21/0.58 tff(238,plain,
% 0.21/0.58 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(239,plain,
% 0.21/0.58 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.21/0.58 tff(240,plain,
% 0.21/0.58 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[239, 149])).
% 0.21/0.58 tff(241,plain,
% 0.21/0.58 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(242,plain,
% 0.21/0.58 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.21/0.58 tff(243,plain,
% 0.21/0.58 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(244,plain,
% 0.21/0.58 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[243, 240])).
% 0.21/0.58 tff(245,plain,
% 0.21/0.58 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(246,plain,
% 0.21/0.58 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(247,plain,
% 0.21/0.59 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.21/0.59 tff(248,plain,
% 0.21/0.59 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[247, 115, 121])).
% 0.21/0.59 tff(249,plain,
% 0.21/0.59 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(250,plain,
% 0.21/0.59 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.21/0.59 tff(251,plain,
% 0.21/0.59 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(252,plain,
% 0.21/0.59 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[251, 248])).
% 0.21/0.59 tff(253,plain,
% 0.21/0.59 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(254,plain,
% 0.21/0.59 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[253, 113])).
% 0.21/0.59 tff(255,plain,
% 0.21/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(256,plain,
% 0.21/0.59 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(257,plain,
% 0.21/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.21/0.59 inference(monotonicity,[status(thm)],[256])).
% 0.21/0.59 tff(258,plain,
% 0.21/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.46/0.60 inference(transitivity,[status(thm)],[257, 255])).
% 0.46/0.60 tff(259,plain,
% 0.46/0.60 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(260,plain,
% 0.46/0.60 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.46/0.60 tff(261,plain,
% 0.46/0.60 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[260, 254, 121, 252, 250, 244, 242])).
% 0.46/0.60 tff(262,plain,
% 0.46/0.60 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!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_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(263,plain,
% 0.46/0.60 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(264,plain,
% 0.46/0.60 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(265,plain,
% 0.46/0.60 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[264])).
% 0.46/0.61 tff(266,plain,
% 0.46/0.61 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[265, 263])).
% 0.46/0.61 tff(267,plain,
% 0.46/0.61 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!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_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[266])).
% 0.46/0.61 tff(268,plain,
% 0.46/0.61 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!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_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[267, 262])).
% 0.46/0.61 tff(269,plain,
% 0.46/0.61 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.48/0.61 inference(quant_inst,[status(thm)],[])).
% 0.48/0.61 tff(270,plain,
% 0.48/0.61 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))),
% 0.48/0.61 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.48/0.61 tff(271,plain,
% 0.48/0.61 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))),
% 0.48/0.61 inference(unit_resolution,[status(thm)],[270, 137, 67])).
% 0.48/0.61 tff(272,plain,
% 0.48/0.61 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))),
% 0.48/0.61 inference(tautology,[status(thm)],[])).
% 0.48/0.61 tff(273,plain,
% 0.48/0.61 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.48/0.61 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.48/0.61 tff(274,plain,
% 0.48/0.61 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.48/0.61 inference(rewrite,[status(thm)],[])).
% 0.48/0.61 tff(275,plain,
% 0.48/0.61 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.48/0.61 inference(quant_inst,[status(thm)],[])).
% 0.48/0.61 tff(276,plain,
% 0.48/0.61 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.61 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.48/0.61 tff(277,plain,
% 0.48/0.61 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.61 inference(unit_resolution,[status(thm)],[276, 233, 67])).
% 0.48/0.61 tff(278,plain,
% 0.48/0.61 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.48/0.62 inference(tautology,[status(thm)],[])).
% 0.48/0.62 tff(279,plain,
% 0.48/0.62 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.48/0.62 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.48/0.62 tff(280,plain,
% 0.48/0.62 (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.48/0.62 inference(unit_resolution,[status(thm)],[279, 273])).
% 0.48/0.62 tff(281,plain,
% 0.48/0.62 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.48/0.62 inference(tautology,[status(thm)],[])).
% 0.48/0.62 tff(282,plain,
% 0.48/0.62 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.48/0.62 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.48/0.62 tff(283,plain,
% 0.48/0.62 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.48/0.62 inference(tautology,[status(thm)],[])).
% 0.48/0.62 tff(284,plain,
% 0.48/0.62 (member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.48/0.62 inference(unit_resolution,[status(thm)],[283, 280])).
% 0.48/0.62 tff(285,plain,
% 0.48/0.62 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.48/0.62 inference(tautology,[status(thm)],[])).
% 0.48/0.62 tff(286,plain,
% 0.48/0.62 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.48/0.62 inference(unit_resolution,[status(thm)],[285, 119])).
% 0.48/0.62 tff(287,plain,
% 0.48/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.48/0.62 inference(rewrite,[status(thm)],[])).
% 0.48/0.62 tff(288,plain,
% 0.48/0.62 (((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.48/0.62 inference(rewrite,[status(thm)],[])).
% 0.48/0.62 tff(289,plain,
% 0.48/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[288])).
% 0.48/0.63 tff(290,plain,
% 0.48/0.63 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[289, 287])).
% 0.48/0.63 tff(291,plain,
% 0.48/0.63 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(292,plain,
% 0.48/0.63 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.48/0.63 tff(293,plain,
% 0.48/0.63 (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[292, 254, 67, 121, 286, 284, 282])).
% 0.48/0.63 tff(294,plain,
% 0.48/0.63 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40)),
% 0.48/0.63 inference(symmetry,[status(thm)],[293])).
% 0.48/0.63 tff(295,plain,
% 0.48/0.63 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[294])).
% 0.48/0.63 tff(296,plain,
% 0.48/0.63 (apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.63 inference(symmetry,[status(thm)],[295])).
% 0.48/0.63 tff(297,plain,
% 0.48/0.63 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(298,plain,
% 0.48/0.63 (apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[297, 280])).
% 0.48/0.63 tff(299,plain,
% 0.48/0.63 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[298, 296])).
% 0.48/0.63 tff(300,plain,
% 0.48/0.63 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(301,plain,
% 0.50/0.63 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(302,plain,
% 0.50/0.63 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.50/0.64 inference(monotonicity,[status(thm)],[301])).
% 0.50/0.64 tff(303,plain,
% 0.50/0.64 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.50/0.64 inference(transitivity,[status(thm)],[302, 300])).
% 0.50/0.64 tff(304,plain,
% 0.50/0.64 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.50/0.64 inference(quant_inst,[status(thm)],[])).
% 0.50/0.64 tff(305,plain,
% 0.50/0.64 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.50/0.64 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.50/0.64 tff(306,plain,
% 0.50/0.64 ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.50/0.64 inference(unit_resolution,[status(thm)],[305, 254, 67, 121, 244, 242])).
% 0.50/0.64 tff(307,plain,
% 0.50/0.64 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.50/0.64 inference(unit_resolution,[status(thm)],[306, 299])).
% 0.50/0.64 tff(308,plain,
% 0.50/0.64 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.50/0.64 inference(symmetry,[status(thm)],[307])).
% 0.50/0.64 tff(309,plain,
% 0.50/0.64 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.50/0.64 inference(transitivity,[status(thm)],[308, 261])).
% 0.50/0.64 tff(310,plain,
% 0.50/0.64 (((~![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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.64 inference(rewrite,[status(thm)],[])).
% 0.50/0.64 tff(311,plain,
% 0.50/0.64 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.64 inference(rewrite,[status(thm)],[])).
% 0.50/0.64 tff(312,plain,
% 0.50/0.64 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.50/0.65 inference(rewrite,[status(thm)],[])).
% 0.50/0.65 tff(313,plain,
% 0.50/0.65 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.65 inference(monotonicity,[status(thm)],[312])).
% 0.50/0.65 tff(314,plain,
% 0.50/0.65 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.65 inference(transitivity,[status(thm)],[313, 311])).
% 0.50/0.65 tff(315,plain,
% 0.50/0.65 (((~![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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.50/0.66 inference(monotonicity,[status(thm)],[314])).
% 0.50/0.66 tff(316,plain,
% 0.50/0.66 (((~![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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.66 inference(transitivity,[status(thm)],[315, 310])).
% 0.50/0.66 tff(317,plain,
% 0.50/0.66 ((~![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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(318,plain,
% 0.50/0.66 ((~![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_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.50/0.66 tff(319,plain,
% 0.50/0.66 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[318, 137, 252])).
% 0.50/0.67 tff(320,plain,
% 0.50/0.67 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.50/0.67 inference(tautology,[status(thm)],[])).
% 0.50/0.67 tff(321,plain,
% 0.50/0.67 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.50/0.67 tff(322,plain,
% 0.50/0.67 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(323,plain,
% 0.50/0.67 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(324,plain,
% 0.50/0.67 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.50/0.67 tff(325,plain,
% 0.50/0.67 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[324, 233, 252])).
% 0.50/0.67 tff(326,plain,
% 0.50/0.67 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.50/0.67 inference(tautology,[status(thm)],[])).
% 0.50/0.67 tff(327,plain,
% 0.50/0.67 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[326, 325])).
% 0.50/0.67 tff(328,plain,
% 0.50/0.67 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[327, 321])).
% 0.50/0.68 tff(329,plain,
% 0.50/0.68 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(330,plain,
% 0.50/0.68 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.50/0.68 tff(331,plain,
% 0.50/0.68 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(332,plain,
% 0.50/0.68 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[331, 328])).
% 0.50/0.68 tff(333,plain,
% 0.50/0.68 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(334,plain,
% 0.50/0.68 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(335,plain,
% 0.50/0.68 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.50/0.68 tff(336,plain,
% 0.50/0.68 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[335, 115, 252])).
% 0.50/0.68 tff(337,plain,
% 0.50/0.68 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(338,plain,
% 0.50/0.68 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.50/0.68 tff(339,plain,
% 0.50/0.68 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(340,plain,
% 0.50/0.68 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[339, 336])).
% 0.50/0.68 tff(341,plain,
% 0.50/0.68 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(342,plain,
% 0.50/0.68 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(343,plain,
% 0.50/0.69 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[342])).
% 0.50/0.69 tff(344,plain,
% 0.50/0.69 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[343, 341])).
% 0.50/0.69 tff(345,plain,
% 0.50/0.69 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(346,plain,
% 0.50/0.69 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.50/0.69 tff(347,plain,
% 0.50/0.69 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[346, 254, 252, 340, 338, 332, 330])).
% 0.50/0.69 tff(348,plain,
% 0.50/0.69 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.50/0.69 inference(symmetry,[status(thm)],[347])).
% 0.50/0.69 tff(349,plain,
% 0.50/0.69 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.50/0.69 inference(symmetry,[status(thm)],[261])).
% 0.50/0.69 tff(350,plain,
% 0.50/0.69 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.50/0.70 inference(transitivity,[status(thm)],[349, 307])).
% 0.50/0.70 tff(351,plain,
% 0.50/0.70 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.50/0.70 inference(monotonicity,[status(thm)],[350])).
% 0.50/0.70 tff(352,plain,
% 0.50/0.70 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.50/0.70 inference(symmetry,[status(thm)],[351])).
% 0.50/0.70 tff(353,plain,
% 0.50/0.70 (((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))) | (~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(354,plain,
% 0.50/0.70 (~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[353, 65])).
% 0.50/0.70 tff(355,plain,
% 0.50/0.70 (((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))) | member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(356,plain,
% 0.50/0.70 (member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[355, 65])).
% 0.50/0.70 tff(357,assumption,(member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)), introduced(assumption)).
% 0.50/0.70 tff(358,plain,
% 0.50/0.70 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(359,plain,
% 0.50/0.70 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(360,plain,
% 0.50/0.70 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.50/0.70 tff(361,plain,
% 0.50/0.70 (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[360, 115, 357])).
% 0.50/0.70 tff(362,plain,
% 0.50/0.70 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(363,plain,
% 0.50/0.70 (member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.50/0.70 tff(364,plain,
% 0.50/0.70 (((~![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_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(365,plain,
% 0.50/0.70 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(366,plain,
% 0.50/0.70 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(367,plain,
% 0.50/0.70 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[366])).
% 0.50/0.71 tff(368,plain,
% 0.50/0.71 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.50/0.71 inference(transitivity,[status(thm)],[367, 365])).
% 0.50/0.71 tff(369,plain,
% 0.50/0.71 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[368])).
% 0.50/0.71 tff(370,plain,
% 0.50/0.71 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!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_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.50/0.71 inference(transitivity,[status(thm)],[369, 364])).
% 0.50/0.71 tff(371,plain,
% 0.50/0.71 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.59/0.72 inference(quant_inst,[status(thm)],[])).
% 0.59/0.72 tff(372,plain,
% 0.59/0.72 ((~![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_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.59/0.72 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.59/0.72 tff(373,plain,
% 0.59/0.72 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))),
% 0.59/0.72 inference(unit_resolution,[status(thm)],[372, 137, 363])).
% 0.59/0.72 tff(374,plain,
% 0.59/0.72 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.59/0.72 inference(tautology,[status(thm)],[])).
% 0.59/0.72 tff(375,plain,
% 0.59/0.72 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.59/0.72 inference(unit_resolution,[status(thm)],[374, 373])).
% 0.59/0.72 tff(376,plain,
% 0.59/0.72 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.72 inference(rewrite,[status(thm)],[])).
% 0.59/0.72 tff(377,plain,
% 0.59/0.72 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.72 inference(quant_inst,[status(thm)],[])).
% 0.59/0.72 tff(378,plain,
% 0.59/0.72 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.72 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.59/0.72 tff(379,plain,
% 0.59/0.72 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.72 inference(unit_resolution,[status(thm)],[378, 233, 363])).
% 0.59/0.72 tff(380,plain,
% 0.59/0.72 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.59/0.72 inference(tautology,[status(thm)],[])).
% 0.59/0.72 tff(381,plain,
% 0.59/0.72 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.59/0.72 inference(unit_resolution,[status(thm)],[380, 379])).
% 0.59/0.72 tff(382,plain,
% 0.59/0.72 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[381, 375])).
% 0.59/0.73 tff(383,plain,
% 0.59/0.73 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.59/0.73 inference(tautology,[status(thm)],[])).
% 0.59/0.73 tff(384,plain,
% 0.59/0.73 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.59/0.73 tff(385,plain,
% 0.59/0.73 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.73 inference(tautology,[status(thm)],[])).
% 0.59/0.73 tff(386,plain,
% 0.59/0.73 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[385, 382])).
% 0.59/0.73 tff(387,plain,
% 0.59/0.73 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.59/0.73 inference(rewrite,[status(thm)],[])).
% 0.59/0.73 tff(388,plain,
% 0.59/0.73 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.59/0.73 inference(quant_inst,[status(thm)],[])).
% 0.59/0.73 tff(389,plain,
% 0.59/0.73 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.59/0.73 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.59/0.73 tff(390,plain,
% 0.59/0.73 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[389, 115, 363])).
% 0.59/0.73 tff(391,plain,
% 0.59/0.73 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.59/0.73 inference(tautology,[status(thm)],[])).
% 0.59/0.73 tff(392,plain,
% 0.59/0.73 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.59/0.73 tff(393,plain,
% 0.59/0.73 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.59/0.73 inference(tautology,[status(thm)],[])).
% 0.59/0.73 tff(394,plain,
% 0.59/0.73 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[393, 390])).
% 0.59/0.73 tff(395,plain,
% 0.59/0.73 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.59/0.73 inference(rewrite,[status(thm)],[])).
% 0.59/0.73 tff(396,plain,
% 0.59/0.73 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.59/0.73 inference(rewrite,[status(thm)],[])).
% 0.59/0.73 tff(397,plain,
% 0.59/0.73 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.59/0.74 inference(monotonicity,[status(thm)],[396])).
% 0.59/0.74 tff(398,plain,
% 0.59/0.74 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.59/0.74 inference(transitivity,[status(thm)],[397, 395])).
% 0.59/0.74 tff(399,plain,
% 0.59/0.74 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.59/0.74 inference(quant_inst,[status(thm)],[])).
% 0.59/0.74 tff(400,plain,
% 0.59/0.74 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.59/0.74 tff(401,plain,
% 0.59/0.74 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[400, 254, 363, 394, 392, 386, 384])).
% 0.59/0.74 tff(402,plain,
% 0.59/0.74 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(403,plain,
% 0.59/0.74 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(404,plain,
% 0.59/0.74 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(405,plain,
% 0.59/0.75 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[404])).
% 0.59/0.75 tff(406,plain,
% 0.59/0.75 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.59/0.75 inference(transitivity,[status(thm)],[405, 403])).
% 0.59/0.75 tff(407,plain,
% 0.59/0.75 (((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[406])).
% 0.59/0.75 tff(408,plain,
% 0.59/0.75 (((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.59/0.75 inference(transitivity,[status(thm)],[407, 402])).
% 0.59/0.75 tff(409,plain,
% 0.59/0.75 ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(410,plain,
% 0.59/0.76 ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.59/0.76 tff(411,plain,
% 0.59/0.76 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[410, 137, 357])).
% 0.59/0.76 tff(412,plain,
% 0.59/0.76 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(413,plain,
% 0.59/0.76 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[412, 411])).
% 0.59/0.76 tff(414,plain,
% 0.59/0.76 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(415,plain,
% 0.59/0.76 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(416,plain,
% 0.59/0.76 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.59/0.76 tff(417,plain,
% 0.59/0.76 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[416, 233, 357])).
% 0.59/0.76 tff(418,plain,
% 0.59/0.76 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(419,plain,
% 0.59/0.76 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.59/0.76 tff(420,plain,
% 0.59/0.76 (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[419, 413])).
% 0.59/0.76 tff(421,plain,
% 0.59/0.76 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(422,plain,
% 0.59/0.76 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[421, 420])).
% 0.59/0.76 tff(423,plain,
% 0.59/0.76 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(424,plain,
% 0.59/0.76 (member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[423, 420])).
% 0.59/0.76 tff(425,plain,
% 0.59/0.76 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(426,plain,
% 0.59/0.76 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[425, 361])).
% 0.59/0.77 tff(427,plain,
% 0.59/0.77 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(428,plain,
% 0.59/0.77 (((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(429,plain,
% 0.59/0.77 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.59/0.77 inference(monotonicity,[status(thm)],[428])).
% 0.59/0.77 tff(430,plain,
% 0.59/0.77 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.77 inference(transitivity,[status(thm)],[429, 427])).
% 0.59/0.77 tff(431,plain,
% 0.59/0.77 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))),
% 0.59/0.77 inference(quant_inst,[status(thm)],[])).
% 0.59/0.77 tff(432,plain,
% 0.59/0.77 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.59/0.77 tff(433,plain,
% 0.59/0.77 (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[432, 254, 357, 363, 426, 424, 422])).
% 0.59/0.77 tff(434,plain,
% 0.59/0.77 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40)),
% 0.59/0.77 inference(symmetry,[status(thm)],[433])).
% 0.59/0.77 tff(435,plain,
% 0.59/0.77 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.77 inference(monotonicity,[status(thm)],[434])).
% 0.59/0.77 tff(436,plain,
% 0.59/0.77 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.77 inference(symmetry,[status(thm)],[435])).
% 0.59/0.77 tff(437,plain,
% 0.59/0.77 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.77 inference(tautology,[status(thm)],[])).
% 0.59/0.77 tff(438,plain,
% 0.59/0.77 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[437, 420])).
% 0.59/0.77 tff(439,plain,
% 0.59/0.77 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[438, 436])).
% 0.59/0.77 tff(440,plain,
% 0.59/0.77 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(441,plain,
% 0.59/0.78 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.59/0.78 inference(rewrite,[status(thm)],[])).
% 0.59/0.78 tff(442,plain,
% 0.59/0.78 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.59/0.78 inference(monotonicity,[status(thm)],[441])).
% 0.59/0.78 tff(443,plain,
% 0.59/0.78 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.59/0.78 inference(transitivity,[status(thm)],[442, 440])).
% 0.59/0.78 tff(444,plain,
% 0.59/0.78 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.65/0.78 inference(quant_inst,[status(thm)],[])).
% 0.65/0.78 tff(445,plain,
% 0.65/0.78 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.65/0.78 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.65/0.78 tff(446,plain,
% 0.65/0.78 ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.65/0.78 inference(unit_resolution,[status(thm)],[445, 254, 357, 363, 386, 384])).
% 0.65/0.78 tff(447,plain,
% 0.65/0.78 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.65/0.78 inference(unit_resolution,[status(thm)],[446, 439])).
% 0.65/0.78 tff(448,plain,
% 0.65/0.78 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.65/0.78 inference(symmetry,[status(thm)],[447])).
% 0.65/0.78 tff(449,plain,
% 0.65/0.78 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.65/0.78 inference(transitivity,[status(thm)],[448, 401])).
% 0.65/0.78 tff(450,plain,
% 0.65/0.78 (((~![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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.79 inference(rewrite,[status(thm)],[])).
% 0.65/0.79 tff(451,plain,
% 0.65/0.79 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.79 inference(rewrite,[status(thm)],[])).
% 0.65/0.79 tff(452,plain,
% 0.65/0.79 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.65/0.79 inference(rewrite,[status(thm)],[])).
% 0.65/0.79 tff(453,plain,
% 0.65/0.79 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[452])).
% 0.65/0.80 tff(454,plain,
% 0.65/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.80 inference(transitivity,[status(thm)],[453, 451])).
% 0.65/0.80 tff(455,plain,
% 0.65/0.80 (((~![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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[454])).
% 0.65/0.80 tff(456,plain,
% 0.65/0.80 (((~![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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.80 inference(transitivity,[status(thm)],[455, 450])).
% 0.65/0.80 tff(457,plain,
% 0.65/0.80 ((~![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_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(458,plain,
% 0.65/0.81 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.65/0.81 tff(459,plain,
% 0.65/0.81 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[458, 137, 394])).
% 0.65/0.81 tff(460,plain,
% 0.65/0.81 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.65/0.81 inference(tautology,[status(thm)],[])).
% 0.65/0.81 tff(461,plain,
% 0.65/0.81 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[460, 459])).
% 0.65/0.81 tff(462,plain,
% 0.65/0.81 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(463,plain,
% 0.65/0.81 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(464,plain,
% 0.65/0.81 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.65/0.81 tff(465,plain,
% 0.65/0.81 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[464, 233, 394])).
% 0.65/0.81 tff(466,plain,
% 0.65/0.81 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(467,plain,
% 0.65/0.82 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[466, 465])).
% 0.65/0.82 tff(468,plain,
% 0.65/0.82 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[467, 461])).
% 0.65/0.82 tff(469,plain,
% 0.65/0.82 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(470,plain,
% 0.65/0.82 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[469, 468])).
% 0.65/0.82 tff(471,plain,
% 0.65/0.82 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(472,plain,
% 0.65/0.82 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[471, 468])).
% 0.65/0.82 tff(473,plain,
% 0.65/0.82 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(474,plain,
% 0.65/0.82 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(475,plain,
% 0.65/0.82 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.65/0.82 tff(476,plain,
% 0.65/0.82 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[475, 115, 394])).
% 0.65/0.82 tff(477,plain,
% 0.65/0.82 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(478,plain,
% 0.65/0.82 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[477, 476])).
% 0.65/0.82 tff(479,plain,
% 0.65/0.82 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(480,plain,
% 0.65/0.82 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[479, 476])).
% 0.65/0.82 tff(481,plain,
% 0.65/0.82 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(482,plain,
% 0.65/0.83 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(483,plain,
% 0.65/0.83 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[482])).
% 0.65/0.83 tff(484,plain,
% 0.65/0.83 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[483, 481])).
% 0.65/0.83 tff(485,plain,
% 0.65/0.83 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(486,plain,
% 0.65/0.84 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.65/0.84 tff(487,plain,
% 0.65/0.84 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[486, 254, 394, 480, 478, 472, 470])).
% 0.65/0.84 tff(488,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.65/0.84 inference(symmetry,[status(thm)],[487])).
% 0.65/0.84 tff(489,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.65/0.84 inference(symmetry,[status(thm)],[401])).
% 0.65/0.84 tff(490,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.65/0.84 inference(transitivity,[status(thm)],[489, 447])).
% 0.65/0.84 tff(491,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.65/0.84 inference(monotonicity,[status(thm)],[490])).
% 0.65/0.84 tff(492,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.65/0.84 inference(symmetry,[status(thm)],[491])).
% 0.65/0.84 tff(493,assumption,(~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))), introduced(assumption)).
% 0.65/0.84 tff(494,assumption,(~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))), introduced(assumption)).
% 0.65/0.84 tff(495,plain,
% 0.65/0.84 ((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.84 inference(tautology,[status(thm)],[])).
% 0.65/0.84 tff(496,plain,
% 0.65/0.84 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[495, 494, 493])).
% 0.65/0.84 tff(497,assumption,(member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)), introduced(assumption)).
% 0.65/0.84 tff(498,plain,
% 0.65/0.84 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(499,plain,
% 0.65/0.84 (((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(500,plain,
% 0.65/0.84 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[499])).
% 0.65/0.84 tff(501,plain,
% 0.65/0.84 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[500, 498])).
% 0.65/0.84 tff(502,plain,
% 0.65/0.84 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(503,plain,
% 0.65/0.84 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.65/0.84 tff(504,plain,
% 0.65/0.84 ((~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[503, 254, 497, 357, 363, 426])).
% 0.65/0.84 tff(505,plain,
% 0.65/0.84 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[504, 496])).
% 0.65/0.85 tff(506,plain,
% 0.65/0.85 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.65/0.85 inference(symmetry,[status(thm)],[505])).
% 0.65/0.85 tff(507,plain,
% 0.65/0.85 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.65/0.85 inference(transitivity,[status(thm)],[506, 492, 488])).
% 0.65/0.85 tff(508,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[507, 449])).
% 0.65/0.85 tff(509,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) <=> apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(symmetry,[status(thm)],[508])).
% 0.65/0.85 tff(510,plain,
% 0.65/0.85 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(511,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[510, 468])).
% 0.65/0.85 tff(512,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[511, 509])).
% 0.65/0.85 tff(513,plain,
% 0.65/0.85 ($false),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[494, 512])).
% 0.65/0.85 tff(514,plain,(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.85 tff(515,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[514, 67, 356, 354])).
% 0.65/0.85 tff(516,plain,
% 0.65/0.85 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(517,plain,
% 0.65/0.85 (((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(518,plain,
% 0.65/0.85 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[517])).
% 0.65/0.85 tff(519,plain,
% 0.65/0.85 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.65/0.85 inference(transitivity,[status(thm)],[518, 516])).
% 0.65/0.85 tff(520,plain,
% 0.65/0.85 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(521,plain,
% 0.65/0.85 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.65/0.85 tff(522,plain,
% 0.65/0.85 ((~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[521, 254, 67, 356, 121, 286])).
% 0.65/0.85 tff(523,plain,
% 0.65/0.85 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[522, 515])).
% 0.65/0.85 tff(524,plain,
% 0.65/0.85 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.65/0.85 inference(symmetry,[status(thm)],[523])).
% 0.65/0.85 tff(525,plain,
% 0.65/0.85 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.65/0.85 inference(transitivity,[status(thm)],[524, 352, 348])).
% 0.65/0.85 tff(526,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[525, 309])).
% 0.65/0.85 tff(527,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(symmetry,[status(thm)],[526])).
% 0.65/0.85 tff(528,plain,
% 0.65/0.85 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(529,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[528, 328])).
% 0.65/0.85 tff(530,plain,
% 0.65/0.85 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[529, 527])).
% 0.65/0.85 tff(531,plain,
% 0.65/0.85 ((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(532,plain,
% 0.65/0.85 (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[531, 515, 354])).
% 0.65/0.85 tff(533,plain,
% 0.65/0.85 ($false),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[532, 530])).
% 0.65/0.85 tff(534,plain,((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.85 tff(535,plain,
% 0.65/0.85 ((~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))) | inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(536,plain,
% 0.65/0.85 ((~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))) | inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[535, 534])).
% 0.65/0.85 tff(537,plain,
% 0.65/0.85 (inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[536, 64])).
% 0.65/0.85 tff(538,plain,
% 0.65/0.85 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(539,plain,
% 0.65/0.85 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[538, 215])).
% 0.65/0.85 tff(540,plain,
% 0.65/0.85 ((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[539, 228])).
% 0.65/0.85 tff(541,plain,
% 0.65/0.85 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | (~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(542,plain,
% 0.65/0.85 ((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[541, 540])).
% 0.65/0.85 tff(543,plain,
% 0.65/0.85 (~one_to_one(F!40, A!39, A!39)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[542, 537])).
% 0.65/0.85 tff(544,plain,
% 0.65/0.85 ((~(one_to_one(F!40, A!39, A!39) <=> (~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))))) | one_to_one(F!40, A!39, A!39) | ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))),
% 0.65/0.85 inference(tautology,[status(thm)],[])).
% 0.65/0.85 tff(545,plain,
% 0.65/0.85 ((~(one_to_one(F!40, A!39, A!39) <=> (~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))))) | ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[544, 543])).
% 0.65/0.85 tff(546,plain,
% 0.65/0.85 ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[545, 37])).
% 0.65/0.85 tff(547,assumption,((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))), introduced(assumption)).
% 0.65/0.85 tff(548,plain,
% 0.65/0.85 (^[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))))))))))))),
% 0.65/0.85 inference(bind,[status(th)],[])).
% 0.65/0.85 tff(549,plain,
% 0.65/0.85 (![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)))))))))))),
% 0.65/0.86 inference(quant_intro,[status(thm)],[548])).
% 0.65/0.86 tff(550,plain,
% 0.65/0.86 (^[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))))))))))))),
% 0.65/0.86 inference(bind,[status(th)],[])).
% 0.65/0.86 tff(551,plain,
% 0.65/0.86 (![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)))))))))))),
% 0.65/0.86 inference(quant_intro,[status(thm)],[550])).
% 0.65/0.86 tff(552,plain,
% 0.65/0.86 (![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)))))))))))),
% 0.65/0.86 inference(transitivity,[status(thm)],[551, 549])).
% 0.65/0.86 tff(553,plain,
% 0.65/0.86 (^[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)))))))))))))),
% 0.65/0.86 inference(bind,[status(th)],[])).
% 0.65/0.86 tff(554,plain,
% 0.65/0.86 (![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)))))))))))),
% 0.65/0.86 inference(quant_intro,[status(thm)],[553])).
% 0.65/0.86 tff(555,plain,
% 0.65/0.86 (^[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))))))))),
% 0.65/0.86 inference(bind,[status(th)],[])).
% 0.65/0.86 tff(556,plain,
% 0.65/0.86 (![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)))))))),
% 0.65/0.86 inference(quant_intro,[status(thm)],[555])).
% 0.65/0.86 tff(557,plain,
% 0.65/0.86 (![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))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(558,plain,
% 0.65/0.86 (^[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)))))),
% 0.65/0.86 inference(bind,[status(th)],[])).
% 0.65/0.86 tff(559,plain,
% 0.65/0.86 (![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))))),
% 0.65/0.86 inference(quant_intro,[status(thm)],[558])).
% 0.65/0.86 tff(560,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')).
% 0.65/0.86 tff(561,plain,
% 0.65/0.86 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.65/0.86 tff(562,plain,
% 0.65/0.86 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[561, 557])).
% 0.65/0.86 tff(563,plain,(
% 0.65/0.86 ![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)))))))),
% 0.65/0.86 inference(skolemize,[status(sab)],[562])).
% 0.65/0.86 tff(564,plain,
% 0.65/0.86 (![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)))))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[563, 556])).
% 0.65/0.86 tff(565,plain,
% 0.65/0.86 (![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)))))))))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[564, 554])).
% 0.65/0.86 tff(566,plain,
% 0.65/0.86 (![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)))))))))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[565, 552])).
% 0.65/0.86 tff(567,plain,
% 0.65/0.86 ((~![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!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(568,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[567, 566, 547])).
% 0.65/0.86 tff(569,plain,(~((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(570,plain,
% 0.65/0.86 (((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))) | (surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))),
% 0.65/0.86 inference(tautology,[status(thm)],[])).
% 0.65/0.86 tff(571,plain,
% 0.65/0.86 (surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[570, 569])).
% 0.65/0.86 tff(572,assumption,(~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))), introduced(assumption)).
% 0.65/0.86 tff(573,plain,
% 0.65/0.86 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))) | member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)),
% 0.65/0.86 inference(tautology,[status(thm)],[])).
% 0.65/0.86 tff(574,plain,
% 0.65/0.86 (member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[573, 572])).
% 0.65/0.86 tff(575,plain,
% 0.65/0.86 (((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.86 inference(rewrite,[status(thm)],[])).
% 0.73/0.86 tff(576,plain,
% 0.73/0.86 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.86 inference(rewrite,[status(thm)],[])).
% 0.73/0.86 tff(577,plain,
% 0.73/0.86 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))),
% 0.73/0.86 inference(rewrite,[status(thm)],[])).
% 0.73/0.86 tff(578,plain,
% 0.73/0.86 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.86 inference(monotonicity,[status(thm)],[577])).
% 0.73/0.86 tff(579,plain,
% 0.73/0.86 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.87 inference(transitivity,[status(thm)],[578, 576])).
% 0.73/0.87 tff(580,plain,
% 0.73/0.87 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.73/0.87 inference(monotonicity,[status(thm)],[579])).
% 0.73/0.87 tff(581,plain,
% 0.73/0.87 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.87 inference(transitivity,[status(thm)],[580, 575])).
% 0.73/0.87 tff(582,plain,
% 0.73/0.87 ((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.73/0.87 inference(quant_inst,[status(thm)],[])).
% 0.73/0.87 tff(583,plain,
% 0.73/0.87 ((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))),
% 0.73/0.87 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.73/0.87 tff(584,plain,
% 0.73/0.87 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[583, 137, 574])).
% 0.73/0.87 tff(585,plain,
% 0.73/0.87 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(586,plain,
% 0.73/0.87 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[585, 584])).
% 0.73/0.87 tff(587,plain,
% 0.73/0.87 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.73/0.87 inference(rewrite,[status(thm)],[])).
% 0.73/0.87 tff(588,plain,
% 0.73/0.87 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.73/0.87 inference(quant_inst,[status(thm)],[])).
% 0.73/0.87 tff(589,plain,
% 0.73/0.87 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.73/0.87 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.73/0.87 tff(590,plain,
% 0.73/0.87 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[589, 233, 574])).
% 0.73/0.87 tff(591,plain,
% 0.73/0.87 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(592,plain,
% 0.73/0.87 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[591, 590])).
% 0.73/0.87 tff(593,plain,
% 0.73/0.87 (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[592, 586])).
% 0.73/0.87 tff(594,plain,
% 0.73/0.87 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(595,plain,
% 0.73/0.87 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[594, 593])).
% 0.73/0.87 tff(596,plain,
% 0.73/0.87 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(597,plain,
% 0.73/0.87 (member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[596, 593])).
% 0.73/0.87 tff(598,plain,
% 0.73/0.87 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))) | ![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(599,plain,
% 0.73/0.87 (![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[598, 572])).
% 0.73/0.87 tff(600,plain,
% 0.73/0.87 (((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))) <=> ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.73/0.87 inference(rewrite,[status(thm)],[])).
% 0.73/0.87 tff(601,plain,
% 0.73/0.87 ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.73/0.87 inference(quant_inst,[status(thm)],[])).
% 0.73/0.87 tff(602,plain,
% 0.73/0.87 ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.73/0.87 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.73/0.87 tff(603,plain,
% 0.73/0.87 ($false),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[602, 599, 597, 595])).
% 0.73/0.87 tff(604,plain,((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.87 tff(605,plain,
% 0.73/0.87 ((~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))) | surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))),
% 0.73/0.87 inference(tautology,[status(thm)],[])).
% 0.73/0.87 tff(606,plain,
% 0.73/0.87 ((~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))) | surjective(F!40, A!39, A!39)),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[605, 604])).
% 0.73/0.87 tff(607,plain,
% 0.73/0.87 (surjective(F!40, A!39, A!39)),
% 0.73/0.87 inference(unit_resolution,[status(thm)],[606, 571])).
% 0.73/0.87 tff(608,plain,
% 0.73/0.87 ((~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))) | (~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))),
% 0.75/0.88 inference(tautology,[status(thm)],[])).
% 0.75/0.88 tff(609,plain,
% 0.75/0.88 (~injective(F!40, A!39, A!39)),
% 0.75/0.88 inference(unit_resolution,[status(thm)],[608, 607, 546])).
% 0.75/0.88 tff(610,plain,
% 0.75/0.88 ((~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))) | injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))),
% 0.75/0.88 inference(tautology,[status(thm)],[])).
% 0.75/0.88 tff(611,plain,
% 0.75/0.88 ((~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))),
% 0.75/0.88 inference(unit_resolution,[status(thm)],[610, 609])).
% 0.75/0.88 tff(612,plain,
% 0.75/0.88 (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))),
% 0.75/0.88 inference(unit_resolution,[status(thm)],[611, 25])).
% 0.75/0.88 tff(613,plain,
% 0.75/0.88 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)),
% 0.75/0.88 inference(tautology,[status(thm)],[])).
% 0.75/0.88 tff(614,plain,
% 0.75/0.88 (member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)),
% 0.75/0.88 inference(unit_resolution,[status(thm)],[613, 612])).
% 0.75/0.88 tff(615,plain,
% 0.75/0.88 (((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!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_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.88 inference(rewrite,[status(thm)],[])).
% 0.75/0.88 tff(616,plain,
% 0.75/0.88 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.88 inference(rewrite,[status(thm)],[])).
% 0.75/0.88 tff(617,plain,
% 0.75/0.88 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))),
% 0.75/0.88 inference(rewrite,[status(thm)],[])).
% 0.75/0.88 tff(618,plain,
% 0.75/0.88 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.88 inference(monotonicity,[status(thm)],[617])).
% 0.75/0.88 tff(619,plain,
% 0.75/0.88 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.88 inference(transitivity,[status(thm)],[618, 616])).
% 0.75/0.88 tff(620,plain,
% 0.75/0.88 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!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_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.75/0.88 inference(monotonicity,[status(thm)],[619])).
% 0.75/0.88 tff(621,plain,
% 0.75/0.88 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!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_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.89 inference(transitivity,[status(thm)],[620, 615])).
% 0.75/0.89 tff(622,plain,
% 0.75/0.89 ((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.75/0.89 inference(quant_inst,[status(thm)],[])).
% 0.75/0.89 tff(623,plain,
% 0.75/0.89 ((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))),
% 0.75/0.89 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.75/0.89 tff(624,plain,
% 0.75/0.89 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[623, 137, 614])).
% 0.75/0.89 tff(625,plain,
% 0.75/0.89 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(626,plain,
% 0.75/0.89 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[625, 624])).
% 0.75/0.89 tff(627,plain,
% 0.75/0.89 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.75/0.89 inference(rewrite,[status(thm)],[])).
% 0.75/0.89 tff(628,plain,
% 0.75/0.89 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.75/0.89 inference(quant_inst,[status(thm)],[])).
% 0.75/0.89 tff(629,plain,
% 0.75/0.89 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.89 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.75/0.89 tff(630,plain,
% 0.75/0.89 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[629, 233, 614])).
% 0.75/0.89 tff(631,plain,
% 0.75/0.89 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(632,plain,
% 0.75/0.89 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[631, 630])).
% 0.75/0.89 tff(633,plain,
% 0.75/0.89 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[632, 626])).
% 0.75/0.89 tff(634,plain,
% 0.75/0.89 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(635,plain,
% 0.75/0.89 (apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[634, 633])).
% 0.75/0.89 tff(636,plain,
% 0.75/0.89 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(637,plain,
% 0.75/0.89 (member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[636, 633])).
% 0.75/0.89 tff(638,plain,
% 0.75/0.89 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(639,plain,
% 0.75/0.89 (member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[638, 612])).
% 0.75/0.89 tff(640,plain,
% 0.75/0.89 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.75/0.89 inference(tautology,[status(thm)],[])).
% 0.75/0.89 tff(641,plain,
% 0.75/0.89 (apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.75/0.89 inference(unit_resolution,[status(thm)],[640, 612])).
% 0.75/0.89 tff(642,plain,
% 0.75/0.89 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(643,plain,
% 0.75/0.90 (((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(644,plain,
% 0.75/0.90 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[643])).
% 0.75/0.90 tff(645,plain,
% 0.75/0.90 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[644, 642])).
% 0.75/0.90 tff(646,plain,
% 0.75/0.90 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(647,plain,
% 0.75/0.90 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.75/0.90 tff(648,plain,
% 0.75/0.90 (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[647, 254, 641, 614, 639, 637, 635])).
% 0.75/0.90 tff(649,plain,
% 0.75/0.90 (tptp_fun_Y_16(A!39, A!39, F!40) = tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40)),
% 0.75/0.90 inference(symmetry,[status(thm)],[648])).
% 0.75/0.90 tff(650,plain,
% 0.75/0.90 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[649])).
% 0.75/0.90 tff(651,plain,
% 0.75/0.90 (apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.90 inference(symmetry,[status(thm)],[650])).
% 0.75/0.90 tff(652,plain,
% 0.75/0.90 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.90 inference(tautology,[status(thm)],[])).
% 0.75/0.90 tff(653,plain,
% 0.75/0.90 (apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[652, 633])).
% 0.75/0.90 tff(654,plain,
% 0.75/0.90 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[653, 651])).
% 0.75/0.90 tff(655,plain,
% 0.75/0.90 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)),
% 0.75/0.90 inference(tautology,[status(thm)],[])).
% 0.75/0.90 tff(656,plain,
% 0.75/0.90 (member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[655, 612])).
% 0.75/0.90 tff(657,plain,
% 0.75/0.90 (((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!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_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(658,plain,
% 0.75/0.90 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(659,plain,
% 0.75/0.90 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(660,plain,
% 0.75/0.90 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[659])).
% 0.75/0.90 tff(661,plain,
% 0.75/0.90 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[660, 658])).
% 0.75/0.90 tff(662,plain,
% 0.75/0.90 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!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_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[661])).
% 0.75/0.91 tff(663,plain,
% 0.75/0.91 (((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!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_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.91 inference(transitivity,[status(thm)],[662, 657])).
% 0.75/0.91 tff(664,plain,
% 0.75/0.91 ((~![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(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(665,plain,
% 0.75/0.91 ((~![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(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.75/0.91 tff(666,plain,
% 0.75/0.91 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[665, 137, 656])).
% 0.78/0.91 tff(667,plain,
% 0.78/0.91 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))),
% 0.78/0.91 inference(tautology,[status(thm)],[])).
% 0.78/0.91 tff(668,plain,
% 0.78/0.91 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[667, 666])).
% 0.78/0.91 tff(669,plain,
% 0.78/0.91 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.78/0.91 inference(rewrite,[status(thm)],[])).
% 0.78/0.91 tff(670,plain,
% 0.78/0.91 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.78/0.91 inference(quant_inst,[status(thm)],[])).
% 0.78/0.91 tff(671,plain,
% 0.78/0.91 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.91 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.78/0.91 tff(672,plain,
% 0.78/0.91 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[671, 233, 656])).
% 0.78/0.91 tff(673,plain,
% 0.78/0.91 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.78/0.91 inference(tautology,[status(thm)],[])).
% 0.78/0.91 tff(674,plain,
% 0.78/0.91 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[673, 672])).
% 0.78/0.91 tff(675,plain,
% 0.78/0.91 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[674, 668])).
% 0.78/0.91 tff(676,plain,
% 0.78/0.91 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.78/0.91 inference(tautology,[status(thm)],[])).
% 0.78/0.91 tff(677,plain,
% 0.78/0.91 (apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[676, 675])).
% 0.78/0.91 tff(678,plain,
% 0.78/0.91 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.78/0.91 inference(tautology,[status(thm)],[])).
% 0.78/0.91 tff(679,plain,
% 0.78/0.91 (member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.78/0.91 inference(unit_resolution,[status(thm)],[678, 675])).
% 0.78/0.91 tff(680,plain,
% 0.78/0.91 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.78/0.92 inference(tautology,[status(thm)],[])).
% 0.78/0.92 tff(681,plain,
% 0.78/0.92 (apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.78/0.92 inference(unit_resolution,[status(thm)],[680, 612])).
% 0.78/0.92 tff(682,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.78/0.92 inference(rewrite,[status(thm)],[])).
% 0.78/0.92 tff(683,plain,
% 0.78/0.92 (((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.78/0.92 inference(rewrite,[status(thm)],[])).
% 0.78/0.92 tff(684,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))))),
% 0.78/0.92 inference(monotonicity,[status(thm)],[683])).
% 0.78/0.92 tff(685,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.78/0.92 inference(transitivity,[status(thm)],[684, 682])).
% 0.78/0.92 tff(686,plain,
% 0.78/0.92 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.78/0.92 inference(quant_inst,[status(thm)],[])).
% 0.78/0.92 tff(687,plain,
% 0.78/0.92 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.78/0.92 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.78/0.92 tff(688,plain,
% 0.78/0.92 (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)),
% 0.78/0.92 inference(unit_resolution,[status(thm)],[687, 254, 681, 656, 639, 679, 677])).
% 0.78/0.92 tff(689,plain,
% 0.78/0.92 (tptp_fun_Y_16(A!39, A!39, F!40) = tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40)),
% 0.78/0.92 inference(symmetry,[status(thm)],[688])).
% 0.78/0.92 tff(690,plain,
% 0.78/0.92 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(monotonicity,[status(thm)],[689])).
% 0.78/0.92 tff(691,plain,
% 0.78/0.92 (apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(symmetry,[status(thm)],[690])).
% 0.78/0.92 tff(692,plain,
% 0.78/0.92 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(tautology,[status(thm)],[])).
% 0.78/0.92 tff(693,plain,
% 0.78/0.92 (apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(unit_resolution,[status(thm)],[692, 675])).
% 0.78/0.92 tff(694,plain,
% 0.78/0.92 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(modus_ponens,[status(thm)],[693, 691])).
% 0.78/0.92 tff(695,plain,
% 0.78/0.92 ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) <=> (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(commutativity,[status(thm)],[])).
% 0.78/0.92 tff(696,plain,
% 0.78/0.92 ((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) <=> (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.78/0.92 inference(symmetry,[status(thm)],[695])).
% 0.78/0.92 tff(697,plain,
% 0.78/0.92 ((~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) <=> (~(tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.78/0.92 inference(monotonicity,[status(thm)],[696])).
% 0.78/0.92 tff(698,plain,
% 0.78/0.92 (((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))) | (~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.78/0.92 inference(tautology,[status(thm)],[])).
% 0.78/0.92 tff(699,plain,
% 0.78/0.92 (~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.78/0.92 inference(unit_resolution,[status(thm)],[698, 612])).
% 0.78/0.92 tff(700,plain,
% 0.78/0.92 (~(tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.78/0.92 inference(modus_ponens,[status(thm)],[699, 697])).
% 0.78/0.92 tff(701,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.78/0.92 inference(rewrite,[status(thm)],[])).
% 0.78/0.92 tff(702,plain,
% 0.78/0.92 (((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.78/0.92 inference(rewrite,[status(thm)],[])).
% 0.78/0.92 tff(703,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.78/0.92 inference(monotonicity,[status(thm)],[702])).
% 0.78/0.92 tff(704,plain,
% 0.78/0.92 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.78/0.92 inference(transitivity,[status(thm)],[703, 701])).
% 0.78/0.92 tff(705,plain,
% 0.78/0.92 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(706,plain,
% 0.78/0.93 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.78/0.93 tff(707,plain,
% 0.78/0.93 ((~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[706, 254, 614, 656, 639])).
% 0.78/0.93 tff(708,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[707, 700, 694, 654])).
% 0.78/0.93 % SZS output end Proof
%------------------------------------------------------------------------------