%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET735+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:26:14 AM UTC 2025
% Result : Theorem 1.24s 1.40s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET735+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:39:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.24/1.40 % SZS status Theorem
% 1.24/1.40 % SZS output start Proof
% 1.24/1.40 tff(tptp_fun_Y2_12_type, type, (
% 1.24/1.40 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_F1_43_type, type, (
% 1.24/1.40 tptp_fun_F1_43: $i)).
% 1.24/1.40 tff(tptp_fun_F2_42_type, type, (
% 1.24/1.40 tptp_fun_F2_42: $i)).
% 1.24/1.40 tff(tptp_fun_A_40_type, type, (
% 1.24/1.40 tptp_fun_A_40: $i)).
% 1.24/1.40 tff(tptp_fun_B_39_type, type, (
% 1.24/1.40 tptp_fun_B_39: $i)).
% 1.24/1.40 tff(tptp_fun_Y1_13_type, type, (
% 1.24/1.40 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_Y_3_type, type, (
% 1.24/1.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_X_14_type, type, (
% 1.24/1.40 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 1.24/1.40 tff(apply_type, type, (
% 1.24/1.40 apply: ( $i * $i * $i ) > $o)).
% 1.24/1.40 tff(member_type, type, (
% 1.24/1.40 member: ( $i * $i ) > $o)).
% 1.24/1.40 tff(equal_maps_type, type, (
% 1.24/1.40 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 1.24/1.40 tff(equal_set_type, type, (
% 1.24/1.40 equal_set: ( $i * $i ) > $o)).
% 1.24/1.40 tff(image3_type, type, (
% 1.24/1.40 image3: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(identity_type, type, (
% 1.24/1.40 identity: ( $i * $i ) > $o)).
% 1.24/1.40 tff(compose_function_type, type, (
% 1.24/1.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_G_41_type, type, (
% 1.24/1.40 tptp_fun_G_41: $i)).
% 1.24/1.40 tff(maps_type, type, (
% 1.24/1.40 maps: ( $i * $i * $i ) > $o)).
% 1.24/1.40 tff(tptp_fun_Y2_5_type, type, (
% 1.24/1.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_Y1_6_type, type, (
% 1.24/1.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_X_7_type, type, (
% 1.24/1.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_X_4_type, type, (
% 1.24/1.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_Y_8_type, type, (
% 1.24/1.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_X_15_type, type, (
% 1.24/1.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 1.24/1.40 tff(tptp_fun_X_24_type, type, (
% 1.24/1.40 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 1.24/1.40 tff(subset_type, type, (
% 1.24/1.40 subset: ( $i * $i ) > $o)).
% 1.24/1.40 tff(tptp_fun_X_0_type, type, (
% 1.24/1.40 tptp_fun_X_0: ( $i * $i ) > $i)).
% 1.24/1.40 tff(1,plain,
% 1.24/1.40 (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(2,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[1])).
% 1.24/1.40 tff(3,plain,
% 1.24/1.40 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(4,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[3])).
% 1.24/1.40 tff(5,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[4, 2])).
% 1.24/1.40 tff(6,plain,
% 1.24/1.40 (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(7,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[6])).
% 1.24/1.40 tff(8,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(9,plain,
% 1.24/1.40 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(10,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[9])).
% 1.24/1.40 tff(11,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 1.24/1.40 tff(12,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.24/1.40 tff(13,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.24/1.40 tff(14,plain,(
% 1.24/1.40 ![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))),
% 1.24/1.40 inference(skolemize,[status(sab)],[13])).
% 1.24/1.40 tff(15,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.24/1.40 tff(16,plain,
% 1.24/1.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.24/1.40 tff(17,plain,
% 1.24/1.40 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(18,plain,
% 1.24/1.41 ((~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))) <=> (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(19,plain,
% 1.24/1.41 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[18])).
% 1.24/1.41 tff(20,plain,
% 1.24/1.41 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[19, 17])).
% 1.24/1.41 tff(21,plain,
% 1.24/1.41 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(22,plain,
% 1.24/1.41 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.24/1.41 tff(23,plain,
% 1.24/1.41 (~((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[22, 16])).
% 1.24/1.41 tff(24,plain,
% 1.24/1.41 (((~((~equal_maps(F1!43, F2!42, A!40, B!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y2))))) | (~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))))) | (equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))),
% 1.24/1.41 inference(tautology,[status(thm)],[])).
% 1.24/1.41 tff(25,plain,
% 1.24/1.41 (equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 1.24/1.41 tff(26,plain,
% 1.24/1.41 ((~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))) <=> (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(27,plain,
% 1.24/1.41 ((~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((((((maps(F1, A, B) & maps(F2, A, B)) & maps(G, B, A)) & identity(compose_function(G, F1, A, B, A), A)) & identity(compose_function(G, F2, A, B, A), A)) & equal_set(image3(F1, A, B), image3(F2, A, B))) => equal_maps(F1, F2, A, B))) <=> (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(28,axiom,(~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((((((maps(F1, A, B) & maps(F2, A, B)) & maps(G, B, A)) & identity(compose_function(G, F1, A, B, A), A)) & identity(compose_function(G, F2, A, B, A), A)) & equal_set(image3(F1, A, B), image3(F2, A, B))) => equal_maps(F1, F2, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII26')).
% 1.24/1.41 tff(29,plain,
% 1.24/1.41 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.24/1.41 tff(30,plain,
% 1.24/1.41 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 1.24/1.41 tff(31,plain,
% 1.24/1.41 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.24/1.41 tff(32,plain,
% 1.24/1.41 (~![F1: $i, F2: $i, G: $i, A: $i, B: $i] : ((~(maps(F1, A, B) & maps(F2, A, B) & maps(G, B, A) & identity(compose_function(G, F1, A, B, A), A) & identity(compose_function(G, F2, A, B, A), A) & equal_set(image3(F1, A, B), image3(F2, A, B)))) | equal_maps(F1, F2, A, B))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 1.24/1.41 tff(33,plain,(
% 1.24/1.41 ~((~(maps(F1!43, A!40, B!39) & maps(F2!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) & identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) & equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)))) | equal_maps(F1!43, F2!42, A!40, B!39))),
% 1.24/1.41 inference(skolemize,[status(sab)],[32])).
% 1.24/1.41 tff(34,plain,
% 1.24/1.41 (~equal_maps(F1!43, F2!42, A!40, B!39)),
% 1.24/1.41 inference(or_elim,[status(thm)],[33])).
% 1.24/1.41 tff(35,plain,
% 1.24/1.41 ((~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))) | equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.41 inference(tautology,[status(thm)],[])).
% 1.24/1.41 tff(36,plain,
% 1.24/1.41 ((~(equal_maps(F1!43, F2!42, A!40, B!39) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 1.24/1.41 tff(37,plain,
% 1.24/1.41 (~((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[36, 25])).
% 1.24/1.41 tff(38,plain,
% 1.24/1.41 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)),
% 1.24/1.41 inference(tautology,[status(thm)],[])).
% 1.24/1.41 tff(39,plain,
% 1.24/1.41 (member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 1.24/1.41 tff(40,plain,
% 1.24/1.41 (^[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)))))))))))),
% 1.24/1.41 inference(bind,[status(th)],[])).
% 1.24/1.41 tff(41,plain,
% 1.24/1.41 (![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))))))))))),
% 1.24/1.41 inference(quant_intro,[status(thm)],[40])).
% 1.24/1.41 tff(42,plain,
% 1.24/1.41 (^[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)))))))))),
% 1.24/1.41 inference(bind,[status(th)],[])).
% 1.24/1.41 tff(43,plain,
% 1.24/1.41 (![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))))))))),
% 1.24/1.41 inference(quant_intro,[status(thm)],[42])).
% 1.24/1.41 tff(44,plain,
% 1.24/1.41 (^[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)))))))))),
% 1.24/1.41 inference(bind,[status(th)],[])).
% 1.24/1.41 tff(45,plain,
% 1.24/1.41 (![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))))))))),
% 1.24/1.41 inference(quant_intro,[status(thm)],[44])).
% 1.24/1.41 tff(46,plain,
% 1.24/1.41 (![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))))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[45, 43])).
% 1.24/1.41 tff(47,plain,
% 1.24/1.41 (^[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(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)))))))), 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))))), ((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) | (~((~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) | (~((~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) | (~((~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) | (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) | (~((~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) | (~((~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) | (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))))))))))),
% 1.24/1.42 inference(bind,[status(th)],[])).
% 1.24/1.42 tff(48,plain,
% 1.24/1.42 (![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))))))))),
% 1.24/1.42 inference(quant_intro,[status(thm)],[47])).
% 1.24/1.42 tff(49,plain,
% 1.24/1.42 (^[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))))))))),
% 1.24/1.42 inference(bind,[status(th)],[])).
% 1.24/1.42 tff(50,plain,
% 1.24/1.42 (![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)))))))),
% 1.24/1.42 inference(quant_intro,[status(thm)],[49])).
% 1.24/1.42 tff(51,plain,
% 1.24/1.42 (![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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(52,plain,
% 1.24/1.42 (^[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)))))))),
% 1.24/1.42 inference(bind,[status(th)],[])).
% 1.24/1.42 tff(53,plain,
% 1.24/1.42 (![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))))))),
% 1.24/1.42 inference(quant_intro,[status(thm)],[52])).
% 1.24/1.42 tff(54,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')).
% 1.24/1.42 tff(55,plain,
% 1.24/1.42 (![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))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.24/1.42 tff(56,plain,
% 1.24/1.42 (![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))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.24/1.42 tff(57,plain,(
% 1.24/1.42 ![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))))))))),
% 1.24/1.42 inference(skolemize,[status(sab)],[56])).
% 1.24/1.42 tff(58,plain,
% 1.24/1.42 (![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)))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.24/1.42 tff(59,plain,
% 1.24/1.42 (![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))))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[58, 48])).
% 1.24/1.42 tff(60,plain,
% 1.24/1.42 (![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))))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[59, 46])).
% 1.24/1.42 tff(61,plain,
% 1.24/1.42 (![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))))))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[60, 41])).
% 1.24/1.42 tff(62,plain,
% 1.24/1.42 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)))))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(63,plain,
% 1.24/1.42 ((~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))))))) <=> (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42))))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(64,plain,
% 1.24/1.42 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[63])).
% 1.24/1.42 tff(65,plain,
% 1.24/1.42 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)))))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[64, 62])).
% 1.24/1.42 tff(66,plain,
% 1.24/1.42 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F2!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y))))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(67,plain,
% 1.24/1.42 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42))))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.24/1.42 tff(68,plain,
% 1.24/1.42 (~((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[67, 61])).
% 1.24/1.42 tff(69,plain,
% 1.24/1.42 (((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~(maps(F2!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F2!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_4(B!39, A!40, F2!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F2!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y2_5(B!39, A!40, F2!42))) | (~apply(F2!42, tptp_fun_X_7(B!39, A!40, F2!42), tptp_fun_Y1_6(B!39, A!40, F2!42))) | (tptp_fun_Y1_6(B!39, A!40, F2!42) = tptp_fun_Y2_5(B!39, A!40, F2!42))))))) | ((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(70,plain,
% 1.24/1.43 ((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.24/1.43 tff(71,plain,
% 1.24/1.43 (maps(F1!43, A!40, B!39) & maps(F2!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) & identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) & equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 1.24/1.43 inference(or_elim,[status(thm)],[33])).
% 1.24/1.43 tff(72,plain,
% 1.24/1.43 (maps(F2!42, A!40, B!39)),
% 1.24/1.43 inference(and_elim,[status(thm)],[71])).
% 1.24/1.43 tff(73,plain,
% 1.24/1.43 ((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(74,plain,
% 1.24/1.43 ((~((~maps(F2!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.24/1.43 tff(75,plain,
% 1.24/1.43 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[74, 70])).
% 1.24/1.43 tff(76,plain,
% 1.24/1.43 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(77,plain,
% 1.24/1.43 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[76, 75])).
% 1.24/1.43 tff(78,plain,
% 1.24/1.43 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(79,plain,
% 1.24/1.43 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(80,plain,
% 1.24/1.43 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.24/1.43 tff(81,plain,
% 1.24/1.43 (~((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[80, 77, 39])).
% 1.24/1.43 tff(82,plain,
% 1.24/1.43 (((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))) | apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(83,plain,
% 1.24/1.43 (apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[82, 81])).
% 1.24/1.43 tff(84,plain,
% 1.24/1.43 (((~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)))) | member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(85,plain,
% 1.24/1.43 (member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[84, 81])).
% 1.24/1.43 tff(86,plain,
% 1.24/1.43 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(87,plain,
% 1.24/1.43 (member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[86, 37])).
% 1.24/1.43 tff(88,plain,
% 1.24/1.43 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(89,plain,
% 1.24/1.43 (apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[88, 37])).
% 1.24/1.43 tff(90,plain,
% 1.24/1.43 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))),
% 1.24/1.43 inference(tautology,[status(thm)],[])).
% 1.24/1.43 tff(91,plain,
% 1.24/1.43 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[90, 75])).
% 1.24/1.43 tff(92,plain,
% 1.24/1.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(93,plain,
% 1.24/1.43 (((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))) <=> ((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(94,plain,
% 1.24/1.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[93])).
% 1.24/1.43 tff(95,plain,
% 1.24/1.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[94, 92])).
% 1.24/1.43 tff(96,plain,
% 1.24/1.43 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(97,plain,
% 1.24/1.43 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42))) | (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.24/1.43 tff(98,plain,
% 1.24/1.43 (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[97, 91, 89, 87, 39, 85, 83])).
% 1.24/1.43 tff(99,plain,
% 1.24/1.43 (^[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)))))))))),
% 1.24/1.43 inference(bind,[status(th)],[])).
% 1.24/1.43 tff(100,plain,
% 1.24/1.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 1.24/1.43 inference(quant_intro,[status(thm)],[99])).
% 1.24/1.43 tff(101,plain,
% 1.24/1.43 (^[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)))))))))),
% 1.24/1.43 inference(bind,[status(th)],[])).
% 1.24/1.43 tff(102,plain,
% 1.24/1.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 1.24/1.43 inference(quant_intro,[status(thm)],[101])).
% 1.24/1.43 tff(103,plain,
% 1.24/1.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[102, 100])).
% 1.24/1.43 tff(104,plain,
% 1.24/1.43 (^[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))))))))))),
% 1.24/1.44 inference(bind,[status(th)],[])).
% 1.24/1.44 tff(105,plain,
% 1.24/1.44 (![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))))))))),
% 1.24/1.44 inference(quant_intro,[status(thm)],[104])).
% 1.24/1.44 tff(106,plain,
% 1.24/1.44 (![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))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(107,plain,
% 1.24/1.44 (^[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))))))),
% 1.24/1.44 inference(bind,[status(th)],[])).
% 1.24/1.44 tff(108,plain,
% 1.24/1.44 (![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))))),
% 1.24/1.44 inference(quant_intro,[status(thm)],[107])).
% 1.24/1.44 tff(109,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')).
% 1.24/1.44 tff(110,plain,
% 1.24/1.44 (![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))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.24/1.44 tff(111,plain,
% 1.24/1.44 (![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))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.24/1.44 tff(112,plain,(
% 1.24/1.44 ![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))))))),
% 1.24/1.44 inference(skolemize,[status(sab)],[111])).
% 1.24/1.44 tff(113,plain,
% 1.24/1.44 (![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))))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.24/1.44 tff(114,plain,
% 1.24/1.44 (![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))))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[113, 103])).
% 1.24/1.44 tff(115,plain,
% 1.24/1.44 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(116,plain,
% 1.24/1.44 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(117,plain,
% 1.24/1.44 ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))) <=> (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(118,plain,
% 1.24/1.44 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[117])).
% 1.24/1.44 tff(119,plain,
% 1.24/1.44 (((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))) <=> ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[118, 116])).
% 1.24/1.44 tff(120,plain,
% 1.24/1.44 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[119])).
% 1.24/1.44 tff(121,plain,
% 1.24/1.44 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[120, 115])).
% 1.24/1.45 tff(122,plain,
% 1.24/1.45 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(123,plain,
% 1.24/1.45 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.24/1.45 tff(124,plain,
% 1.24/1.45 (~((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[123, 114, 39])).
% 1.24/1.45 tff(125,plain,
% 1.24/1.45 (((~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), Y)) | (~apply(G!41, Y, tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))) | (~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))))) | ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))),
% 1.24/1.45 inference(tautology,[status(thm)],[])).
% 1.24/1.45 tff(126,plain,
% 1.24/1.45 ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[125, 124])).
% 1.24/1.45 tff(127,plain,
% 1.24/1.45 (^[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)))))))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(128,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[127])).
% 1.24/1.45 tff(129,plain,
% 1.24/1.45 (^[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)))))))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(130,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[129])).
% 1.24/1.45 tff(131,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[130, 128])).
% 1.24/1.45 tff(132,plain,
% 1.24/1.45 (^[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))))))))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(133,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[132])).
% 1.24/1.45 tff(134,plain,
% 1.24/1.45 (![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)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(135,plain,
% 1.24/1.45 (^[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))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(136,plain,
% 1.24/1.45 (![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)))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[135])).
% 1.24/1.45 tff(137,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')).
% 1.24/1.45 tff(138,plain,
% 1.24/1.45 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.24/1.45 tff(139,plain,
% 1.24/1.45 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.24/1.45 tff(140,plain,(
% 1.24/1.45 ![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))))))),
% 1.24/1.45 inference(skolemize,[status(sab)],[139])).
% 1.24/1.45 tff(141,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.24/1.45 tff(142,plain,
% 1.24/1.45 (![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))))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[141, 131])).
% 1.24/1.45 tff(143,plain,
% 1.24/1.45 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(144,plain,
% 1.24/1.45 (~((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40))))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.24/1.45 tff(145,plain,
% 1.24/1.45 (((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F1!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))),
% 1.24/1.45 inference(tautology,[status(thm)],[])).
% 1.24/1.45 tff(146,plain,
% 1.24/1.45 ((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.24/1.45 tff(147,plain,
% 1.24/1.45 (identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)),
% 1.24/1.45 inference(and_elim,[status(thm)],[71])).
% 1.24/1.45 tff(148,plain,
% 1.24/1.45 ((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 1.24/1.45 inference(tautology,[status(thm)],[])).
% 1.24/1.45 tff(149,plain,
% 1.24/1.45 ((~((~identity(compose_function(G!41, F1!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[148, 147])).
% 1.24/1.45 tff(150,plain,
% 1.24/1.45 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[149, 146])).
% 1.24/1.45 tff(151,plain,
% 1.24/1.45 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(152,plain,
% 1.24/1.45 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(153,plain,
% 1.24/1.45 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.24/1.45 tff(154,plain,
% 1.24/1.45 (apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[153, 39, 150])).
% 1.24/1.45 tff(155,plain,
% 1.24/1.45 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 1.24/1.45 inference(tautology,[status(thm)],[])).
% 1.24/1.45 tff(156,plain,
% 1.24/1.45 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[155, 154])).
% 1.24/1.46 tff(157,plain,
% 1.24/1.46 (~((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[156, 126])).
% 1.24/1.46 tff(158,plain,
% 1.24/1.46 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))),
% 1.24/1.46 inference(tautology,[status(thm)],[])).
% 1.24/1.46 tff(159,plain,
% 1.24/1.46 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[158, 157])).
% 1.24/1.46 tff(160,plain,
% 1.24/1.46 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)),
% 1.24/1.46 inference(tautology,[status(thm)],[])).
% 1.24/1.46 tff(161,plain,
% 1.24/1.46 (member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[160, 157])).
% 1.24/1.46 tff(162,plain,
% 1.24/1.46 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)),
% 1.24/1.46 inference(tautology,[status(thm)],[])).
% 1.24/1.46 tff(163,plain,
% 1.24/1.46 (member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[162, 37])).
% 1.24/1.46 tff(164,plain,
% 1.24/1.46 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.24/1.46 inference(tautology,[status(thm)],[])).
% 1.24/1.46 tff(165,plain,
% 1.24/1.46 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[164, 37])).
% 1.24/1.46 tff(166,plain,
% 1.24/1.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(167,plain,
% 1.24/1.46 ((~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))))))) <=> (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(168,plain,
% 1.24/1.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[167])).
% 1.24/1.46 tff(169,plain,
% 1.24/1.46 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[168, 166])).
% 1.24/1.46 tff(170,plain,
% 1.24/1.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y))))))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(171,plain,
% 1.24/1.46 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43))))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.24/1.46 tff(172,plain,
% 1.24/1.46 (~((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43)))))))),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[171, 61])).
% 1.31/1.46 tff(173,plain,
% 1.31/1.46 (((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F1!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F1!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_4(B!39, A!40, F1!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F1!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y2_5(B!39, A!40, F1!43))) | (~apply(F1!43, tptp_fun_X_7(B!39, A!40, F1!43), tptp_fun_Y1_6(B!39, A!40, F1!43))) | (tptp_fun_Y1_6(B!39, A!40, F1!43) = tptp_fun_Y2_5(B!39, A!40, F1!43))))))) | ((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 1.31/1.46 inference(tautology,[status(thm)],[])).
% 1.31/1.46 tff(174,plain,
% 1.31/1.46 ((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[173, 172])).
% 1.31/1.46 tff(175,plain,
% 1.31/1.46 (maps(F1!43, A!40, B!39)),
% 1.31/1.46 inference(and_elim,[status(thm)],[71])).
% 1.31/1.46 tff(176,plain,
% 1.31/1.46 ((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 1.31/1.46 inference(tautology,[status(thm)],[])).
% 1.31/1.46 tff(177,plain,
% 1.31/1.46 ((~((~maps(F1!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[176, 175])).
% 1.31/1.46 tff(178,plain,
% 1.31/1.46 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 1.31/1.46 inference(unit_resolution,[status(thm)],[177, 174])).
% 1.31/1.47 tff(179,plain,
% 1.31/1.47 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 1.31/1.47 inference(tautology,[status(thm)],[])).
% 1.31/1.47 tff(180,plain,
% 1.31/1.47 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[179, 178])).
% 1.31/1.47 tff(181,plain,
% 1.31/1.47 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(182,plain,
% 1.31/1.47 (((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39))) <=> ((~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(183,plain,
% 1.31/1.47 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[182])).
% 1.32/1.47 tff(184,plain,
% 1.32/1.47 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 1.32/1.47 inference(transitivity,[status(thm)],[183, 181])).
% 1.32/1.47 tff(185,plain,
% 1.32/1.47 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(186,plain,
% 1.32/1.47 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.32/1.47 tff(187,plain,
% 1.32/1.47 (tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[186, 180, 165, 163, 39, 161, 159])).
% 1.32/1.47 tff(188,plain,
% 1.32/1.47 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41)),
% 1.32/1.47 inference(symmetry,[status(thm)],[187])).
% 1.32/1.47 tff(189,plain,
% 1.32/1.47 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[188])).
% 1.32/1.47 tff(190,plain,
% 1.32/1.47 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)) <=> apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(symmetry,[status(thm)],[189])).
% 1.32/1.47 tff(191,plain,
% 1.32/1.47 (((~member(tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(tautology,[status(thm)],[])).
% 1.32/1.47 tff(192,plain,
% 1.32/1.47 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F1!43, G!41), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[191, 157])).
% 1.32/1.47 tff(193,plain,
% 1.32/1.47 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[192, 190])).
% 1.32/1.47 tff(194,plain,
% 1.32/1.47 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(195,plain,
% 1.32/1.47 ((~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))))) <=> (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))),
% 1.32/1.47 inference(rewrite,[status(thm)],[])).
% 1.32/1.47 tff(196,plain,
% 1.32/1.47 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 1.32/1.47 inference(monotonicity,[status(thm)],[195])).
% 1.32/1.47 tff(197,plain,
% 1.32/1.47 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 1.32/1.47 inference(transitivity,[status(thm)],[196, 194])).
% 1.32/1.47 tff(198,plain,
% 1.32/1.47 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(199,plain,
% 1.32/1.48 ((~![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))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.32/1.48 tff(200,plain,
% 1.32/1.48 (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[199, 61])).
% 1.32/1.48 tff(201,plain,
% 1.32/1.48 (((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))) | ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(202,plain,
% 1.32/1.48 ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[201, 200])).
% 1.32/1.48 tff(203,plain,
% 1.32/1.48 (maps(G!41, B!39, A!40)),
% 1.32/1.48 inference(and_elim,[status(thm)],[71])).
% 1.32/1.48 tff(204,plain,
% 1.32/1.48 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(205,plain,
% 1.32/1.48 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[204, 203])).
% 1.32/1.48 tff(206,plain,
% 1.32/1.48 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[205, 202])).
% 1.32/1.48 tff(207,plain,
% 1.32/1.48 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(208,plain,
% 1.32/1.48 (![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[207, 206])).
% 1.32/1.48 tff(209,plain,
% 1.32/1.48 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(210,plain,
% 1.32/1.48 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(211,plain,
% 1.32/1.48 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[210, 209])).
% 1.32/1.48 tff(212,plain,
% 1.32/1.48 (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[211, 208, 163])).
% 1.32/1.48 tff(213,plain,
% 1.32/1.48 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))) | apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(214,plain,
% 1.32/1.48 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[213, 212])).
% 1.32/1.48 tff(215,plain,
% 1.32/1.48 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(216,plain,
% 1.32/1.48 (member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[215, 212])).
% 1.32/1.48 tff(217,plain,
% 1.32/1.48 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(218,plain,
% 1.32/1.48 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[217, 206])).
% 1.32/1.48 tff(219,plain,
% 1.32/1.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(220,plain,
% 1.32/1.48 (((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(221,plain,
% 1.32/1.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[220])).
% 1.32/1.48 tff(222,plain,
% 1.32/1.48 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))))),
% 1.32/1.48 inference(transitivity,[status(thm)],[221, 219])).
% 1.32/1.48 tff(223,plain,
% 1.32/1.48 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(224,plain,
% 1.32/1.48 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.32/1.48 tff(225,plain,
% 1.32/1.48 ((tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_14(B!39, A!40, F2!42, F1!43)))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[224, 218, 163, 39, 216, 214])).
% 1.32/1.48 tff(226,plain,
% 1.32/1.48 (tptp_fun_X_14(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[225, 193])).
% 1.32/1.48 tff(227,plain,
% 1.32/1.48 (tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42)),
% 1.32/1.48 inference(monotonicity,[status(thm)],[226])).
% 1.32/1.48 tff(228,plain,
% 1.32/1.48 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), B!39, F2!42)),
% 1.32/1.48 inference(symmetry,[status(thm)],[227])).
% 1.32/1.48 tff(229,plain,
% 1.32/1.48 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(230,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[229])).
% 1.32/1.49 tff(231,plain,
% 1.32/1.49 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(232,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[231])).
% 1.32/1.49 tff(233,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(transitivity,[status(thm)],[232, 230])).
% 1.32/1.49 tff(234,plain,
% 1.32/1.49 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(235,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[234])).
% 1.32/1.49 tff(236,plain,
% 1.32/1.49 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(237,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[236])).
% 1.32/1.49 tff(238,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(239,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image3')).
% 1.32/1.49 tff(240,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.32/1.49 tff(241,plain,(
% 1.32/1.49 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 1.32/1.49 inference(skolemize,[status(sab)],[240])).
% 1.32/1.49 tff(242,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[241, 237])).
% 1.32/1.49 tff(243,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[242, 235])).
% 1.32/1.49 tff(244,plain,
% 1.32/1.49 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[243, 233])).
% 1.32/1.49 tff(245,plain,
% 1.32/1.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(246,plain,
% 1.32/1.49 ((~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))) <=> (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(247,plain,
% 1.32/1.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[246])).
% 1.32/1.49 tff(248,plain,
% 1.32/1.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))))),
% 1.32/1.49 inference(transitivity,[status(thm)],[247, 245])).
% 1.32/1.49 tff(249,plain,
% 1.32/1.49 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(250,plain,
% 1.32/1.49 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.32/1.49 tff(251,plain,
% 1.32/1.49 (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[250, 244])).
% 1.32/1.49 tff(252,plain,
% 1.32/1.49 (((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F2!42, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(253,plain,
% 1.32/1.49 ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[252, 251])).
% 1.32/1.49 tff(254,assumption,(~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))), introduced(assumption)).
% 1.32/1.49 tff(255,assumption,((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))), introduced(assumption)).
% 1.32/1.49 tff(256,plain,
% 1.32/1.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(257,plain,
% 1.32/1.49 ((~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))) <=> (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(258,plain,
% 1.32/1.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[257])).
% 1.32/1.50 tff(259,plain,
% 1.32/1.50 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[258, 256])).
% 1.32/1.50 tff(260,plain,
% 1.32/1.50 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(261,plain,
% 1.32/1.50 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.32/1.50 tff(262,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[261, 244, 255])).
% 1.32/1.50 tff(263,plain,(~((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(264,plain,
% 1.32/1.50 (((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), A!40)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 1.32/1.50 inference(tautology,[status(thm)],[])).
% 1.32/1.50 tff(265,plain,
% 1.32/1.50 ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[264, 263])).
% 1.32/1.50 tff(266,assumption,(![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))), introduced(assumption)).
% 1.32/1.50 tff(267,plain,
% 1.32/1.50 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_X_14(B!39, A!40, F2!42, F1!43)),
% 1.32/1.50 inference(symmetry,[status(thm)],[226])).
% 1.32/1.50 tff(268,plain,
% 1.32/1.50 (apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) <=> apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[267])).
% 1.32/1.50 tff(269,plain,
% 1.32/1.50 (apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) <=> apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.35/1.50 inference(symmetry,[status(thm)],[268])).
% 1.35/1.50 tff(270,plain,
% 1.35/1.50 (apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[165, 269])).
% 1.35/1.50 tff(271,plain,
% 1.35/1.50 (((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(272,plain,
% 1.35/1.50 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(273,plain,
% 1.35/1.50 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(F1!43, tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.35/1.50 tff(274,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[273, 216, 270, 266])).
% 1.35/1.50 tff(275,plain,(~![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(276,plain,
% 1.35/1.50 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.35/1.50 inference(tautology,[status(thm)],[])).
% 1.35/1.50 tff(277,plain,
% 1.35/1.50 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F1!43, X, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[276, 163, 275])).
% 1.35/1.50 tff(278,plain,
% 1.35/1.50 (member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[277, 265])).
% 1.35/1.50 tff(279,plain,
% 1.35/1.50 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(280,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[279])).
% 1.35/1.50 tff(281,plain,
% 1.35/1.50 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(282,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[281])).
% 1.35/1.50 tff(283,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[282, 280])).
% 1.35/1.50 tff(284,plain,
% 1.35/1.50 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(285,plain,
% 1.35/1.50 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[284])).
% 1.35/1.50 tff(286,plain,
% 1.35/1.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(287,plain,
% 1.35/1.50 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(288,plain,
% 1.35/1.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[287])).
% 1.35/1.50 tff(289,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 1.35/1.50 tff(290,plain,
% 1.35/1.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.35/1.50 tff(291,plain,
% 1.35/1.50 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[290, 286])).
% 1.35/1.50 tff(292,plain,(
% 1.35/1.50 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 1.35/1.50 inference(skolemize,[status(sab)],[291])).
% 1.35/1.50 tff(293,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[292, 285])).
% 1.35/1.50 tff(294,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[293, 283])).
% 1.35/1.50 tff(295,plain,
% 1.35/1.50 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39))))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(296,plain,
% 1.35/1.50 (~((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39)))))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[295, 294])).
% 1.35/1.50 tff(297,plain,
% 1.35/1.50 (((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~(subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)) | (~((~member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F1!43, A!40, B!39))) | member(tptp_fun_X_0(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)), image3(F2!42, A!40, B!39))))))) | ((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))),
% 1.35/1.50 inference(tautology,[status(thm)],[])).
% 1.35/1.50 tff(298,plain,
% 1.35/1.50 ((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[297, 296])).
% 1.35/1.50 tff(299,plain,
% 1.35/1.50 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(300,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[299])).
% 1.35/1.50 tff(301,plain,
% 1.35/1.50 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 1.35/1.50 inference(bind,[status(th)],[])).
% 1.35/1.50 tff(302,plain,
% 1.35/1.50 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 1.35/1.50 inference(quant_intro,[status(thm)],[301])).
% 1.35/1.50 tff(303,plain,
% 1.35/1.50 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(304,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 1.35/1.50 tff(305,plain,
% 1.35/1.50 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.35/1.50 tff(306,plain,(
% 1.35/1.50 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 1.35/1.50 inference(skolemize,[status(sab)],[305])).
% 1.35/1.50 tff(307,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[306, 302])).
% 1.35/1.50 tff(308,plain,
% 1.35/1.50 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[307, 300])).
% 1.35/1.50 tff(309,plain,
% 1.35/1.50 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) <=> equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(310,plain,
% 1.35/1.50 (~(((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) <=> equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[309, 308])).
% 1.35/1.50 tff(311,plain,
% 1.35/1.50 (equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 1.35/1.50 inference(and_elim,[status(thm)],[71])).
% 1.35/1.50 tff(312,plain,
% 1.35/1.50 ((((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) <=> equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))) | (~equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39)))),
% 1.35/1.50 inference(tautology,[status(thm)],[])).
% 1.35/1.50 tff(313,plain,
% 1.35/1.50 ((((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) <=> equal_set(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[312, 311])).
% 1.35/1.50 tff(314,plain,
% 1.35/1.50 (~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[313, 310])).
% 1.35/1.50 tff(315,plain,
% 1.35/1.50 (((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | (~subset(image3(F2!42, A!40, B!39), image3(F1!43, A!40, B!39)))) | subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 1.35/1.50 inference(tautology,[status(thm)],[])).
% 1.35/1.50 tff(316,plain,
% 1.35/1.50 (subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[315, 314])).
% 1.35/1.50 tff(317,plain,
% 1.35/1.50 ((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | (~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 1.35/1.51 inference(tautology,[status(thm)],[])).
% 1.35/1.51 tff(318,plain,
% 1.35/1.51 ((~((~subset(image3(F1!43, A!40, B!39), image3(F2!42, A!40, B!39))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39))))) | ![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[317, 316])).
% 1.35/1.51 tff(319,plain,
% 1.35/1.51 (![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[318, 298])).
% 1.35/1.51 tff(320,plain,
% 1.35/1.51 (((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)))) <=> ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(321,plain,
% 1.35/1.51 ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39)))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(322,plain,
% 1.35/1.51 ((~![X: $i] : ((~member(X, image3(F1!43, A!40, B!39))) | member(X, image3(F2!42, A!40, B!39)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F1!43, A!40, B!39))) | member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.35/1.51 tff(323,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[322, 319, 278, 254])).
% 1.35/1.51 tff(324,plain,(member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(325,plain,
% 1.35/1.51 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 1.35/1.51 inference(tautology,[status(thm)],[])).
% 1.35/1.51 tff(326,plain,
% 1.35/1.51 ((~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), image3(F2!42, A!40, B!39))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))))) | (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[325, 324])).
% 1.35/1.51 tff(327,plain,
% 1.35/1.51 (~((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[326, 253])).
% 1.35/1.51 tff(328,plain,
% 1.35/1.51 (((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) | member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)),
% 1.35/1.51 inference(tautology,[status(thm)],[])).
% 1.35/1.51 tff(329,plain,
% 1.35/1.51 (member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[328, 327])).
% 1.35/1.51 tff(330,plain,
% 1.35/1.51 (((~![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))))))))) | ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!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))))))))) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(331,plain,
% 1.35/1.51 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(332,plain,
% 1.35/1.51 ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) <=> (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(333,plain,
% 1.35/1.51 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[332])).
% 1.35/1.51 tff(334,plain,
% 1.35/1.51 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[333, 331])).
% 1.35/1.51 tff(335,plain,
% 1.35/1.51 (((~![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_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[334])).
% 1.35/1.52 tff(336,plain,
% 1.35/1.52 (((~![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_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[335, 330])).
% 1.35/1.52 tff(337,plain,
% 1.35/1.52 ((~![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_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(338,plain,
% 1.35/1.52 ((~![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))))))))) | (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.35/1.52 tff(339,plain,
% 1.35/1.52 (~((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[338, 114, 329])).
% 1.35/1.52 tff(340,plain,
% 1.35/1.52 (((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))),
% 1.35/1.52 inference(tautology,[status(thm)],[])).
% 1.35/1.52 tff(341,plain,
% 1.35/1.52 ((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[340, 339])).
% 1.35/1.52 tff(342,plain,
% 1.35/1.52 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(343,plain,
% 1.35/1.52 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(344,plain,
% 1.35/1.52 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.35/1.52 tff(345,plain,
% 1.35/1.52 (apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[344, 150, 329])).
% 1.35/1.52 tff(346,plain,
% 1.35/1.52 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.35/1.52 inference(tautology,[status(thm)],[])).
% 1.35/1.52 tff(347,plain,
% 1.35/1.52 ((~((~apply(compose_function(G!41, F1!43, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[346, 345])).
% 1.35/1.53 tff(348,plain,
% 1.35/1.53 (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[347, 341])).
% 1.35/1.53 tff(349,plain,
% 1.35/1.53 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))),
% 1.35/1.53 inference(tautology,[status(thm)],[])).
% 1.35/1.53 tff(350,plain,
% 1.35/1.53 (apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[349, 348])).
% 1.35/1.53 tff(351,plain,
% 1.35/1.53 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)),
% 1.35/1.53 inference(tautology,[status(thm)],[])).
% 1.35/1.53 tff(352,plain,
% 1.35/1.53 (member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[351, 348])).
% 1.35/1.53 tff(353,plain,
% 1.35/1.53 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))),
% 1.35/1.53 inference(tautology,[status(thm)],[])).
% 1.35/1.53 tff(354,plain,
% 1.35/1.53 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[353, 178])).
% 1.35/1.53 tff(355,plain,
% 1.35/1.53 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(356,plain,
% 1.35/1.53 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(357,plain,
% 1.35/1.53 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F1!43), B!39)) | (~apply(F1!43, X, tptp_fun_Y_3(X, B!39, F1!43))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.35/1.53 tff(358,plain,
% 1.35/1.53 (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[357, 354, 329])).
% 1.35/1.53 tff(359,plain,
% 1.35/1.53 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)))) | apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))),
% 1.38/1.53 inference(tautology,[status(thm)],[])).
% 1.38/1.53 tff(360,plain,
% 1.38/1.53 (apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))),
% 1.38/1.53 inference(unit_resolution,[status(thm)],[359, 358])).
% 1.38/1.53 tff(361,plain,
% 1.38/1.53 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)),
% 1.38/1.53 inference(tautology,[status(thm)],[])).
% 1.38/1.53 tff(362,plain,
% 1.38/1.53 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)),
% 1.38/1.53 inference(unit_resolution,[status(thm)],[361, 358])).
% 1.38/1.53 tff(363,plain,
% 1.38/1.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.53 inference(rewrite,[status(thm)],[])).
% 1.38/1.53 tff(364,plain,
% 1.38/1.53 (((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.53 inference(rewrite,[status(thm)],[])).
% 1.38/1.53 tff(365,plain,
% 1.38/1.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.53 inference(monotonicity,[status(thm)],[364])).
% 1.38/1.53 tff(366,plain,
% 1.38/1.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.53 inference(transitivity,[status(thm)],[365, 363])).
% 1.38/1.53 tff(367,plain,
% 1.38/1.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(368,plain,
% 1.38/1.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F1!43, X, Y1)) | (~apply(F1!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.38/1.54 tff(369,plain,
% 1.38/1.54 (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[368, 180, 329, 362, 360, 352, 350])).
% 1.38/1.54 tff(370,plain,
% 1.38/1.54 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43) = tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41)),
% 1.38/1.54 inference(symmetry,[status(thm)],[369])).
% 1.38/1.54 tff(371,plain,
% 1.38/1.54 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.54 inference(monotonicity,[status(thm)],[370])).
% 1.38/1.54 tff(372,plain,
% 1.38/1.54 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.54 inference(symmetry,[status(thm)],[371])).
% 1.38/1.54 tff(373,plain,
% 1.38/1.54 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), B!39)) | (~apply(F1!43, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.54 inference(tautology,[status(thm)],[])).
% 1.38/1.54 tff(374,plain,
% 1.38/1.54 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[373, 348])).
% 1.38/1.54 tff(375,plain,
% 1.38/1.54 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[374, 372])).
% 1.38/1.54 tff(376,plain,
% 1.38/1.54 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(377,plain,
% 1.38/1.54 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))))),
% 1.38/1.54 inference(quant_inst,[status(thm)],[])).
% 1.38/1.54 tff(378,plain,
% 1.38/1.54 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))))),
% 1.38/1.54 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.38/1.54 tff(379,plain,
% 1.38/1.54 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[378, 208, 362])).
% 1.38/1.54 tff(380,plain,
% 1.38/1.54 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))) | apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))),
% 1.38/1.54 inference(tautology,[status(thm)],[])).
% 1.38/1.54 tff(381,plain,
% 1.38/1.54 (apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[380, 379])).
% 1.38/1.54 tff(382,plain,
% 1.38/1.54 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)),
% 1.38/1.54 inference(tautology,[status(thm)],[])).
% 1.38/1.54 tff(383,plain,
% 1.38/1.54 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)),
% 1.38/1.54 inference(unit_resolution,[status(thm)],[382, 379])).
% 1.38/1.54 tff(384,plain,
% 1.38/1.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(385,plain,
% 1.38/1.54 (((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.54 inference(rewrite,[status(thm)],[])).
% 1.38/1.54 tff(386,plain,
% 1.38/1.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[385])).
% 1.38/1.55 tff(387,plain,
% 1.38/1.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.55 inference(transitivity,[status(thm)],[386, 384])).
% 1.38/1.55 tff(388,plain,
% 1.38/1.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(389,plain,
% 1.38/1.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), B!39)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.38/1.55 tff(390,plain,
% 1.38/1.55 ((~apply(G!41, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[389, 218, 329, 362, 383, 381])).
% 1.38/1.55 tff(391,plain,
% 1.38/1.55 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[390, 375])).
% 1.38/1.55 tff(392,plain,
% 1.38/1.55 (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)),
% 1.38/1.55 inference(symmetry,[status(thm)],[391])).
% 1.38/1.55 tff(393,plain,
% 1.38/1.55 (((~![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))))))))) | ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!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))))))))) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(394,plain,
% 1.38/1.55 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(395,plain,
% 1.38/1.55 ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) <=> (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(396,plain,
% 1.38/1.55 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[395])).
% 1.38/1.55 tff(397,plain,
% 1.38/1.55 (((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))))) <=> ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[396, 394])).
% 1.38/1.56 tff(398,plain,
% 1.38/1.56 (((~![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_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[397])).
% 1.38/1.56 tff(399,plain,
% 1.38/1.56 (((~![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_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.56 inference(transitivity,[status(thm)],[398, 393])).
% 1.38/1.56 tff(400,plain,
% 1.38/1.56 ((~![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_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(401,plain,
% 1.38/1.56 ((~![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))))))))) | (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.38/1.56 tff(402,plain,
% 1.38/1.56 (~((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[401, 114, 329])).
% 1.38/1.56 tff(403,plain,
% 1.38/1.56 (((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~(apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), Y)) | (~apply(G!41, Y, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | ((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(404,plain,
% 1.38/1.56 ((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[403, 402])).
% 1.38/1.56 tff(405,plain,
% 1.38/1.56 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)))))))))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(406,plain,
% 1.38/1.56 (~((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40))))))))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[405, 142])).
% 1.38/1.56 tff(407,plain,
% 1.38/1.56 (((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F2!42, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(408,plain,
% 1.38/1.56 ((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[407, 406])).
% 1.38/1.56 tff(409,plain,
% 1.38/1.56 (identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)),
% 1.38/1.56 inference(and_elim,[status(thm)],[71])).
% 1.38/1.57 tff(410,plain,
% 1.38/1.57 ((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(411,plain,
% 1.38/1.57 ((~((~identity(compose_function(G!41, F2!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[410, 409])).
% 1.38/1.57 tff(412,plain,
% 1.38/1.57 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[411, 408])).
% 1.38/1.57 tff(413,plain,
% 1.38/1.57 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(414,plain,
% 1.38/1.57 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(415,plain,
% 1.38/1.57 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.38/1.57 tff(416,plain,
% 1.38/1.57 (apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[415, 412, 329])).
% 1.38/1.57 tff(417,plain,
% 1.38/1.57 ((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(418,plain,
% 1.38/1.57 ((~((~apply(compose_function(G!41, F2!42, A!40, B!39, A!40), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[417, 416])).
% 1.38/1.57 tff(419,plain,
% 1.38/1.57 (~((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[418, 404])).
% 1.38/1.57 tff(420,plain,
% 1.38/1.57 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(421,plain,
% 1.38/1.57 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[420, 419])).
% 1.38/1.57 tff(422,plain,
% 1.38/1.57 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(423,plain,
% 1.38/1.57 (member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[422, 419])).
% 1.38/1.57 tff(424,plain,
% 1.38/1.57 (((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(425,plain,
% 1.38/1.57 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[424, 327])).
% 1.38/1.57 tff(426,plain,
% 1.38/1.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(427,plain,
% 1.38/1.57 (((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(428,plain,
% 1.38/1.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[427])).
% 1.38/1.58 tff(429,plain,
% 1.38/1.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[428, 426])).
% 1.38/1.58 tff(430,plain,
% 1.38/1.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(431,plain,
% 1.38/1.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.38/1.58 tff(432,plain,
% 1.38/1.58 (tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[431, 91, 163, 329, 425, 423, 421])).
% 1.38/1.58 tff(433,plain,
% 1.38/1.58 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41)),
% 1.38/1.58 inference(symmetry,[status(thm)],[432])).
% 1.38/1.58 tff(434,plain,
% 1.38/1.58 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[433])).
% 1.38/1.58 tff(435,plain,
% 1.38/1.58 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)) <=> apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.58 inference(symmetry,[status(thm)],[434])).
% 1.38/1.58 tff(436,plain,
% 1.38/1.58 (((~member(tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.58 inference(tautology,[status(thm)],[])).
% 1.38/1.58 tff(437,plain,
% 1.38/1.58 (apply(G!41, tptp_fun_Y_8(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42, G!41), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[436, 419])).
% 1.38/1.58 tff(438,plain,
% 1.38/1.58 (apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[437, 435])).
% 1.38/1.58 tff(439,plain,
% 1.38/1.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(440,plain,
% 1.38/1.58 (((tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(441,plain,
% 1.38/1.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[440])).
% 1.38/1.58 tff(442,plain,
% 1.38/1.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.58 inference(transitivity,[status(thm)],[441, 439])).
% 1.38/1.58 tff(443,plain,
% 1.38/1.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(444,plain,
% 1.38/1.58 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41))) | (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.38/1.58 tff(445,plain,
% 1.38/1.58 ((tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)) | (~apply(G!41, tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[444, 218, 163, 216, 214, 329])).
% 1.38/1.58 tff(446,plain,
% 1.38/1.58 (tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42) = tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41)),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[445, 438])).
% 1.38/1.58 tff(447,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42)),
% 1.38/1.58 inference(symmetry,[status(thm)],[446])).
% 1.38/1.58 tff(448,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41)),
% 1.38/1.58 inference(transitivity,[status(thm)],[447, 392])).
% 1.38/1.58 tff(449,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42)),
% 1.38/1.58 inference(monotonicity,[status(thm)],[448])).
% 1.38/1.58 tff(450,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, G!41), B!39, F2!42)),
% 1.38/1.58 inference(symmetry,[status(thm)],[449])).
% 1.38/1.58 tff(451,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42)),
% 1.38/1.58 inference(monotonicity,[status(thm)],[391])).
% 1.38/1.58 tff(452,plain,
% 1.38/1.58 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F1!43), A!40, G!41), B!39, F2!42)),
% 1.38/1.58 inference(symmetry,[status(thm)],[451])).
% 1.38/1.58 tff(453,plain,
% 1.38/1.58 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(454,plain,
% 1.38/1.58 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | ((~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(455,plain,
% 1.38/1.59 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F2!42), B!39)) | (~apply(F2!42, X, tptp_fun_Y_3(X, B!39, F2!42))))))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42)))))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.38/1.59 tff(456,plain,
% 1.38/1.59 (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[455, 77, 329])).
% 1.38/1.59 tff(457,plain,
% 1.38/1.59 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42)))) | apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))),
% 1.38/1.59 inference(tautology,[status(thm)],[])).
% 1.38/1.59 tff(458,plain,
% 1.38/1.59 (apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[457, 456])).
% 1.38/1.59 tff(459,plain,
% 1.38/1.59 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)),
% 1.38/1.59 inference(tautology,[status(thm)],[])).
% 1.38/1.59 tff(460,plain,
% 1.38/1.59 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[459, 456])).
% 1.38/1.59 tff(461,plain,
% 1.38/1.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(462,plain,
% 1.38/1.59 (((tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)))) <=> ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(463,plain,
% 1.38/1.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))))),
% 1.38/1.59 inference(monotonicity,[status(thm)],[462])).
% 1.38/1.59 tff(464,plain,
% 1.38/1.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)))),
% 1.38/1.59 inference(transitivity,[status(thm)],[463, 461])).
% 1.38/1.59 tff(465,plain,
% 1.38/1.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | ((tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(466,plain,
% 1.38/1.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~apply(F2!42, X, Y1)) | (~apply(F2!42, X, Y2)))) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42), B!39)) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42))) | (~apply(F2!42, tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), A!40))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.38/1.59 tff(467,plain,
% 1.38/1.59 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42) = tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[466, 91, 163, 329, 425, 460, 458])).
% 1.38/1.59 tff(468,plain,
% 1.38/1.59 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), A!40, F2!42), B!39, F2!42)),
% 1.38/1.59 inference(symmetry,[status(thm)],[467])).
% 1.38/1.59 tff(469,plain,
% 1.38/1.59 (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)),
% 1.38/1.59 inference(transitivity,[status(thm)],[468, 452, 450, 228, 98])).
% 1.38/1.59 tff(470,plain,
% 1.38/1.59 (((~apply(F2!42, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~apply(F1!43, tptp_fun_X_14(B!39, A!40, F2!42, F1!43), tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43))) | (~member(tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43), B!39)) | (~member(tptp_fun_X_14(B!39, A!40, F2!42, F1!43), A!40)) | (tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))) | (~(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43)))),
% 1.38/1.59 inference(tautology,[status(thm)],[])).
% 1.38/1.59 tff(471,plain,
% 1.38/1.59 (~(tptp_fun_Y1_13(B!39, A!40, F2!42, F1!43) = tptp_fun_Y2_12(B!39, A!40, F2!42, F1!43))),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[470, 37])).
% 1.38/1.59 tff(472,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[471, 469])).
% 1.38/1.59 % SZS output end Proof
% 1.38/1.60 % E exiting
%------------------------------------------------------------------------------