%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET730+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET730+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:39:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(apply_type, type, (
% 0.19/0.48 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.48 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_F_42_type, type, (
% 0.19/0.48 tptp_fun_F_42: $i)).
% 0.19/0.48 tff(tptp_fun_B_39_type, type, (
% 0.19/0.48 tptp_fun_B_39: $i)).
% 0.19/0.48 tff(tptp_fun_X_4_type, type, (
% 0.19/0.48 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_G_41_type, type, (
% 0.19/0.48 tptp_fun_G_41: $i)).
% 0.19/0.48 tff(tptp_fun_A_40_type, type, (
% 0.19/0.48 tptp_fun_A_40: $i)).
% 0.19/0.48 tff(image2_type, type, (
% 0.19/0.48 image2: ( $i * $i ) > $i)).
% 0.19/0.48 tff(member_type, type, (
% 0.19/0.48 member: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_X_23_type, type, (
% 0.19/0.48 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.48 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.48 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(tptp_fun_X_7_type, type, (
% 0.19/0.48 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.48 tff(subset_type, type, (
% 0.19/0.48 subset: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_X_0_type, type, (
% 0.19/0.48 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.48 tff(maps_type, type, (
% 0.19/0.48 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.48 tff(1,assumption,((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))), introduced(assumption)).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (^[F: $i, A: $i, Y: $i] : refl((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.48 tff(4,plain,
% 0.19/0.48 (^[F: $i, A: $i, Y: $i] : rewrite((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 (^[F: $i, A: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) <=> ((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))), rewrite((member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y))) <=> ![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(10,axiom,(![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image2')).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.48 tff(12,plain,(
% 0.19/0.48 ![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[11])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))) <=> (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.49 tff(21,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[20, 14, 1])).
% 0.19/0.49 tff(22,plain,(~((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 (((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), A!40, F!42), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))))) | (member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(24,plain,
% 0.19/0.49 (member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.49 tff(25,assumption,(~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))), introduced(assumption)).
% 0.19/0.49 tff(26,plain,
% 0.19/0.49 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.49 tff(38,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')).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.49 tff(41,plain,(
% 0.19/0.49 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[40])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 ((~![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(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39)))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (~((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~(subset(image2(F!42, A!40), B!39) | (~((~member(tptp_fun_X_0(B!39, image2(F!42, A!40)), image2(F!42, A!40))) | member(tptp_fun_X_0(B!39, image2(F!42, A!40)), B!39)))))) | ((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 ((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 ((subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & (~maps(G!41, A!40, image2(F!42, A!40)))) <=> (subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & (~maps(G!41, A!40, image2(F!42, A!40))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 ((~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A)))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) => maps(G, A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(51,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & subset(C, B)) & (image2(F, A) = C)) & ![X: $i, Y: $i] : ((member(X, A) & member(Y, C)) => (apply(G, X, Y) <=> apply(F, X, Y)))) => maps(G, A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII21')).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (~![F: $i, G: $i, A: $i, B: $i] : ((~subset(image2(F, A), B)) | (~maps(F, A, B)) | (~![X: $i, Y: $i] : ((~(member(X, A) & member(Y, image2(F, A)))) | (apply(G, X, Y) <=> apply(F, X, Y)))) | maps(G, A, image2(F, A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (subset(image2(F!42, A!40), B!39) & maps(F!42, A!40, B!39) & ![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) & (~maps(G!41, A!40, image2(F!42, A!40)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (subset(image2(F!42, A!40), B!39)),
% 0.19/0.49 inference(and_elim,[status(thm)],[56])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 ((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | (~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 ((~((~subset(image2(F!42, A!40), B!39)) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39)))) | ![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[59, 47])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39))) <=> ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[63, 60, 27])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 (member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[65, 25])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 (((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39))) <=> ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | ((~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, image2(F!42, A!40))) | member(X, B!39))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.49 tff(70,plain,
% 0.19/0.49 (member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[69, 60, 66])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 (member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[71, 25])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 (^[X: $i, Y: $i] : refl(((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) <=> ![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A!40) & member(Y, image2(F!42, A!40))) <=> (~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))), ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) <=> (~(~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))))), rewrite((~(~((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))) <=> ((~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))), ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) <=> ((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))))), (((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> (((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))))), rewrite((((~member(X, A!40)) | (~member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))), (((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y))) <=> ![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((~(member(X, A!40) & member(Y, image2(F!42, A!40)))) | (apply(G!41, X, Y) <=> apply(F!42, X, Y)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[56])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))) <=> ((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[85, 79, 27, 72])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[87, 25])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 ((~(apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 ((~(apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))) | apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 (apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[90, 86])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40)))) <=> ((~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[97, 79, 66, 72])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 (apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[99, 25])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 ((~(apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 ((~(apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)) <=> apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41)))) | apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (~(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[104, 25])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (^[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))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.51 tff(120,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.51 tff(123,plain,(
% 0.19/0.51 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[122])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[125, 112])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[126, 107])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!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(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(129,plain,
% 0.19/0.52 ((~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))))))) <=> (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(130,plain,
% 0.19/0.52 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!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(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[129])).
% 0.19/0.52 tff(131,plain,
% 0.19/0.52 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!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(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[130, 128])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[133, 127])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 (((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))) | ((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 ((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (maps(F!42, A!40, B!39)),
% 0.19/0.52 inference(and_elim,[status(thm)],[56])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 ((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 ((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.52 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 (((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39))) <=> ((~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(F!42, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), B!39)) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), B!39))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[148, 142, 72, 105, 103, 91, 70, 64])).
% 0.19/0.53 tff(150,plain,((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 (((~![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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, 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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 ((~((~((~maps(G!41, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, image2(F!42, A!40))) | (~member(Y2, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))))))) <=> (~((~((~maps(G!41, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(153,plain,
% 0.19/0.53 (((~![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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, image2(F!42, A!40))) | (~member(Y2, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, 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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.54 tff(154,plain,
% 0.19/0.54 (((~![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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, image2(F!42, A!40))) | (~member(Y2, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, 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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[153, 151])).
% 0.19/0.54 tff(155,plain,
% 0.19/0.54 ((~![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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, A!40)) | (~member(Y1, image2(F!42, A!40))) | (~member(Y2, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))))) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y))))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(156,plain,
% 0.19/0.54 ((~![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, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.54 tff(157,plain,
% 0.19/0.54 (~((~((~maps(G!41, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[156, 127])).
% 0.19/0.54 tff(158,plain,
% 0.19/0.54 (((~((~maps(G!41, A!40, image2(F!42, A!40))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, image2(F!42, A!40), G!41), image2(F!42, A!40))) | (~apply(G!41, X, tptp_fun_Y_3(X, image2(F!42, A!40), G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, image2(F!42, A!40))) | (~member(X, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(Y1, image2(F!42, A!40))))))))) | (~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))))) | (maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(159,plain,
% 0.19/0.54 (maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.54 tff(160,plain,
% 0.19/0.54 (~maps(G!41, A!40, image2(F!42, A!40))),
% 0.19/0.54 inference(and_elim,[status(thm)],[56])).
% 0.19/0.54 tff(161,plain,
% 0.19/0.54 ((~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))) | maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(162,plain,
% 0.19/0.54 ((~(maps(G!41, A!40, image2(F!42, A!40)) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41)))))) | (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.19/0.55 tff(163,plain,
% 0.19/0.55 ((~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41), image2(F!42, A!40))) | (~member(tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))) | (~apply(G!41, tptp_fun_X_7(image2(F!42, A!40), A!40, G!41), tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41))) | (tptp_fun_Y1_6(image2(F!42, A!40), A!40, G!41) = tptp_fun_Y2_5(image2(F!42, A!40), A!40, G!41))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.19/0.55 tff(164,plain,
% 0.19/0.55 (~((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[163, 150])).
% 0.19/0.55 tff(165,plain,
% 0.19/0.55 (((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y))))) | member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(166,plain,
% 0.19/0.55 (member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.55 tff(167,assumption,(![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))), introduced(assumption)).
% 0.19/0.55 tff(168,assumption,(member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)), introduced(assumption)).
% 0.19/0.55 tff(169,plain,
% 0.19/0.55 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(170,plain,
% 0.19/0.55 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[169, 140])).
% 0.19/0.55 tff(171,plain,
% 0.19/0.55 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(172,plain,
% 0.19/0.55 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(173,plain,
% 0.19/0.55 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.55 tff(174,plain,
% 0.19/0.55 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[173, 170, 168])).
% 0.19/0.55 tff(175,plain,
% 0.19/0.55 (((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))) | apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(176,plain,
% 0.19/0.55 (apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.19/0.55 tff(177,plain,
% 0.19/0.55 (((~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(178,plain,
% 0.19/0.55 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(179,plain,
% 0.19/0.55 ((~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.55 tff(180,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[179, 168, 176, 167])).
% 0.19/0.55 tff(181,plain,((~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(182,plain,
% 0.19/0.55 (~![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[181, 166])).
% 0.19/0.55 tff(183,plain,
% 0.19/0.55 ((~(member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))))) | member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)) | ![X: $i] : ((~member(X, A!40)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(184,plain,
% 0.19/0.55 (member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[183, 182, 24])).
% 0.19/0.55 tff(185,plain,
% 0.19/0.55 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(186,plain,
% 0.19/0.55 (((apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)))) <=> ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(187,plain,
% 0.19/0.55 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[186])).
% 0.19/0.55 tff(188,plain,
% 0.19/0.55 (((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))) <=> ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[187, 185])).
% 0.19/0.55 tff(189,plain,
% 0.19/0.55 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | ((apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(190,plain,
% 0.19/0.55 ((~![X: $i, Y: $i] : ((apply(G!41, X, Y) <=> apply(F!42, X, Y)) | (~member(X, A!40)) | (~member(Y, image2(F!42, A!40))))) | (~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.55 tff(191,plain,
% 0.19/0.55 (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[190, 79, 166, 184])).
% 0.19/0.55 tff(192,plain,
% 0.19/0.55 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), B!39)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[173, 170, 166])).
% 0.19/0.55 tff(193,plain,
% 0.19/0.55 (apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[175, 192])).
% 0.19/0.55 tff(194,plain,
% 0.19/0.55 ((~(apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))) | apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) | (~apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(195,plain,
% 0.19/0.55 ((~(apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)) <=> apply(F!42, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))) | apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.19/0.56 tff(196,plain,
% 0.19/0.56 (apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[195, 191])).
% 0.19/0.56 tff(197,plain,
% 0.19/0.56 (((~member(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), A!40)) | (~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y))))) | ![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(198,plain,
% 0.19/0.56 (![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[197, 164])).
% 0.19/0.56 tff(199,plain,
% 0.19/0.56 (((~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))) <=> ((~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(200,plain,
% 0.19/0.56 ((~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(201,plain,
% 0.19/0.56 ((~![Y: $i] : ((~member(Y, image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42), image2(F!42, A!40))) | (~apply(G!41, tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), tptp_fun_Y_3(tptp_fun_X_4(image2(F!42, A!40), A!40, G!41), B!39, F!42)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.56 tff(202,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[201, 198, 184, 196])).
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56 % E exiting
%------------------------------------------------------------------------------