%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET752+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:16 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET752+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:41:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_40_type, type, (
% 0.19/0.39 tptp_fun_X_40: $i)).
% 0.19/0.39 tff(tptp_fun_X_23_type, type, (
% 0.19/0.39 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_F_43_type, type, (
% 0.19/0.39 tptp_fun_F_43: $i)).
% 0.19/0.39 tff(tptp_fun_Y_39_type, type, (
% 0.19/0.39 tptp_fun_Y_39: $i)).
% 0.19/0.39 tff(tptp_fun_X_0_type, type, (
% 0.19/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.39 tff(union_type, type, (
% 0.19/0.39 union: ( $i * $i ) > $i)).
% 0.19/0.39 tff(image2_type, type, (
% 0.19/0.39 image2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(apply_type, type, (
% 0.19/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(equal_set_type, type, (
% 0.19/0.39 equal_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_A_42_type, type, (
% 0.19/0.39 tptp_fun_A_42: $i)).
% 0.19/0.39 tff(maps_type, type, (
% 0.19/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_B_41_type, type, (
% 0.19/0.39 tptp_fun_B_41: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,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')).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) | ((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,assumption,((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))), introduced(assumption)).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[29, 13, 23])).
% 0.19/0.42 tff(31,plain,(~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) | ((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 ((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.43 tff(34,assumption,(~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))), introduced(assumption)).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))) | apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.43 tff(41,assumption,(~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))), introduced(assumption)).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.43 tff(47,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.43 tff(50,plain,(
% 0.19/0.43 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[49])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40))) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[57, 51, 41])).
% 0.19/0.44 tff(59,plain,(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[61, 40])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))) <=> ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[65, 63])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 ((~![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_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (~((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[68, 13])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))) | (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (^[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))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (^[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))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (^[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)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![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)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.45 tff(82,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')).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.46 tff(85,plain,(
% 0.19/0.46 ![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)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[84])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 ((~![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(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(X, image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (~((~((~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(X, image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (((~((~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(X, image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))))))) | (subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.46 tff(92,assumption,((~((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, union(X!40, Y!39)))) | member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))))))), introduced(assumption)).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 ((~![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!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, union(X!40, Y!39)))) | member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[93, 87, 92])).
% 0.19/0.46 tff(95,plain,(~((~((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, union(X!40, Y!39)))) | member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (((~((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, union(X!40, Y!39)))) | member(X, union(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[98, 51])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 ((~((~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[105, 13])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) | ((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 ((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.48 tff(109,assumption,(~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))), introduced(assumption)).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 108])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))) | (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 ((~(member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))) | (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[118, 99])).
% 0.19/0.48 tff(120,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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 ((~((~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(122,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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.48 tff(123,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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[125, 13])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) | (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[129, 51])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[131, 109])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 ((member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[139, 128])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))) | apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[141, 114])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 (((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) <=> ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[145, 142, 140])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 ((~((~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))) <=> ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 ((~![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_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 (~((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[152, 13])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 (((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))))) | (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 (member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 ((member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 (~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[156, 135])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(159,plain,
% 0.19/0.50 ((~(member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))))) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.50 tff(160,plain,
% 0.19/0.50 (![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[159, 155])).
% 0.19/0.50 tff(161,plain,
% 0.19/0.50 (((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) <=> ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(162,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(163,plain,
% 0.19/0.50 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.50 tff(164,plain,
% 0.19/0.50 (~member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[163, 142, 160])).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 ((~(member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[165, 164, 146, 119])).
% 0.19/0.50 tff(167,plain,((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(168,plain,
% 0.19/0.51 ((~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 ((~(subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.19/0.51 tff(170,plain,
% 0.19/0.51 (subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[169, 97])).
% 0.19/0.51 tff(171,plain,
% 0.19/0.51 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(172,plain,
% 0.19/0.51 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.51 tff(173,plain,
% 0.19/0.51 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(176,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.51 tff(177,plain,
% 0.19/0.51 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.51 tff(178,plain,(
% 0.19/0.51 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[177])).
% 0.19/0.51 tff(179,plain,
% 0.19/0.51 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))) <=> equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 (~(((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))) <=> equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, A)) & subset(Y, A)) => equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(185,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, A)) & subset(Y, A)) => equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa02')).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.19/0.51 tff(187,plain,
% 0.19/0.51 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.19/0.51 tff(188,plain,
% 0.19/0.51 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.51 tff(189,plain,
% 0.19/0.51 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image2(F, union(X, Y)), union(image2(F, X), image2(F, Y))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[188, 183])).
% 0.19/0.51 tff(190,plain,(
% 0.19/0.51 ~((~(maps(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42))) | equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[189])).
% 0.19/0.51 tff(191,plain,
% 0.19/0.51 (~equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.51 inference(or_elim,[status(thm)],[190])).
% 0.19/0.51 tff(192,plain,
% 0.19/0.51 ((((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))) <=> equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))) | equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(193,plain,
% 0.19/0.51 ((((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))) <=> equal_set(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | ((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.19/0.51 tff(194,plain,
% 0.19/0.51 ((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[193, 182])).
% 0.19/0.51 tff(195,plain,
% 0.19/0.51 ((~((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))))) | (~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(196,plain,
% 0.19/0.51 ((~subset(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.19/0.51 tff(197,plain,
% 0.19/0.51 (~subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[196, 170])).
% 0.19/0.51 tff(198,plain,
% 0.19/0.51 ((~(subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))))) | subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(199,plain,
% 0.19/0.51 ((~(subset(union(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))))) | (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.19/0.51 tff(200,plain,
% 0.19/0.51 (~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[199, 91])).
% 0.19/0.51 tff(201,plain,
% 0.19/0.51 (((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(202,plain,
% 0.19/0.51 (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.19/0.51 tff(203,plain,
% 0.19/0.51 ((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(204,plain,
% 0.19/0.51 ((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))) | ![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 (![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[204, 71])).
% 0.19/0.51 tff(206,plain,
% 0.19/0.51 (((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) <=> ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[208, 205, 62, 36])).
% 0.19/0.51 tff(210,plain,((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(211,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), X!40, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.19/0.52 tff(213,plain,
% 0.19/0.52 (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[212, 33])).
% 0.19/0.52 tff(214,plain,
% 0.19/0.52 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(215,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[214, 51])).
% 0.19/0.52 tff(216,plain,
% 0.19/0.52 (((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(217,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[216, 200])).
% 0.19/0.52 tff(218,plain,
% 0.19/0.52 ((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))))) | (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39)))) | (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(219,plain,
% 0.19/0.52 ((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), union(image2(F!43, X!40), image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))))) | (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.19/0.52 tff(220,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[219, 215])).
% 0.19/0.52 tff(221,plain,
% 0.19/0.52 ((~(member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40)))) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(222,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39)) | member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, X!40))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.19/0.52 tff(223,plain,
% 0.19/0.52 (member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[222, 213])).
% 0.19/0.52 tff(224,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(225,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.19/0.52 tff(226,plain,
% 0.19/0.52 (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[225, 22])).
% 0.19/0.52 tff(227,plain,
% 0.19/0.52 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(228,plain,
% 0.19/0.52 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.19/0.52 tff(229,plain,
% 0.19/0.52 ((member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(230,plain,
% 0.19/0.52 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.19/0.52 tff(231,plain,
% 0.19/0.52 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))) | apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(232,plain,
% 0.19/0.52 (apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[231, 226])).
% 0.19/0.52 tff(233,plain,
% 0.19/0.52 (((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) <=> ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(234,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(235,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, union(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.52 tff(236,plain,
% 0.19/0.52 (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[235, 205, 232])).
% 0.19/0.52 tff(237,plain,
% 0.19/0.52 ((~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)))) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(238,plain,
% 0.19/0.52 (~(member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[237, 236, 230])).
% 0.19/0.52 tff(239,plain,
% 0.19/0.52 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, union(X!40, Y!39)), union(image2(F!43, X!40), image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(240,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[239, 51, 238])).
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53 % E exiting
%------------------------------------------------------------------------------