%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET763+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:18 AM UTC 2025
% Result : Theorem 7.38s 7.54s
% Output : Proof 7.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.14 % Problem : SET763+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.15/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 05:41:24 EDT 2025
% 0.15/0.37 % CPUTime :
% 7.38/7.54 % SZS status Theorem
% 7.38/7.54 % SZS output start Proof
% 7.38/7.54 tff(member_type, type, (
% 7.38/7.54 member: ( $i * $i ) > $o)).
% 7.38/7.54 tff(empty_set_type, type, (
% 7.38/7.54 empty_set: $i)).
% 7.38/7.54 tff(tptp_fun_Y_3_type, type, (
% 7.38/7.54 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_F_42_type, type, (
% 7.38/7.54 tptp_fun_F_42: $i)).
% 7.38/7.54 tff(tptp_fun_B_40_type, type, (
% 7.38/7.54 tptp_fun_B_40: $i)).
% 7.38/7.54 tff(tptp_fun_X_0_type, type, (
% 7.38/7.54 tptp_fun_X_0: ( $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_X_39_type, type, (
% 7.38/7.54 tptp_fun_X_39: $i)).
% 7.38/7.54 tff(image2_type, type, (
% 7.38/7.54 image2: ( $i * $i ) > $i)).
% 7.38/7.54 tff(apply_type, type, (
% 7.38/7.54 apply: ( $i * $i * $i ) > $o)).
% 7.38/7.54 tff(subset_type, type, (
% 7.38/7.54 subset: ( $i * $i ) > $o)).
% 7.38/7.54 tff(equal_set_type, type, (
% 7.38/7.54 equal_set: ( $i * $i ) > $o)).
% 7.38/7.54 tff(tptp_fun_A_41_type, type, (
% 7.38/7.54 tptp_fun_A_41: $i)).
% 7.38/7.54 tff(maps_type, type, (
% 7.38/7.54 maps: ( $i * $i * $i ) > $o)).
% 7.38/7.54 tff(tptp_fun_Y2_5_type, type, (
% 7.38/7.54 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_Y1_6_type, type, (
% 7.38/7.54 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_X_7_type, type, (
% 7.38/7.54 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_X_4_type, type, (
% 7.38/7.54 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(tptp_fun_X_23_type, type, (
% 7.38/7.54 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 7.38/7.54 tff(1,assumption,(~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)), introduced(assumption)).
% 7.38/7.54 tff(2,assumption,((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))), introduced(assumption)).
% 7.38/7.54 tff(3,plain,
% 7.38/7.54 (^[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))))))))),
% 7.38/7.54 inference(bind,[status(th)],[])).
% 7.38/7.54 tff(4,plain,
% 7.38/7.54 (![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)))))))),
% 7.38/7.54 inference(quant_intro,[status(thm)],[3])).
% 7.38/7.54 tff(5,plain,
% 7.38/7.54 (^[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))))))))),
% 7.38/7.54 inference(bind,[status(th)],[])).
% 7.38/7.54 tff(6,plain,
% 7.38/7.54 (![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)))))))),
% 7.38/7.54 inference(quant_intro,[status(thm)],[5])).
% 7.38/7.54 tff(7,plain,
% 7.38/7.54 (![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)))))))),
% 7.38/7.54 inference(transitivity,[status(thm)],[6, 4])).
% 7.38/7.54 tff(8,plain,
% 7.38/7.54 (^[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)))))))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(9,plain,
% 7.38/7.55 (![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)))))))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[8])).
% 7.38/7.55 tff(10,plain,
% 7.38/7.55 (![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)))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(11,plain,
% 7.38/7.55 (^[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))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(12,plain,
% 7.38/7.55 (![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)))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[11])).
% 7.38/7.55 tff(13,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')).
% 7.38/7.55 tff(14,plain,
% 7.38/7.55 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[13, 12])).
% 7.38/7.55 tff(15,plain,
% 7.38/7.55 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[14, 10])).
% 7.38/7.55 tff(16,plain,(
% 7.38/7.55 ![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)))))),
% 7.38/7.55 inference(skolemize,[status(sab)],[15])).
% 7.38/7.55 tff(17,plain,
% 7.38/7.55 (![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)))))))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[16, 9])).
% 7.38/7.55 tff(18,plain,
% 7.38/7.55 (![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)))))))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[17, 7])).
% 7.38/7.55 tff(19,plain,
% 7.38/7.55 ((~![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(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(20,plain,
% 7.38/7.55 ($false),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[19, 18, 2])).
% 7.38/7.55 tff(21,plain,(~((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.55 tff(22,plain,
% 7.38/7.55 (((~((~subset(empty_set, X!39)) | ![X: $i] : ((~member(X, empty_set)) | member(X, X!39)))) | (~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))))) | (subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(23,plain,
% 7.38/7.55 (subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[22, 21])).
% 7.38/7.55 tff(24,assumption,(member(tptp_fun_X_0(X!39, empty_set), empty_set)), introduced(assumption)).
% 7.38/7.55 tff(25,plain,
% 7.38/7.55 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(26,plain,
% 7.38/7.55 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[25])).
% 7.38/7.55 tff(27,plain,
% 7.38/7.55 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(28,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 7.38/7.55 tff(29,plain,
% 7.38/7.55 (![X: $i] : (~member(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[28, 27])).
% 7.38/7.55 tff(30,plain,(
% 7.38/7.55 ![X: $i] : (~member(X, empty_set))),
% 7.38/7.55 inference(skolemize,[status(sab)],[29])).
% 7.38/7.55 tff(31,plain,
% 7.38/7.55 (![X: $i] : (~member(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[30, 26])).
% 7.38/7.55 tff(32,plain,
% 7.38/7.55 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(X!39, empty_set), empty_set))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(33,plain,
% 7.38/7.55 ($false),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 7.38/7.55 tff(34,plain,(~member(tptp_fun_X_0(X!39, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 7.38/7.55 tff(35,plain,
% 7.38/7.55 (((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)) | member(tptp_fun_X_0(X!39, empty_set), empty_set)),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(36,plain,
% 7.38/7.55 ((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[35, 34])).
% 7.38/7.55 tff(37,plain,
% 7.38/7.55 ((~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))) | subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39)))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(38,plain,
% 7.38/7.55 ((~(subset(empty_set, X!39) | (~((~member(tptp_fun_X_0(X!39, empty_set), empty_set)) | member(tptp_fun_X_0(X!39, empty_set), X!39))))) | subset(empty_set, X!39)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[37, 36])).
% 7.38/7.55 tff(39,plain,
% 7.38/7.55 (subset(empty_set, X!39)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[38, 23])).
% 7.38/7.55 tff(40,plain,
% 7.38/7.55 (^[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))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(41,plain,
% 7.38/7.55 (![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)))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[40])).
% 7.38/7.55 tff(42,plain,
% 7.38/7.55 (^[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)))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(43,plain,
% 7.38/7.55 (![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)))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[42])).
% 7.38/7.55 tff(44,plain,
% 7.38/7.55 (![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)))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(45,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')).
% 7.38/7.55 tff(46,plain,
% 7.38/7.55 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[45, 44])).
% 7.38/7.55 tff(47,plain,(
% 7.38/7.55 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 7.38/7.55 inference(skolemize,[status(sab)],[46])).
% 7.38/7.55 tff(48,plain,
% 7.38/7.55 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[47, 43])).
% 7.38/7.55 tff(49,plain,
% 7.38/7.55 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[48, 41])).
% 7.38/7.55 tff(50,plain,
% 7.38/7.55 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))) <=> equal_set(X!39, empty_set)))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(51,plain,
% 7.38/7.55 (~(((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))) <=> equal_set(X!39, empty_set))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[50, 49])).
% 7.38/7.55 tff(52,plain,
% 7.38/7.55 ((~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set)))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(53,plain,
% 7.38/7.55 ((~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & subset(X, A)) & equal_set(image2(F, X), empty_set)) => equal_set(X, empty_set))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set)))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(54,axiom,(~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & subset(X, A)) & equal_set(image2(F, X), empty_set)) => equal_set(X, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa13')).
% 7.38/7.55 tff(55,plain,
% 7.38/7.55 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[54, 53])).
% 7.38/7.55 tff(56,plain,
% 7.38/7.55 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[55, 52])).
% 7.38/7.55 tff(57,plain,
% 7.38/7.55 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[56, 52])).
% 7.38/7.55 tff(58,plain,
% 7.38/7.55 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & subset(X, A) & equal_set(image2(F, X), empty_set))) | equal_set(X, empty_set))),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[57, 52])).
% 7.38/7.55 tff(59,plain,(
% 7.38/7.55 ~((~(maps(F!42, A!41, B!40) & subset(X!39, A!41) & equal_set(image2(F!42, X!39), empty_set))) | equal_set(X!39, empty_set))),
% 7.38/7.55 inference(skolemize,[status(sab)],[58])).
% 7.38/7.55 tff(60,plain,
% 7.38/7.55 (~equal_set(X!39, empty_set)),
% 7.38/7.55 inference(or_elim,[status(thm)],[59])).
% 7.38/7.55 tff(61,plain,
% 7.38/7.55 ((((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))) <=> equal_set(X!39, empty_set)) | ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))) | equal_set(X!39, empty_set)),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(62,plain,
% 7.38/7.55 ((((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))) <=> equal_set(X!39, empty_set)) | ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[61, 60])).
% 7.38/7.55 tff(63,plain,
% 7.38/7.55 ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[62, 51])).
% 7.38/7.55 tff(64,plain,
% 7.38/7.55 ((~((~subset(X!39, empty_set)) | (~subset(empty_set, X!39)))) | (~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(65,plain,
% 7.38/7.55 ((~subset(X!39, empty_set)) | (~subset(empty_set, X!39))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[64, 63])).
% 7.38/7.55 tff(66,plain,
% 7.38/7.55 (~subset(X!39, empty_set)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[65, 39])).
% 7.38/7.55 tff(67,assumption,((~((~subset(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))))), introduced(assumption)).
% 7.38/7.55 tff(68,plain,
% 7.38/7.55 ((~![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(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))))))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(69,plain,
% 7.38/7.55 ($false),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[68, 18, 67])).
% 7.38/7.55 tff(70,plain,(~((~((~subset(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 7.38/7.55 tff(71,plain,
% 7.38/7.55 (((~((~subset(X!39, empty_set)) | ![X: $i] : ((~member(X, X!39)) | member(X, empty_set)))) | (~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))))) | (subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(72,plain,
% 7.38/7.55 (subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[71, 70])).
% 7.38/7.55 tff(73,plain,
% 7.38/7.55 ((~(subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))))) | subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(74,plain,
% 7.38/7.55 (subset(X!39, empty_set) | (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[73, 72])).
% 7.38/7.55 tff(75,plain,
% 7.38/7.55 (~((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[74, 66])).
% 7.38/7.55 tff(76,plain,
% 7.38/7.55 (((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), empty_set)) | member(tptp_fun_X_0(empty_set, X!39), X!39)),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(77,plain,
% 7.38/7.55 (member(tptp_fun_X_0(empty_set, X!39), X!39)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[76, 75])).
% 7.38/7.55 tff(78,assumption,(![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))), introduced(assumption)).
% 7.38/7.55 tff(79,assumption,(member(tptp_fun_X_0(empty_set, X!39), X!39)), introduced(assumption)).
% 7.38/7.55 tff(80,plain,
% 7.38/7.55 ((~![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(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(81,plain,
% 7.38/7.55 (~((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41))))))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[80, 18])).
% 7.38/7.55 tff(82,plain,
% 7.38/7.55 (((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))) | ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(83,plain,
% 7.38/7.55 ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[82, 81])).
% 7.38/7.55 tff(84,plain,
% 7.38/7.55 (maps(F!42, A!41, B!40) & subset(X!39, A!41) & equal_set(image2(F!42, X!39), empty_set)),
% 7.38/7.55 inference(or_elim,[status(thm)],[59])).
% 7.38/7.55 tff(85,plain,
% 7.38/7.55 (subset(X!39, A!41)),
% 7.38/7.55 inference(and_elim,[status(thm)],[84])).
% 7.38/7.55 tff(86,plain,
% 7.38/7.55 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 7.38/7.55 inference(tautology,[status(thm)],[])).
% 7.38/7.55 tff(87,plain,
% 7.38/7.55 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[86, 85])).
% 7.38/7.55 tff(88,plain,
% 7.38/7.55 (![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[87, 83])).
% 7.38/7.55 tff(89,plain,
% 7.38/7.55 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))),
% 7.38/7.55 inference(rewrite,[status(thm)],[])).
% 7.38/7.55 tff(90,plain,
% 7.38/7.55 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41))),
% 7.38/7.55 inference(quant_inst,[status(thm)],[])).
% 7.38/7.55 tff(91,plain,
% 7.38/7.55 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | member(tptp_fun_X_0(empty_set, X!39), A!41)),
% 7.38/7.55 inference(modus_ponens,[status(thm)],[90, 89])).
% 7.38/7.55 tff(92,plain,
% 7.38/7.55 (member(tptp_fun_X_0(empty_set, X!39), A!41)),
% 7.38/7.55 inference(unit_resolution,[status(thm)],[91, 88, 79])).
% 7.38/7.55 tff(93,plain,
% 7.38/7.55 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(94,plain,
% 7.38/7.55 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[93])).
% 7.38/7.55 tff(95,plain,
% 7.38/7.55 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(96,plain,
% 7.38/7.55 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[95])).
% 7.38/7.55 tff(97,plain,
% 7.38/7.55 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(98,plain,
% 7.38/7.55 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[97])).
% 7.38/7.55 tff(99,plain,
% 7.38/7.55 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.55 inference(transitivity,[status(thm)],[98, 96])).
% 7.38/7.55 tff(100,plain,
% 7.38/7.55 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 7.38/7.55 inference(bind,[status(th)],[])).
% 7.38/7.55 tff(101,plain,
% 7.38/7.55 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.55 inference(quant_intro,[status(thm)],[100])).
% 7.38/7.56 tff(102,plain,
% 7.38/7.56 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.56 inference(bind,[status(th)],[])).
% 7.38/7.56 tff(103,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 7.38/7.56 inference(quant_intro,[status(thm)],[102])).
% 7.38/7.56 tff(104,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 7.38/7.56 inference(rewrite,[status(thm)],[])).
% 7.38/7.56 tff(105,plain,
% 7.38/7.56 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 7.38/7.56 inference(bind,[status(th)],[])).
% 7.38/7.56 tff(106,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 7.38/7.56 inference(quant_intro,[status(thm)],[105])).
% 7.38/7.56 tff(107,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 7.38/7.56 tff(108,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[107, 106])).
% 7.38/7.56 tff(109,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[108, 104])).
% 7.38/7.56 tff(110,plain,(
% 7.38/7.56 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.56 inference(skolemize,[status(sab)],[109])).
% 7.38/7.56 tff(111,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[110, 103])).
% 7.38/7.56 tff(112,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[111, 101])).
% 7.38/7.56 tff(113,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[112, 99])).
% 7.38/7.56 tff(114,plain,
% 7.38/7.56 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 7.38/7.56 inference(modus_ponens,[status(thm)],[113, 94])).
% 7.38/7.56 tff(115,plain,
% 7.38/7.56 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 7.38/7.56 inference(rewrite,[status(thm)],[])).
% 7.38/7.56 tff(116,plain,
% 7.38/7.56 ((~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))) <=> (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 7.38/7.56 inference(rewrite,[status(thm)],[])).
% 7.38/7.56 tff(117,plain,
% 7.38/7.56 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 7.41/7.56 inference(monotonicity,[status(thm)],[116])).
% 7.41/7.56 tff(118,plain,
% 7.41/7.56 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 7.41/7.56 inference(transitivity,[status(thm)],[117, 115])).
% 7.41/7.56 tff(119,plain,
% 7.41/7.56 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))),
% 7.41/7.56 inference(quant_inst,[status(thm)],[])).
% 7.41/7.56 tff(120,plain,
% 7.41/7.56 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[119, 118])).
% 7.41/7.57 tff(121,plain,
% 7.41/7.57 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[120, 114])).
% 7.41/7.57 tff(122,plain,
% 7.41/7.57 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(123,plain,
% 7.41/7.57 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[122, 121])).
% 7.41/7.57 tff(124,plain,
% 7.41/7.57 (maps(F!42, A!41, B!40)),
% 7.41/7.57 inference(and_elim,[status(thm)],[84])).
% 7.41/7.57 tff(125,plain,
% 7.41/7.57 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(126,plain,
% 7.41/7.57 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[125, 124])).
% 7.41/7.57 tff(127,plain,
% 7.41/7.57 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[126, 123])).
% 7.41/7.57 tff(128,plain,
% 7.41/7.57 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(129,plain,
% 7.41/7.57 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[128, 127])).
% 7.41/7.57 tff(130,plain,
% 7.41/7.57 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(131,plain,
% 7.41/7.57 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(132,plain,
% 7.41/7.57 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(empty_set, X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[131, 130])).
% 7.41/7.57 tff(133,plain,
% 7.41/7.57 (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[132, 129, 92])).
% 7.41/7.57 tff(134,plain,
% 7.41/7.57 (((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))) | apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(135,plain,
% 7.41/7.57 (apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[134, 133])).
% 7.41/7.57 tff(136,plain,
% 7.41/7.57 (((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) <=> ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(137,plain,
% 7.41/7.57 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(138,plain,
% 7.41/7.57 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(empty_set, X!39), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[137, 136])).
% 7.41/7.57 tff(139,plain,
% 7.41/7.57 ($false),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[138, 79, 135, 78])).
% 7.41/7.57 tff(140,plain,((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(empty_set, X!39), X!39))), inference(lemma,lemma(discharge,[]))).
% 7.41/7.57 tff(141,plain,
% 7.41/7.57 (~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[140, 77])).
% 7.41/7.57 tff(142,assumption,((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))), introduced(assumption)).
% 7.41/7.57 tff(143,plain,
% 7.41/7.57 (^[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))))))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(144,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[143])).
% 7.41/7.57 tff(145,plain,
% 7.41/7.57 (^[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))))))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(146,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[145])).
% 7.41/7.57 tff(147,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(transitivity,[status(thm)],[146, 144])).
% 7.41/7.57 tff(148,plain,
% 7.41/7.57 (^[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)))))))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(149,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[148])).
% 7.41/7.57 tff(150,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(151,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')).
% 7.41/7.57 tff(152,plain,
% 7.41/7.57 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[151, 150])).
% 7.41/7.57 tff(153,plain,(
% 7.41/7.57 ![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)))))),
% 7.41/7.57 inference(skolemize,[status(sab)],[152])).
% 7.41/7.57 tff(154,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[153, 149])).
% 7.41/7.57 tff(155,plain,
% 7.41/7.57 (![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)))))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[154, 147])).
% 7.41/7.57 tff(156,plain,
% 7.41/7.57 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(157,plain,
% 7.41/7.57 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))) <=> (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(158,plain,
% 7.41/7.57 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 7.41/7.57 inference(monotonicity,[status(thm)],[157])).
% 7.41/7.57 tff(159,plain,
% 7.41/7.57 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))))),
% 7.41/7.57 inference(transitivity,[status(thm)],[158, 156])).
% 7.41/7.57 tff(160,plain,
% 7.41/7.57 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(161,plain,
% 7.41/7.57 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[160, 159])).
% 7.41/7.57 tff(162,plain,
% 7.41/7.57 ($false),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[161, 155, 142])).
% 7.41/7.57 tff(163,plain,(~((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))))))), inference(lemma,lemma(discharge,[]))).
% 7.41/7.57 tff(164,plain,
% 7.41/7.57 (((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | (~((~member(tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_23(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))))) | (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(165,plain,
% 7.41/7.57 (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[164, 163])).
% 7.41/7.57 tff(166,plain,
% 7.41/7.57 ((~(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42)))))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(tautology,[status(thm)],[])).
% 7.41/7.57 tff(167,plain,
% 7.41/7.57 (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42))))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[166, 165])).
% 7.41/7.57 tff(168,plain,
% 7.41/7.57 (member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[167, 141])).
% 7.41/7.57 tff(169,plain,
% 7.41/7.57 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set)))))))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(170,plain,
% 7.41/7.57 (~((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set))))))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[169, 18])).
% 7.41/7.58 tff(171,plain,
% 7.41/7.58 (((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~(subset(image2(F!42, X!39), empty_set) | (~((~member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), image2(F!42, X!39))) | member(tptp_fun_X_0(empty_set, image2(F!42, X!39)), empty_set)))))) | ((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))),
% 7.41/7.58 inference(tautology,[status(thm)],[])).
% 7.41/7.58 tff(172,plain,
% 7.41/7.58 ((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[171, 170])).
% 7.41/7.58 tff(173,plain,
% 7.41/7.58 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))) <=> equal_set(image2(F!42, X!39), empty_set)))),
% 7.41/7.58 inference(quant_inst,[status(thm)],[])).
% 7.41/7.58 tff(174,plain,
% 7.41/7.58 (~(((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))) <=> equal_set(image2(F!42, X!39), empty_set))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[173, 49])).
% 7.41/7.58 tff(175,plain,
% 7.41/7.58 (equal_set(image2(F!42, X!39), empty_set)),
% 7.41/7.58 inference(and_elim,[status(thm)],[84])).
% 7.41/7.58 tff(176,plain,
% 7.41/7.58 ((((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))) <=> equal_set(image2(F!42, X!39), empty_set)) | (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39))))) | (~equal_set(image2(F!42, X!39), empty_set))),
% 7.41/7.58 inference(tautology,[status(thm)],[])).
% 7.41/7.58 tff(177,plain,
% 7.41/7.58 ((((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))) <=> equal_set(image2(F!42, X!39), empty_set)) | (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[176, 175])).
% 7.41/7.58 tff(178,plain,
% 7.41/7.58 (~((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39))))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[177, 174])).
% 7.41/7.58 tff(179,plain,
% 7.41/7.58 (((~subset(image2(F!42, X!39), empty_set)) | (~subset(empty_set, image2(F!42, X!39)))) | subset(image2(F!42, X!39), empty_set)),
% 7.41/7.58 inference(tautology,[status(thm)],[])).
% 7.41/7.58 tff(180,plain,
% 7.41/7.58 (subset(image2(F!42, X!39), empty_set)),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[179, 178])).
% 7.41/7.58 tff(181,plain,
% 7.41/7.58 ((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | (~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 7.41/7.58 inference(tautology,[status(thm)],[])).
% 7.41/7.58 tff(182,plain,
% 7.41/7.58 ((~((~subset(image2(F!42, X!39), empty_set)) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set)))) | ![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[181, 180])).
% 7.41/7.58 tff(183,plain,
% 7.41/7.58 (![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[182, 172])).
% 7.41/7.58 tff(184,plain,
% 7.41/7.58 (((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))) <=> ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 7.41/7.58 inference(rewrite,[status(thm)],[])).
% 7.41/7.58 tff(185,plain,
% 7.41/7.58 ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 7.41/7.58 inference(quant_inst,[status(thm)],[])).
% 7.41/7.58 tff(186,plain,
% 7.41/7.59 ((~![X: $i] : ((~member(X, image2(F!42, X!39))) | member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), image2(F!42, X!39))) | member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)),
% 7.41/7.59 inference(modus_ponens,[status(thm)],[185, 184])).
% 7.41/7.59 tff(187,plain,
% 7.41/7.59 ($false),
% 7.41/7.59 inference(unit_resolution,[status(thm)],[186, 183, 168, 1])).
% 7.41/7.59 tff(188,plain,(member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set)), inference(lemma,lemma(discharge,[]))).
% 7.41/7.59 tff(189,plain,
% 7.41/7.59 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(empty_set, X!39), B!40, F!42), empty_set))),
% 7.41/7.59 inference(quant_inst,[status(thm)],[])).
% 7.41/7.59 tff(190,plain,
% 7.41/7.59 ($false),
% 7.41/7.59 inference(unit_resolution,[status(thm)],[189, 31, 188])).
% 7.41/7.59 % SZS output end Proof
% 7.41/7.60 % E exiting
%------------------------------------------------------------------------------