%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET697+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:10 AM UTC 2025
% Result : Theorem 11.26s 11.41s
% Output : Proof 11.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET697+4 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:38:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 11.26/11.41 % SZS status Theorem
% 11.26/11.41 % SZS output start Proof
% 11.26/11.41 tff(member_type, type, (
% 11.26/11.41 member: ( $i * $i ) > $o)).
% 11.26/11.41 tff(empty_set_type, type, (
% 11.26/11.41 empty_set: $i)).
% 11.26/11.41 tff(tptp_fun_X_0_type, type, (
% 11.26/11.41 tptp_fun_X_0: ( $i * $i ) > $i)).
% 11.26/11.41 tff(union_type, type, (
% 11.26/11.41 union: ( $i * $i ) > $i)).
% 11.26/11.41 tff(tptp_fun_A_5_type, type, (
% 11.26/11.41 tptp_fun_A_5: $i)).
% 11.26/11.41 tff(tptp_fun_B_4_type, type, (
% 11.26/11.41 tptp_fun_B_4: $i)).
% 11.26/11.41 tff(intersection_type, type, (
% 11.26/11.41 intersection: ( $i * $i ) > $i)).
% 11.26/11.41 tff(difference_type, type, (
% 11.26/11.41 difference: ( $i * $i ) > $i)).
% 11.26/11.41 tff(tptp_fun_E_3_type, type, (
% 11.26/11.41 tptp_fun_E_3: $i)).
% 11.26/11.41 tff(subset_type, type, (
% 11.26/11.41 subset: ( $i * $i ) > $o)).
% 11.26/11.41 tff(power_set_type, type, (
% 11.26/11.41 power_set: $i > $i)).
% 11.26/11.41 tff(sum_type, type, (
% 11.26/11.41 sum: $i > $i)).
% 11.26/11.41 tff(tptp_fun_Y_1_type, type, (
% 11.26/11.41 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 11.26/11.41 tff(equal_set_type, type, (
% 11.26/11.41 equal_set: ( $i * $i ) > $o)).
% 11.26/11.41 tff(1,assumption,(~member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set)), introduced(assumption)).
% 11.26/11.41 tff(2,assumption,(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))), introduced(assumption)).
% 11.26/11.41 tff(3,plain,
% 11.26/11.41 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 11.26/11.41 inference(bind,[status(th)],[])).
% 11.26/11.41 tff(4,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 11.26/11.41 inference(quant_intro,[status(thm)],[3])).
% 11.26/11.41 tff(5,plain,
% 11.26/11.41 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 11.26/11.41 inference(bind,[status(th)],[])).
% 11.26/11.41 tff(6,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 11.26/11.41 inference(quant_intro,[status(thm)],[5])).
% 11.26/11.41 tff(7,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 11.26/11.41 inference(rewrite,[status(thm)],[])).
% 11.26/11.41 tff(8,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 11.26/11.41 tff(9,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 11.26/11.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 11.26/11.41 tff(10,plain,(
% 11.26/11.41 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 11.26/11.41 inference(skolemize,[status(sab)],[9])).
% 11.26/11.41 tff(11,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 11.26/11.41 inference(modus_ponens,[status(thm)],[10, 6])).
% 11.26/11.41 tff(12,plain,
% 11.26/11.41 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 11.26/11.41 inference(modus_ponens,[status(thm)],[11, 4])).
% 11.26/11.41 tff(13,plain,
% 11.26/11.41 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))))),
% 11.26/11.41 inference(quant_inst,[status(thm)],[])).
% 11.26/11.41 tff(14,plain,
% 11.26/11.41 ($false),
% 11.26/11.41 inference(unit_resolution,[status(thm)],[13, 12, 2])).
% 11.26/11.41 tff(15,plain,(~(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.41 tff(16,assumption,(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))), introduced(assumption)).
% 11.26/11.41 tff(17,plain,
% 11.26/11.41 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 11.26/11.41 inference(bind,[status(th)],[])).
% 11.26/11.41 tff(18,plain,
% 11.26/11.41 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 11.26/11.41 inference(quant_intro,[status(thm)],[17])).
% 11.26/11.41 tff(19,plain,
% 11.26/11.41 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 11.26/11.41 inference(bind,[status(th)],[])).
% 11.26/11.41 tff(20,plain,
% 11.26/11.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 11.26/11.41 inference(quant_intro,[status(thm)],[19])).
% 11.26/11.41 tff(21,plain,
% 11.26/11.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 11.26/11.41 inference(rewrite,[status(thm)],[])).
% 11.26/11.41 tff(22,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 11.26/11.41 tff(23,plain,
% 11.26/11.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 11.26/11.42 tff(24,plain,(
% 11.26/11.42 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 11.26/11.42 inference(skolemize,[status(sab)],[23])).
% 11.26/11.42 tff(25,plain,
% 11.26/11.42 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 11.26/11.42 tff(26,plain,
% 11.26/11.42 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 11.26/11.42 tff(27,plain,
% 11.26/11.42 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(28,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[27, 26, 16])).
% 11.26/11.42 tff(29,plain,(~(((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(30,plain,
% 11.26/11.42 (^[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))))))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(31,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[30])).
% 11.26/11.42 tff(32,plain,
% 11.26/11.42 (^[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))))))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(33,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[32])).
% 11.26/11.42 tff(34,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(transitivity,[status(thm)],[33, 31])).
% 11.26/11.42 tff(35,plain,
% 11.26/11.42 (^[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)))))))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(36,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[35])).
% 11.26/11.42 tff(37,plain,
% 11.26/11.42 (![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)))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(38,plain,
% 11.26/11.42 (^[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))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(39,plain,
% 11.26/11.42 (![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)))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[38])).
% 11.26/11.42 tff(40,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 11.26/11.42 tff(41,plain,
% 11.26/11.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 11.26/11.42 tff(42,plain,
% 11.26/11.42 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[41, 37])).
% 11.26/11.42 tff(43,plain,(
% 11.26/11.42 ![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)))))),
% 11.26/11.42 inference(skolemize,[status(sab)],[42])).
% 11.26/11.42 tff(44,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[43, 36])).
% 11.26/11.42 tff(45,plain,
% 11.26/11.42 (![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)))))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[44, 34])).
% 11.26/11.42 tff(46,plain,
% 11.26/11.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(A!5, A!5), B!4)) | ![X: $i] : ((~member(X, union(A!5, A!5))) | member(X, B!4)))) | (~(subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)))))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(47,plain,
% 11.26/11.42 (~((~((~subset(union(A!5, A!5), B!4)) | ![X: $i] : ((~member(X, union(A!5, A!5))) | member(X, B!4)))) | (~(subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))))))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 11.26/11.42 tff(48,plain,
% 11.26/11.42 (((~((~subset(union(A!5, A!5), B!4)) | ![X: $i] : ((~member(X, union(A!5, A!5))) | member(X, B!4)))) | (~(subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)))))) | (subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(49,plain,
% 11.26/11.42 (subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 11.26/11.42 tff(50,plain,
% 11.26/11.42 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(51,plain,
% 11.26/11.42 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[50])).
% 11.26/11.42 tff(52,plain,
% 11.26/11.42 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(53,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','power_set')).
% 11.26/11.42 tff(54,plain,
% 11.26/11.42 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 11.26/11.42 tff(55,plain,(
% 11.26/11.42 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 11.26/11.42 inference(skolemize,[status(sab)],[54])).
% 11.26/11.42 tff(56,plain,
% 11.26/11.42 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 11.26/11.42 tff(57,plain,
% 11.26/11.42 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(union(A!5, A!5), power_set(B!4)) <=> subset(union(A!5, A!5), B!4))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(58,plain,
% 11.26/11.42 (member(union(A!5, A!5), power_set(B!4)) <=> subset(union(A!5, A!5), B!4)),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[57, 56])).
% 11.26/11.42 tff(59,assumption,(subset(A!5, B!4)), introduced(assumption)).
% 11.26/11.42 tff(60,plain,
% 11.26/11.42 ((~![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(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(61,plain,
% 11.26/11.42 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[60, 45])).
% 11.26/11.42 tff(62,plain,
% 11.26/11.42 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(63,plain,
% 11.26/11.42 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[62, 61])).
% 11.26/11.42 tff(64,plain,
% 11.26/11.42 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(65,plain,
% 11.26/11.42 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[64, 63])).
% 11.26/11.42 tff(66,plain,
% 11.26/11.42 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[65, 59])).
% 11.26/11.42 tff(67,assumption,(~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))), introduced(assumption)).
% 11.26/11.42 tff(68,plain,
% 11.26/11.42 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(69,plain,
% 11.26/11.42 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[68, 67])).
% 11.26/11.42 tff(70,assumption,(![X: $i] : ((~member(X, A!5)) | member(X, B!4))), introduced(assumption)).
% 11.26/11.42 tff(71,plain,
% 11.26/11.42 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(72,plain,
% 11.26/11.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(73,plain,
% 11.26/11.42 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 11.26/11.42 tff(74,plain,
% 11.26/11.42 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[73, 70, 69])).
% 11.26/11.42 tff(75,plain,
% 11.26/11.42 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(76,plain,
% 11.26/11.42 (~(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[75, 26])).
% 11.26/11.42 tff(77,plain,
% 11.26/11.42 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(78,plain,
% 11.26/11.42 (member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[77, 67])).
% 11.26/11.42 tff(79,plain,
% 11.26/11.42 ((((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(80,plain,
% 11.26/11.42 ((((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 11.26/11.42 tff(81,plain,
% 11.26/11.42 (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[80, 76])).
% 11.26/11.42 tff(82,plain,
% 11.26/11.42 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), B!4))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(83,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[82, 81, 74])).
% 11.26/11.42 tff(84,plain,(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | (~![X: $i] : ((~member(X, A!5)) | member(X, B!4)))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(85,plain,
% 11.26/11.42 ((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[84, 66])).
% 11.26/11.42 tff(86,assumption,(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))), introduced(assumption)).
% 11.26/11.42 tff(87,plain,
% 11.26/11.42 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(88,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[87, 12, 86])).
% 11.26/11.42 tff(89,plain,(~(((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(90,plain,
% 11.26/11.42 ((((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(91,plain,
% 11.26/11.42 ((~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[90, 89])).
% 11.26/11.42 tff(92,plain,
% 11.26/11.42 (~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[91, 85])).
% 11.26/11.42 tff(93,assumption,((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))), introduced(assumption)).
% 11.26/11.42 tff(94,plain,
% 11.26/11.42 ((~![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(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(95,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[94, 45, 93])).
% 11.26/11.42 tff(96,plain,(~((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(97,plain,
% 11.26/11.42 (((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))) | (subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(98,plain,
% 11.26/11.42 (subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[97, 96])).
% 11.26/11.42 tff(99,assumption,((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))), introduced(assumption)).
% 11.26/11.42 tff(100,plain,
% 11.26/11.42 ((~![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, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(101,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[100, 45, 99])).
% 11.26/11.42 tff(102,plain,(~((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(103,plain,
% 11.26/11.42 (((~((~subset(empty_set, intersection(A!5, difference(E!3, B!4)))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(A!5, difference(E!3, B!4)))))) | (~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))))) | (subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(104,plain,
% 11.26/11.42 (subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 11.26/11.42 tff(105,assumption,(member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)), introduced(assumption)).
% 11.26/11.42 tff(106,plain,
% 11.26/11.42 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(107,plain,
% 11.26/11.42 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[106])).
% 11.26/11.42 tff(108,plain,
% 11.26/11.42 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(109,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 11.26/11.42 tff(110,plain,
% 11.26/11.42 (![X: $i] : (~member(X, empty_set))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 11.26/11.42 tff(111,plain,(
% 11.26/11.42 ![X: $i] : (~member(X, empty_set))),
% 11.26/11.42 inference(skolemize,[status(sab)],[110])).
% 11.26/11.42 tff(112,plain,
% 11.26/11.42 (![X: $i] : (~member(X, empty_set))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[111, 107])).
% 11.26/11.42 tff(113,plain,
% 11.26/11.42 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(114,plain,
% 11.26/11.42 ($false),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[113, 112, 105])).
% 11.26/11.42 tff(115,plain,(~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 11.26/11.42 tff(116,plain,
% 11.26/11.42 (((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(117,plain,
% 11.26/11.42 ((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[116, 115])).
% 11.26/11.42 tff(118,plain,
% 11.26/11.42 ((~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))) | subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4)))))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(119,plain,
% 11.26/11.42 ((~(subset(empty_set, intersection(A!5, difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(A!5, difference(E!3, B!4)), empty_set), intersection(A!5, difference(E!3, B!4))))))) | subset(empty_set, intersection(A!5, difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 11.26/11.42 tff(120,plain,
% 11.26/11.42 (subset(empty_set, intersection(A!5, difference(E!3, B!4)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[119, 104])).
% 11.26/11.42 tff(121,plain,
% 11.26/11.42 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set))))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(122,plain,
% 11.26/11.42 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set))))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(123,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI31')).
% 11.26/11.42 tff(124,plain,
% 11.26/11.42 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 11.26/11.42 tff(125,plain,
% 11.26/11.42 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[124, 121])).
% 11.26/11.42 tff(126,plain,
% 11.26/11.42 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[125, 121])).
% 11.26/11.42 tff(127,plain,
% 11.26/11.42 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(intersection(A, difference(E, B)), empty_set)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[126, 121])).
% 11.26/11.42 tff(128,plain,(
% 11.26/11.42 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)))),
% 11.26/11.42 inference(skolemize,[status(sab)],[127])).
% 11.26/11.42 tff(129,plain,
% 11.26/11.42 (~(subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.26/11.42 inference(or_elim,[status(thm)],[128])).
% 11.26/11.42 tff(130,plain,
% 11.26/11.42 ((subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(A!5, B!4)) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(131,plain,
% 11.26/11.42 ((~subset(A!5, B!4)) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[130, 129])).
% 11.26/11.42 tff(132,plain,
% 11.26/11.42 (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[131, 59])).
% 11.26/11.42 tff(133,plain,
% 11.26/11.42 (^[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))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(134,plain,
% 11.26/11.42 (![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)))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[133])).
% 11.26/11.42 tff(135,plain,
% 11.26/11.42 (^[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)))))),
% 11.26/11.42 inference(bind,[status(th)],[])).
% 11.26/11.42 tff(136,plain,
% 11.26/11.42 (![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)))),
% 11.26/11.42 inference(quant_intro,[status(thm)],[135])).
% 11.26/11.42 tff(137,plain,
% 11.26/11.42 (![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)))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(138,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 11.26/11.42 tff(139,plain,
% 11.26/11.42 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 11.26/11.42 tff(140,plain,(
% 11.26/11.42 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 11.26/11.43 inference(skolemize,[status(sab)],[139])).
% 11.26/11.43 tff(141,plain,
% 11.26/11.43 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 11.26/11.43 inference(modus_ponens,[status(thm)],[140, 136])).
% 11.26/11.43 tff(142,plain,
% 11.26/11.43 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 11.26/11.43 inference(modus_ponens,[status(thm)],[141, 134])).
% 11.26/11.43 tff(143,plain,
% 11.26/11.43 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)))),
% 11.26/11.43 inference(quant_inst,[status(thm)],[])).
% 11.26/11.43 tff(144,plain,
% 11.26/11.43 (~(((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[143, 142])).
% 11.26/11.43 tff(145,plain,
% 11.26/11.43 ((((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(146,plain,
% 11.26/11.43 (((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[145, 144])).
% 11.26/11.43 tff(147,plain,
% 11.26/11.43 ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[146, 132])).
% 11.26/11.43 tff(148,plain,
% 11.26/11.43 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))) | (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(149,plain,
% 11.26/11.43 (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[148, 147, 120])).
% 11.26/11.43 tff(150,plain,
% 11.26/11.43 ((~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))))) | subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(151,plain,
% 11.26/11.43 (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[150, 149, 98])).
% 11.26/11.43 tff(152,plain,
% 11.26/11.43 (((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(153,plain,
% 11.26/11.43 ($false),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[152, 151, 92])).
% 11.26/11.43 tff(154,plain,(~subset(A!5, B!4)), inference(lemma,lemma(discharge,[]))).
% 11.26/11.43 tff(155,plain,
% 11.26/11.43 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(156,plain,
% 11.26/11.43 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[155, 61])).
% 11.26/11.43 tff(157,plain,
% 11.26/11.43 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(158,plain,
% 11.26/11.43 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[157, 156])).
% 11.26/11.43 tff(159,plain,
% 11.26/11.43 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[158, 154])).
% 11.26/11.43 tff(160,plain,
% 11.26/11.43 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(161,plain,
% 11.26/11.43 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[160, 159])).
% 11.26/11.43 tff(162,plain,
% 11.26/11.43 ((~![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(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))) | (~(subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4) | (~((~member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), B!4)))))))),
% 11.26/11.43 inference(quant_inst,[status(thm)],[])).
% 11.26/11.43 tff(163,plain,
% 11.26/11.43 (~((~((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))) | (~(subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4) | (~((~member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), B!4))))))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[162, 45])).
% 11.26/11.43 tff(164,plain,
% 11.26/11.43 (((~((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))) | (~(subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4) | (~((~member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))), B!4)))))) | ((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))),
% 11.26/11.43 inference(tautology,[status(thm)],[])).
% 11.26/11.43 tff(165,plain,
% 11.26/11.43 ((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[164, 163])).
% 11.26/11.43 tff(166,plain,
% 11.26/11.43 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4)) <=> subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4))),
% 11.26/11.43 inference(quant_inst,[status(thm)],[])).
% 11.26/11.43 tff(167,plain,
% 11.26/11.43 (member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4)) <=> subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)),
% 11.26/11.43 inference(unit_resolution,[status(thm)],[166, 56])).
% 11.26/11.43 tff(168,assumption,(~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))), introduced(assumption)).
% 11.28/11.43 tff(169,plain,
% 11.28/11.43 (((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))) | member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(170,plain,
% 11.28/11.43 (member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[169, 168])).
% 11.28/11.43 tff(171,plain,
% 11.28/11.43 ((~(member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4)) <=> subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4))) | (~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(172,plain,
% 11.28/11.43 ((~(member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4)) <=> subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4))) | subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[171, 170])).
% 11.28/11.43 tff(173,plain,
% 11.28/11.43 (subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[172, 167])).
% 11.28/11.43 tff(174,plain,
% 11.28/11.43 ((~((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))) | (~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(175,plain,
% 11.28/11.43 ((~((~subset(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), B!4)) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[174, 173])).
% 11.28/11.43 tff(176,plain,
% 11.28/11.43 (![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[175, 165])).
% 11.28/11.43 tff(177,plain,
% 11.28/11.43 (((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))) | member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(178,plain,
% 11.28/11.43 (member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[177, 168])).
% 11.28/11.43 tff(179,assumption,(~member(tptp_fun_X_0(B!4, A!5), B!4)), introduced(assumption)).
% 11.28/11.43 tff(180,plain,
% 11.28/11.43 (((~![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 11.28/11.43 inference(rewrite,[status(thm)],[])).
% 11.28/11.43 tff(181,plain,
% 11.28/11.43 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 11.28/11.43 inference(quant_inst,[status(thm)],[])).
% 11.28/11.43 tff(182,plain,
% 11.28/11.43 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 11.28/11.43 inference(modus_ponens,[status(thm)],[181, 180])).
% 11.28/11.43 tff(183,plain,
% 11.28/11.43 ($false),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[182, 179, 178, 176])).
% 11.28/11.43 tff(184,plain,(((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))) | member(tptp_fun_X_0(B!4, A!5), B!4)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.43 tff(185,plain,
% 11.28/11.43 ((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[184, 161])).
% 11.28/11.43 tff(186,plain,
% 11.28/11.43 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 11.28/11.43 inference(bind,[status(th)],[])).
% 11.28/11.43 tff(187,plain,
% 11.28/11.43 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(quant_intro,[status(thm)],[186])).
% 11.28/11.43 tff(188,plain,
% 11.28/11.43 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 11.28/11.43 inference(bind,[status(th)],[])).
% 11.28/11.43 tff(189,plain,
% 11.28/11.43 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(quant_intro,[status(thm)],[188])).
% 11.28/11.43 tff(190,plain,
% 11.28/11.43 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(transitivity,[status(thm)],[189, 187])).
% 11.28/11.43 tff(191,plain,
% 11.28/11.43 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 11.28/11.43 inference(bind,[status(th)],[])).
% 11.28/11.43 tff(192,plain,
% 11.28/11.43 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(quant_intro,[status(thm)],[191])).
% 11.28/11.43 tff(193,plain,
% 11.28/11.43 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 11.28/11.43 inference(rewrite,[status(thm)],[])).
% 11.28/11.43 tff(194,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','sum')).
% 11.28/11.43 tff(195,plain,
% 11.28/11.43 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 11.28/11.43 inference(modus_ponens,[status(thm)],[194, 193])).
% 11.28/11.43 tff(196,plain,(
% 11.28/11.43 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 11.28/11.43 inference(skolemize,[status(sab)],[195])).
% 11.28/11.43 tff(197,plain,
% 11.28/11.43 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(modus_ponens,[status(thm)],[196, 192])).
% 11.28/11.43 tff(198,plain,
% 11.28/11.43 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 11.28/11.43 inference(modus_ponens,[status(thm)],[197, 190])).
% 11.28/11.43 tff(199,plain,
% 11.28/11.43 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))))))),
% 11.28/11.43 inference(rewrite,[status(thm)],[])).
% 11.28/11.43 tff(200,plain,
% 11.28/11.43 ((~((~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))) | (~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(Y, power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), Y))))))) <=> (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))))))),
% 11.28/11.43 inference(rewrite,[status(thm)],[])).
% 11.28/11.43 tff(201,plain,
% 11.28/11.43 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))) | (~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(Y, power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))))))),
% 11.28/11.43 inference(monotonicity,[status(thm)],[200])).
% 11.28/11.43 tff(202,plain,
% 11.28/11.43 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))) | (~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(Y, power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))))))),
% 11.28/11.43 inference(transitivity,[status(thm)],[201, 199])).
% 11.28/11.43 tff(203,plain,
% 11.28/11.43 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))) | (~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(Y, power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), Y)))))))),
% 11.28/11.43 inference(quant_inst,[status(thm)],[])).
% 11.28/11.43 tff(204,plain,
% 11.28/11.43 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))))))),
% 11.28/11.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 11.28/11.43 tff(205,plain,
% 11.28/11.43 (~((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[204, 198])).
% 11.28/11.43 tff(206,plain,
% 11.28/11.43 (((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))))) | ((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(207,plain,
% 11.28/11.43 ((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[206, 205])).
% 11.28/11.43 tff(208,plain,
% 11.28/11.43 ((~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)))))))) | (~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(209,plain,
% 11.28/11.43 ((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[208, 207])).
% 11.28/11.43 tff(210,plain,
% 11.28/11.43 (~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[209, 185])).
% 11.28/11.43 tff(211,plain,
% 11.28/11.43 (((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | (~((~member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4)))) | (~((~member(tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5)), power_set(B!4))) | (~member(tptp_fun_X_0(B!4, A!5), tptp_fun_Y_1(power_set(B!4), tptp_fun_X_0(B!4, A!5))))))))) | (member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(212,plain,
% 11.28/11.43 (member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[211, 205])).
% 11.28/11.43 tff(213,plain,
% 11.28/11.43 ((~(member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4)))))) | member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(214,plain,
% 11.28/11.43 (member(tptp_fun_X_0(B!4, A!5), sum(power_set(B!4))) | ![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[213, 212])).
% 11.28/11.43 tff(215,plain,
% 11.28/11.43 (![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[214, 210])).
% 11.28/11.43 tff(216,plain,
% 11.28/11.43 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 11.28/11.43 inference(tautology,[status(thm)],[])).
% 11.28/11.43 tff(217,plain,
% 11.28/11.43 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 11.28/11.43 inference(unit_resolution,[status(thm)],[216, 159])).
% 11.28/11.43 tff(218,plain,
% 11.28/11.43 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 11.28/11.43 inference(bind,[status(th)],[])).
% 11.28/11.43 tff(219,plain,
% 11.28/11.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.43 inference(quant_intro,[status(thm)],[218])).
% 11.28/11.43 tff(220,plain,
% 11.28/11.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.43 inference(rewrite,[status(thm)],[])).
% 11.28/11.43 tff(221,plain,
% 11.28/11.43 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 11.28/11.43 inference(bind,[status(th)],[])).
% 11.28/11.43 tff(222,plain,
% 11.28/11.43 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.44 inference(quant_intro,[status(thm)],[221])).
% 11.28/11.44 tff(223,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 11.28/11.44 tff(224,plain,
% 11.28/11.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[223, 222])).
% 11.28/11.44 tff(225,plain,
% 11.28/11.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[224, 220])).
% 11.28/11.44 tff(226,plain,(
% 11.28/11.44 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.44 inference(skolemize,[status(sab)],[225])).
% 11.28/11.44 tff(227,plain,
% 11.28/11.44 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[226, 219])).
% 11.28/11.44 tff(228,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(229,plain,
% 11.28/11.44 ((member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, A!5), A!5) | member(tptp_fun_X_0(B!4, A!5), A!5))) <=> (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(230,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, A!5), A!5) | member(tptp_fun_X_0(B!4, A!5), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 11.28/11.44 inference(monotonicity,[status(thm)],[229])).
% 11.28/11.44 tff(231,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, A!5), A!5) | member(tptp_fun_X_0(B!4, A!5), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 11.28/11.44 inference(transitivity,[status(thm)],[230, 228])).
% 11.28/11.44 tff(232,plain,
% 11.28/11.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, A!5), A!5) | member(tptp_fun_X_0(B!4, A!5), A!5)))),
% 11.28/11.44 inference(quant_inst,[status(thm)],[])).
% 11.28/11.44 tff(233,plain,
% 11.28/11.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[232, 231])).
% 11.28/11.44 tff(234,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[233, 227])).
% 11.28/11.44 tff(235,plain,
% 11.28/11.44 ((~(member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, A!5), A!5))) | member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(236,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[235, 234])).
% 11.28/11.44 tff(237,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[236, 217])).
% 11.28/11.44 tff(238,plain,
% 11.28/11.44 (((~![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))) | ((~member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5))) | (~member(union(A!5, A!5), power_set(B!4))))) <=> ((~![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5))) | (~member(union(A!5, A!5), power_set(B!4))))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(239,plain,
% 11.28/11.44 ((~![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))) | ((~member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5))) | (~member(union(A!5, A!5), power_set(B!4))))),
% 11.28/11.44 inference(quant_inst,[status(thm)],[])).
% 11.28/11.44 tff(240,plain,
% 11.28/11.44 ((~![Y: $i] : ((~member(tptp_fun_X_0(B!4, A!5), Y)) | (~member(Y, power_set(B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), union(A!5, A!5))) | (~member(union(A!5, A!5), power_set(B!4)))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[239, 238])).
% 11.28/11.44 tff(241,plain,
% 11.28/11.44 (~member(union(A!5, A!5), power_set(B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[240, 237, 215])).
% 11.28/11.44 tff(242,plain,
% 11.28/11.44 ((~(member(union(A!5, A!5), power_set(B!4)) <=> subset(union(A!5, A!5), B!4))) | member(union(A!5, A!5), power_set(B!4)) | (~subset(union(A!5, A!5), B!4))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(243,plain,
% 11.28/11.44 ((~(member(union(A!5, A!5), power_set(B!4)) <=> subset(union(A!5, A!5), B!4))) | (~subset(union(A!5, A!5), B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[242, 241])).
% 11.28/11.44 tff(244,plain,
% 11.28/11.44 (~subset(union(A!5, A!5), B!4)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[243, 58])).
% 11.28/11.44 tff(245,plain,
% 11.28/11.44 ((~(subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))))) | subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(246,plain,
% 11.28/11.44 ((~(subset(union(A!5, A!5), B!4) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))))) | (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[245, 244])).
% 11.28/11.44 tff(247,plain,
% 11.28/11.44 (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[246, 49])).
% 11.28/11.44 tff(248,plain,
% 11.28/11.44 (((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(249,plain,
% 11.28/11.44 (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[248, 247])).
% 11.28/11.44 tff(250,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(251,plain,
% 11.28/11.44 ((member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))) <=> (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(252,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))),
% 11.28/11.44 inference(monotonicity,[status(thm)],[251])).
% 11.28/11.44 tff(253,plain,
% 11.28/11.44 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))),
% 11.28/11.44 inference(transitivity,[status(thm)],[252, 250])).
% 11.28/11.44 tff(254,plain,
% 11.28/11.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> (member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)))),
% 11.28/11.44 inference(quant_inst,[status(thm)],[])).
% 11.28/11.44 tff(255,plain,
% 11.28/11.44 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[254, 253])).
% 11.28/11.44 tff(256,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[255, 227])).
% 11.28/11.44 tff(257,plain,
% 11.28/11.44 (((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(258,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[257, 247])).
% 11.28/11.44 tff(259,plain,
% 11.28/11.44 ((~(member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(260,plain,
% 11.28/11.44 ((~(member(tptp_fun_X_0(B!4, union(A!5, A!5)), union(A!5, A!5)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[259, 258])).
% 11.28/11.44 tff(261,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[260, 256])).
% 11.28/11.44 tff(262,plain,
% 11.28/11.44 ((~![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(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 11.28/11.44 inference(quant_inst,[status(thm)],[])).
% 11.28/11.44 tff(263,plain,
% 11.28/11.44 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[262, 45])).
% 11.28/11.44 tff(264,plain,
% 11.28/11.44 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(265,plain,
% 11.28/11.44 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[264, 263])).
% 11.28/11.44 tff(266,plain,
% 11.28/11.44 (subset(A!5, E!3) & subset(B!4, E!3)),
% 11.28/11.44 inference(or_elim,[status(thm)],[128])).
% 11.28/11.44 tff(267,plain,
% 11.28/11.44 (subset(A!5, E!3)),
% 11.28/11.44 inference(and_elim,[status(thm)],[266])).
% 11.28/11.44 tff(268,plain,
% 11.28/11.44 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(269,plain,
% 11.28/11.44 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[268, 267])).
% 11.28/11.44 tff(270,plain,
% 11.28/11.44 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[269, 265])).
% 11.28/11.44 tff(271,plain,
% 11.28/11.44 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3))),
% 11.28/11.44 inference(rewrite,[status(thm)],[])).
% 11.28/11.44 tff(272,plain,
% 11.28/11.44 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3))),
% 11.28/11.44 inference(quant_inst,[status(thm)],[])).
% 11.28/11.44 tff(273,plain,
% 11.28/11.44 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)),
% 11.28/11.44 inference(modus_ponens,[status(thm)],[272, 271])).
% 11.28/11.44 tff(274,plain,
% 11.28/11.44 ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[273, 270])).
% 11.28/11.44 tff(275,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[274, 261])).
% 11.28/11.44 tff(276,plain,
% 11.28/11.44 ((~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(277,plain,
% 11.28/11.44 (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[276, 275, 249])).
% 11.28/11.44 tff(278,plain,
% 11.28/11.44 ((((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(279,plain,
% 11.28/11.44 ((((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), E!3)) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), B!4)) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[278, 277])).
% 11.28/11.44 tff(280,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[279, 29])).
% 11.28/11.44 tff(281,plain,
% 11.28/11.44 ((~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(282,plain,
% 11.28/11.44 (~((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4))))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[281, 261, 280])).
% 11.28/11.44 tff(283,plain,
% 11.28/11.44 ((((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(284,plain,
% 11.28/11.44 ((((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), A!5)) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[283, 282])).
% 11.28/11.44 tff(285,plain,
% 11.28/11.44 (member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[284, 15])).
% 11.28/11.44 tff(286,plain,
% 11.28/11.44 (((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(empty_set, intersection(A!5, difference(E!3, B!4))), empty_set)))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(287,plain,
% 11.28/11.44 ((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[286, 96])).
% 11.28/11.44 tff(288,plain,
% 11.28/11.44 ((subset(A!5, B!4) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | subset(A!5, B!4) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(289,plain,
% 11.28/11.44 (subset(A!5, B!4) | equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[288, 129])).
% 11.28/11.44 tff(290,plain,
% 11.28/11.44 (equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[289, 154])).
% 11.28/11.44 tff(291,plain,
% 11.28/11.44 ((((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) <=> equal_set(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(292,plain,
% 11.28/11.44 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))) | (~equal_set(intersection(A!5, difference(E!3, B!4)), empty_set))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[291, 144])).
% 11.28/11.44 tff(293,plain,
% 11.28/11.44 (~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4)))))),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[292, 290])).
% 11.28/11.44 tff(294,plain,
% 11.28/11.44 (((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | (~subset(empty_set, intersection(A!5, difference(E!3, B!4))))) | subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.28/11.44 inference(tautology,[status(thm)],[])).
% 11.28/11.44 tff(295,plain,
% 11.28/11.44 (subset(intersection(A!5, difference(E!3, B!4)), empty_set)),
% 11.28/11.44 inference(unit_resolution,[status(thm)],[294, 293])).
% 11.28/11.44 tff(296,plain,
% 11.28/11.44 ((~((~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set)))) | (~subset(intersection(A!5, difference(E!3, B!4)), empty_set)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 11.28/11.45 inference(tautology,[status(thm)],[])).
% 11.28/11.45 tff(297,plain,
% 11.28/11.45 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))),
% 11.28/11.45 inference(unit_resolution,[status(thm)],[296, 295, 287])).
% 11.28/11.45 tff(298,plain,
% 11.28/11.45 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set))) <=> ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set))),
% 11.28/11.45 inference(rewrite,[status(thm)],[])).
% 11.28/11.45 tff(299,plain,
% 11.28/11.45 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | ((~member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set))),
% 11.28/11.45 inference(quant_inst,[status(thm)],[])).
% 11.28/11.45 tff(300,plain,
% 11.28/11.45 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set)),
% 11.28/11.45 inference(modus_ponens,[status(thm)],[299, 298])).
% 11.28/11.45 tff(301,plain,
% 11.28/11.45 ($false),
% 11.28/11.45 inference(unit_resolution,[status(thm)],[300, 297, 285, 1])).
% 11.28/11.45 tff(302,plain,(member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 11.28/11.45 tff(303,plain,
% 11.28/11.45 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(B!4, union(A!5, A!5)), empty_set))),
% 11.28/11.45 inference(quant_inst,[status(thm)],[])).
% 11.28/11.45 tff(304,plain,
% 11.28/11.45 ($false),
% 11.28/11.45 inference(unit_resolution,[status(thm)],[303, 112, 302])).
% 11.28/11.45 % SZS output end Proof
% 11.28/11.45 % E exiting
%------------------------------------------------------------------------------