%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET155+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:25:22 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET155+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:26:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_A_5_type, type, (
% 0.12/0.37 tptp_fun_A_5: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(intersection_type, type, (
% 0.12/0.37 intersection: ( $i * $i ) > $i)).
% 0.12/0.37 tff(difference_type, type, (
% 0.12/0.37 difference: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_4_type, type, (
% 0.12/0.37 tptp_fun_B_4: $i)).
% 0.12/0.37 tff(tptp_fun_E_3_type, type, (
% 0.12/0.37 tptp_fun_E_3: $i)).
% 0.12/0.37 tff(union_type, type, (
% 0.12/0.37 union: ( $i * $i ) > $i)).
% 0.12/0.37 tff(subset_type, type, (
% 0.12/0.37 subset: ( $i * $i ) > $o)).
% 0.12/0.37 tff(equal_set_type, type, (
% 0.12/0.37 equal_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.37 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','difference')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,assumption,((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))))), introduced(assumption)).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[29, 27])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
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% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.12/0.38 tff(42,plain,
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% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 41, 25])).
% 0.12/0.38 tff(44,plain,(~((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ![X: $i] : ((~member(X, difference(E!3, union(A!5, B!4)))) | member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))))) | (~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(45,plain,
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% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
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% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
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% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(52,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.38 tff(54,plain,(
% 0.19/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,assumption,(~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))), introduced(assumption)).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 58])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 22])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 59])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 66])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 10])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) | (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))) | (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (~(member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 75])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 82, 73])).
% 0.19/0.40 tff(85,assumption,(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))), introduced(assumption)).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 22, 85])).
% 0.19/0.40 tff(88,plain,(~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), B!4) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 80])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 93, 73])).
% 0.19/0.41 tff(96,assumption,(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))), introduced(assumption)).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 22, 96])).
% 0.19/0.41 tff(99,plain,(~(((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) <=> member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | ((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), E!3)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), A!5)) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 95])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, B!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 102, 91, 64])).
% 0.19/0.41 tff(105,plain,((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))) | subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~(subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))))) | subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 46])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(114,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.41 tff(116,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))) <=> equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (~(((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))) <=> equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(123,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI26')).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | equal_set(difference(E, union(A, B)), intersection(difference(E, A), difference(E, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 121])).
% 0.19/0.41 tff(128,plain,(
% 0.19/0.41 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (~equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.42 ((((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))) <=> equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))) | equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))) <=> equal_set(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[131, 120])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 ((~((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))))) | (~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~subset(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 108])).
% 0.19/0.42 tff(136,assumption,((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))), introduced(assumption)).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~![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(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 41, 136])).
% 0.19/0.42 tff(139,plain,(~((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (((~((~subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4)))) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(X, difference(E!3, union(A!5, B!4)))))) | (~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))))) | (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 ((~(subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))))) | subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (subset(intersection(difference(E!3, A!5), difference(E!3, B!4)), difference(E!3, union(A!5, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[143, 135])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 24])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, union(A!5, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[150, 144])).
% 0.19/0.43 tff(152,assumption,(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))), introduced(assumption)).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[153, 56, 152])).
% 0.19/0.43 tff(155,plain,(~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 ((~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), intersection(difference(E!3, A!5), difference(E!3, B!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 151])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.43 tff(161,assumption,(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))), introduced(assumption)).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[162, 22, 161])).
% 0.19/0.43 tff(164,plain,(~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 ((~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[166, 160])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 ((~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 ((~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[171, 149])).
% 0.19/0.44 tff(173,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(174,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), union(A!5, B!4)) <=> (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))) | (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[174, 12])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 (~(((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[176, 22])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(179,plain,
% 0.19/0.44 (member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[178, 158])).
% 0.19/0.44 tff(180,plain,
% 0.19/0.44 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(181,plain,
% 0.19/0.44 ((((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) <=> member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 (~((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[181, 177])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (((~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), E!3)) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 (~member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[185, 167])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 ((~(member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), B!4) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5))) | member(tptp_fun_X_0(difference(E!3, union(A!5, B!4)), intersection(difference(E!3, A!5), difference(E!3, B!4))), A!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[188, 184, 175])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------