%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET696+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET696+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.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 05:38:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(member_type, type, (
% 0.11/0.36 member: ( $i * $i ) > $o)).
% 0.11/0.36 tff(empty_set_type, type, (
% 0.11/0.36 empty_set: $i)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.11/0.36 tff(intersection_type, type, (
% 0.11/0.36 intersection: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_A_4_type, type, (
% 0.11/0.36 tptp_fun_A_4: $i)).
% 0.11/0.36 tff(difference_type, type, (
% 0.11/0.36 difference: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_E_3_type, type, (
% 0.11/0.36 tptp_fun_E_3: $i)).
% 0.11/0.36 tff(subset_type, type, (
% 0.11/0.36 subset: ( $i * $i ) > $o)).
% 0.11/0.36 tff(equal_set_type, type, (
% 0.11/0.36 equal_set: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[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))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (^[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))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (^[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)))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[9])).
% 0.11/0.36 tff(11,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')).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.11/0.36 tff(14,plain,(
% 0.11/0.36 ![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)))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![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)))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((~![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(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(difference(E!3, A!4), A!4))))) | (~(subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (~((~((~subset(empty_set, intersection(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(difference(E!3, A!4), A!4))))) | (~(subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4)))))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (((~((~subset(empty_set, intersection(difference(E!3, A!4), A!4))) | ![X: $i] : ((~member(X, empty_set)) | member(X, intersection(difference(E!3, A!4), A!4))))) | (~(subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))))))) | (subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4)))))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.37 tff(21,assumption,((~((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!4), A!4))) | member(X, empty_set)))) | (~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)))))), introduced(assumption)).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((~![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!4), A!4), empty_set)) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!4), A!4))) | member(X, empty_set)))) | (~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.11/0.37 tff(24,plain,(~((~((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!4), A!4))) | member(X, empty_set)))) | (~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set))))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | ![X: $i] : ((~member(X, intersection(difference(E!3, A!4), A!4))) | member(X, empty_set)))) | (~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)))))) | (subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set))))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,assumption,(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))), introduced(assumption)).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (^[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)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(33,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')).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,(
% 0.11/0.37 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 37, 27])).
% 0.11/0.37 tff(40,plain,(~(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(41,assumption,(~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)))), introduced(assumption)).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.11/0.37 tff(46,assumption,(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))), introduced(assumption)).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (^[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)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(52,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')).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.37 tff(54,plain,(
% 0.11/0.37 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[53])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[57, 56, 46])).
% 0.11/0.38 tff(59,plain,(~(((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 ((((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 45])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), E!3)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[63, 62, 43])).
% 0.11/0.38 tff(65,plain,((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 ((((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4)))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 ((((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), difference(E!3, A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), A!4))) <=> member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[67, 40])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 ((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 ((~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set))))) | subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 ((~(subset(intersection(difference(E!3, A!4), A!4), empty_set) | (~((~member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(empty_set, intersection(difference(E!3, A!4), A!4)), empty_set))))) | subset(intersection(difference(E!3, A!4), A!4), empty_set)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (subset(intersection(difference(E!3, A!4), A!4), empty_set)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 26])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[74])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[76])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(79,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')).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.11/0.38 tff(81,plain,(
% 0.11/0.38 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[80])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))) <=> equal_set(intersection(difference(E!3, A!4), A!4), empty_set)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (~(((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))) <=> equal_set(intersection(difference(E!3, A!4), A!4), empty_set))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 ((~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 ((~![A: $i, E: $i] : (subset(A, E) => equal_set(intersection(difference(E, A), A), empty_set))) <=> (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(88,axiom,(~![A: $i, E: $i] : (subset(A, E) => equal_set(intersection(difference(E, A), A), empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI28')).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (~![A: $i, E: $i] : ((~subset(A, E)) | equal_set(intersection(difference(E, A), A), empty_set))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[91, 86])).
% 0.11/0.38 tff(93,plain,(
% 0.11/0.38 ~((~subset(A!4, E!3)) | equal_set(intersection(difference(E!3, A!4), A!4), empty_set))),
% 0.11/0.38 inference(skolemize,[status(sab)],[92])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 (~equal_set(intersection(difference(E!3, A!4), A!4), empty_set)),
% 0.11/0.38 inference(or_elim,[status(thm)],[93])).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 ((((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))) <=> equal_set(intersection(difference(E!3, A!4), A!4), empty_set)) | ((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))) | equal_set(intersection(difference(E!3, A!4), A!4), empty_set)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 ((((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))) <=> equal_set(intersection(difference(E!3, A!4), A!4), empty_set)) | ((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 ((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[96, 85])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 ((~((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4))))) | (~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 ((~subset(intersection(difference(E!3, A!4), A!4), empty_set)) | (~subset(empty_set, intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 (~subset(empty_set, intersection(difference(E!3, A!4), A!4))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[99, 73])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 ((~(subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4)))))) | subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 ((~(subset(empty_set, intersection(difference(E!3, A!4), A!4)) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4)))))) | (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 (~((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[102, 20])).
% 0.11/0.39 tff(104,plain,
% 0.11/0.39 (((~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), intersection(difference(E!3, A!4), A!4))) | member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(105,plain,
% 0.11/0.39 (member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.11/0.39 tff(106,plain,
% 0.11/0.39 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(107,plain,
% 0.11/0.39 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[106])).
% 0.11/0.39 tff(108,plain,
% 0.11/0.39 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(109,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 (![X: $i] : (~member(X, empty_set))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.11/0.39 tff(111,plain,(
% 0.11/0.39 ![X: $i] : (~member(X, empty_set))),
% 0.11/0.39 inference(skolemize,[status(sab)],[110])).
% 0.11/0.39 tff(112,plain,
% 0.11/0.39 (![X: $i] : (~member(X, empty_set))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.11/0.39 tff(113,plain,
% 0.11/0.39 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(intersection(difference(E!3, A!4), A!4), empty_set), empty_set))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(114,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[113, 112, 105])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------