%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET698+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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET698+4 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:38:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(member_type, type, (
% 0.18/0.37 member: ( $i * $i ) > $o)).
% 0.18/0.37 tff(difference_type, type, (
% 0.18/0.37 difference: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_A_5_type, type, (
% 0.18/0.37 tptp_fun_A_5: $i)).
% 0.18/0.37 tff(tptp_fun_E_3_type, type, (
% 0.18/0.37 tptp_fun_E_3: $i)).
% 0.18/0.37 tff(tptp_fun_X_0_type, type, (
% 0.18/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.18/0.37 tff(union_type, type, (
% 0.18/0.37 union: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_B_4_type, type, (
% 0.18/0.37 tptp_fun_B_4: $i)).
% 0.18/0.37 tff(subset_type, type, (
% 0.18/0.37 subset: ( $i * $i ) > $o)).
% 0.18/0.37 tff(equal_set_type, type, (
% 0.18/0.37 equal_set: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![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))))))) <=> ![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![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))))))) <=> ![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![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))))))) <=> ![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)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (^[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)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.38 tff(11,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')).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.38 tff(14,plain,(
% 0.18/0.38 ![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)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[13])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![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)))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 ((~![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)))))))) | (~((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (~((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | ![X: $i] : ((~member(X, union(difference(E!3, A!5), B!4))) | member(X, E!3)))) | (~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))))) | (subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.38 tff(21,assumption,((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))), introduced(assumption)).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 ((~![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)))))))) | (~((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.18/0.38 tff(24,plain,(~((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))) | (subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.38 tff(32,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')).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.38 tff(35,plain,(
% 0.18/0.38 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[34])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.38 tff(39,assumption,(~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))), introduced(assumption)).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) | (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 ((~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))) | (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (~(member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 ((member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (~((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))))) | ((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.39 tff(50,assumption,(~subset(A!5, B!4)), introduced(assumption)).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(53,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI32')).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> equal_set(union(difference(E, A), B), E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.18/0.39 tff(58,plain,(
% 0.18/0.39 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[57])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (~(subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.39 inference(or_elim,[status(thm)],[58])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 ((subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)) | subset(A!5, B!4) | equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (subset(A!5, B!4) | equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[61, 50])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,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')).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.39 tff(70,plain,(
% 0.18/0.39 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[69])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (~(((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) <=> equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 ((((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)) | (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))) | (~equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 ((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))) | (~equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) | subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 ((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | (~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 ((~((~subset(E!3, union(difference(E!3, A!5), B!4))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4))))) | ![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[81, 49])).
% 0.18/0.39 tff(83,assumption,(~(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))), introduced(assumption)).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[84, 36, 83])).
% 0.18/0.39 tff(86,plain,(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[87, 16])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[92, 50])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.18/0.39 tff(96,assumption,(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))), introduced(assumption)).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(102,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')).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.39 tff(104,plain,(
% 0.18/0.39 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[103])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.18/0.39 tff(107,plain,
% 0.18/0.39 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[107, 106, 96])).
% 0.18/0.39 tff(109,plain,(~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(110,plain,
% 0.18/0.39 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[110, 93])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), A!5))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 ((((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), A!5))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[114, 113, 109])).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 ((~(member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))) | member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (~(member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[116, 115, 95])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 ((~(member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5))))) | (~member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))) | (member(tptp_fun_X_0(B!4, A!5), B!4) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, A!5)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (~member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[118, 117, 86])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[120, 16])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.18/0.40 inference(or_elim,[status(thm)],[58])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 (subset(A!5, E!3)),
% 0.18/0.40 inference(and_elim,[status(thm)],[124])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(127,plain,
% 0.18/0.40 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.18/0.40 tff(128,plain,
% 0.18/0.40 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.18/0.40 tff(129,plain,
% 0.18/0.40 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(130,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(131,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.40 tff(132,plain,
% 0.18/0.40 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[131, 128, 111])).
% 0.18/0.40 tff(133,plain,
% 0.18/0.40 (((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))) <=> ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(134,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(135,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, E!3)) | member(X, union(difference(E!3, A!5), B!4)))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), union(difference(E!3, A!5), B!4))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.18/0.40 tff(136,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[135, 132, 119, 82])).
% 0.18/0.40 tff(137,plain,(subset(A!5, B!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(139,plain,
% 0.18/0.40 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[138, 88])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[145, 142, 46])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) <=> member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (~(((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) <=> member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[147, 106])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 ((member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), B!4) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(150,plain,
% 0.18/0.40 (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[149, 44])).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 ((((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) <=> member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(152,plain,
% 0.18/0.40 ((((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)) <=> member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), difference(E!3, A!5))) | ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.18/0.41 tff(153,plain,
% 0.18/0.41 ((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[152, 148])).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 (((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[154, 39])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 ((~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))) | (~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 ((~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5))) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), A!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[157, 153, 146])).
% 0.18/0.41 tff(159,plain,((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 ((~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))) | subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 ((~(subset(E!3, union(difference(E!3, A!5), B!4)) | (~((~member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), E!3)) | member(tptp_fun_X_0(union(difference(E!3, A!5), B!4), E!3), union(difference(E!3, A!5), B!4)))))) | subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.18/0.41 tff(162,plain,
% 0.18/0.41 (subset(E!3, union(difference(E!3, A!5), B!4))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[161, 26])).
% 0.18/0.41 tff(163,plain,
% 0.18/0.41 ((subset(A!5, B!4) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)) | (~subset(A!5, B!4)) | (~equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(164,plain,
% 0.18/0.41 ((~subset(A!5, B!4)) | (~equal_set(union(difference(E!3, A!5), B!4), E!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[163, 59])).
% 0.18/0.41 tff(165,plain,
% 0.18/0.41 (~equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[164, 137])).
% 0.18/0.41 tff(166,plain,
% 0.18/0.41 ((((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) <=> equal_set(union(difference(E!3, A!5), B!4), E!3)) | ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) | equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(167,plain,
% 0.18/0.41 (((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))) | equal_set(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[166, 74])).
% 0.18/0.41 tff(168,plain,
% 0.18/0.41 ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[167, 165])).
% 0.18/0.41 tff(169,plain,
% 0.18/0.41 ((~((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4))))) | (~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(170,plain,
% 0.18/0.41 ((~subset(union(difference(E!3, A!5), B!4), E!3)) | (~subset(E!3, union(difference(E!3, A!5), B!4)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.18/0.41 tff(171,plain,
% 0.18/0.41 (~subset(union(difference(E!3, A!5), B!4), E!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[170, 162])).
% 0.18/0.41 tff(172,plain,
% 0.18/0.41 ((~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))) | subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(173,plain,
% 0.18/0.41 ((~(subset(union(difference(E!3, A!5), B!4), E!3) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))))) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.18/0.41 tff(174,plain,
% 0.18/0.41 (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[173, 20])).
% 0.18/0.41 tff(175,plain,
% 0.18/0.41 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(176,plain,
% 0.18/0.41 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.18/0.41 tff(177,plain,
% 0.18/0.41 ((~![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(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3)))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(178,plain,
% 0.18/0.41 (~((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[177, 16])).
% 0.18/0.41 tff(179,plain,
% 0.18/0.41 (((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~(subset(B!4, E!3) | (~((~member(tptp_fun_X_0(E!3, B!4), B!4)) | member(tptp_fun_X_0(E!3, B!4), E!3)))))) | ((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(180,plain,
% 0.18/0.41 ((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.18/0.41 tff(181,plain,
% 0.18/0.41 (subset(B!4, E!3)),
% 0.18/0.41 inference(and_elim,[status(thm)],[124])).
% 0.18/0.41 tff(182,plain,
% 0.18/0.41 ((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | (~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(183,plain,
% 0.18/0.41 ((~((~subset(B!4, E!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3)))) | ![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.18/0.41 tff(184,plain,
% 0.18/0.41 (![X: $i] : ((~member(X, B!4)) | member(X, E!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[183, 180])).
% 0.18/0.41 tff(185,plain,
% 0.18/0.41 (((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))) <=> ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(186,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(187,plain,
% 0.18/0.41 ((~![X: $i] : ((~member(X, B!4)) | member(X, E!3))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.41 tff(188,plain,
% 0.18/0.41 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[187, 184, 176])).
% 0.18/0.41 tff(189,plain,
% 0.18/0.41 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(190,plain,
% 0.18/0.41 ((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[189, 176])).
% 0.18/0.41 tff(191,assumption,(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))), introduced(assumption)).
% 0.18/0.41 tff(192,plain,
% 0.18/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(193,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[192, 106, 191])).
% 0.18/0.41 tff(194,plain,(~(((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(195,plain,
% 0.18/0.41 ((((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5)) <=> member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))) | (~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(196,plain,
% 0.18/0.41 ((~((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), A!5))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.18/0.41 tff(197,plain,
% 0.18/0.41 (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[196, 190])).
% 0.18/0.41 tff(198,plain,
% 0.18/0.41 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(199,plain,
% 0.18/0.42 (~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[198, 197, 188])).
% 0.18/0.42 tff(200,plain,
% 0.18/0.42 (((~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), E!3)) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(201,plain,
% 0.18/0.42 (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[200, 174])).
% 0.18/0.42 tff(202,plain,
% 0.18/0.42 ((~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))) | (~member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(203,plain,
% 0.18/0.42 (~(member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[202, 201, 199])).
% 0.18/0.42 tff(204,plain,
% 0.18/0.42 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), union(difference(E!3, A!5), B!4)) <=> (member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), B!4) | member(tptp_fun_X_0(E!3, union(difference(E!3, A!5), B!4)), difference(E!3, A!5))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(205,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[204, 36, 203])).
% 0.18/0.42 % SZS output end Proof
% 0.18/0.42 % E exiting
%------------------------------------------------------------------------------