%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET693+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:26:09 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET693+4 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 05:42:04 EDT 2025
% 0.20/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(member_type, type, (
% 0.20/0.38 member: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_B_3_type, type, (
% 0.20/0.38 tptp_fun_B_3: $i)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_A_4_type, type, (
% 0.20/0.38 tptp_fun_A_4: $i)).
% 0.20/0.38 tff(union_type, type, (
% 0.20/0.38 union: ( $i * $i ) > $i)).
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(equal_set_type, type, (
% 0.20/0.38 equal_set: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 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')).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.38 tff(14,plain,(
% 0.20/0.38 ![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)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![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)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~![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(A!4, union(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, union(A!4, B!3))))) | (~(subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~((~((~subset(A!4, union(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, union(A!4, B!3))))) | (~(subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~((~subset(A!4, union(A!4, B!3))) | ![X: $i] : ((~member(X, A!4)) | member(X, union(A!4, B!3))))) | (~(subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))))))) | (subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,assumption,((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))))), introduced(assumption)).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![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(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 0.20/0.38 tff(24,plain,(~((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))))) | (subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.38 tff(27,assumption,(~(member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)))), introduced(assumption)).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,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')).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.38 tff(36,plain,(
% 0.20/0.38 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 37, 27])).
% 0.20/0.39 tff(45,plain,(member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(46,assumption,(~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))), introduced(assumption)).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)))) | (~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[49, 48, 45])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (~member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 52, 50])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (~((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))))) | ((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,assumption,(~subset(B!3, A!4)), introduced(assumption)).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~(equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4))) <=> (~(equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))) <=> (~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,axiom,(~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI20')).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (~![A: $i, B: $i] : (equal_set(A, union(A, B)) <=> subset(B, A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.39 tff(66,plain,(
% 0.20/0.39 ~(equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4))),
% 0.20/0.39 inference(skolemize,[status(sab)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (~(equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ((equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4)) | equal_set(A!4, union(A!4, B!3)) | subset(B!3, A!4)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (equal_set(A!4, union(A!4, B!3)) | subset(B!3, A!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (equal_set(A!4, union(A!4, B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 58])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(76,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')).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.39 tff(78,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[77])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) <=> equal_set(A!4, union(A!4, B!3))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (~(((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) <=> equal_set(A!4, union(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 ((((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) <=> equal_set(A!4, union(A!4, B!3))) | (~((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4)))) | (~equal_set(A!4, union(A!4, B!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4)))) | (~equal_set(A!4, union(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (~((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[84, 70])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) | subset(union(A!4, B!3), A!4)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (subset(union(A!4, B!3), A!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | (~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((~((~subset(union(A!4, B!3), A!4)) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4)))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 57])).
% 0.20/0.39 tff(91,assumption,(~(member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))), introduced(assumption)).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ((member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), B!3) | member(tptp_fun_X_0(A!4, B!3), A!4))) <=> (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), B!3) | member(tptp_fun_X_0(A!4, B!3), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), B!3) | member(tptp_fun_X_0(A!4, B!3), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), B!3) | member(tptp_fun_X_0(A!4, B!3), A!4)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 37, 91])).
% 0.20/0.40 tff(99,plain,(member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ((~![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(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))) | (~(subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (~((~((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))) | (~(subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[100, 16])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (((~((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))) | (~(subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))))) | (subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 ((~(subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4))))) | subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[105, 58])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)) | member(tptp_fun_X_0(A!4, B!3), B!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (member(tptp_fun_X_0(A!4, B!3), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ((member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)) | (~member(tptp_fun_X_0(A!4, B!3), B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 ((~(member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) <=> (member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))) | member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3)) | (~(member(tptp_fun_X_0(A!4, B!3), A!4) | member(tptp_fun_X_0(A!4, B!3), B!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[111, 110, 99])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)) | (~member(tptp_fun_X_0(A!4, B!3), A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(A!4, B!3), A!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (((~![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))) | ((~member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, B!3), A!4))) <=> ((~![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))) | (~member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, B!3), A!4))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))) | ((~member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, B!3), A!4))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, A!4))) | (~member(tptp_fun_X_0(A!4, B!3), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, B!3), A!4)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[117, 114, 112, 90])).
% 0.20/0.40 tff(119,plain,(subset(B!3, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 (((~((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))) | (~(subset(B!3, A!4) | (~((~member(tptp_fun_X_0(A!4, B!3), B!3)) | member(tptp_fun_X_0(A!4, B!3), A!4)))))) | ((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 ((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[120, 101])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 ((~((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4)))) | (~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 ((~subset(B!3, A!4)) | ![X: $i] : ((~member(X, B!3)) | member(X, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 (![X: $i] : ((~member(X, B!3)) | member(X, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[123, 119])).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 (((~![X: $i] : ((~member(X, B!3)) | member(X, A!4))) | ((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))) <=> ((~![X: $i] : ((~member(X, B!3)) | member(X, A!4))) | (~member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, B!3)) | member(X, A!4))) | ((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, B!3)) | member(X, A!4))) | (~member(tptp_fun_X_0(A!4, union(A!4, B!3)), B!3)) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[127, 124, 52, 54])).
% 0.20/0.40 tff(129,plain,((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 ((~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))))) | subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 ((~(subset(union(A!4, B!3), A!4) | (~((~member(tptp_fun_X_0(A!4, union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(A!4, union(A!4, B!3)), A!4))))) | subset(union(A!4, B!3), A!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 (subset(union(A!4, B!3), A!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[131, 26])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 ((equal_set(A!4, union(A!4, B!3)) <=> subset(B!3, A!4)) | (~equal_set(A!4, union(A!4, B!3))) | (~subset(B!3, A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 ((~equal_set(A!4, union(A!4, B!3))) | (~subset(B!3, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[133, 67])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 (~equal_set(A!4, union(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[134, 119])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 ((((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) <=> equal_set(A!4, union(A!4, B!3))) | ((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) | equal_set(A!4, union(A!4, B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))) | equal_set(A!4, union(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[136, 82])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 ((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 ((~((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4)))) | (~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 ((~subset(A!4, union(A!4, B!3))) | (~subset(union(A!4, B!3), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 (~subset(A!4, union(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[140, 132])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 ((~(subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))))) | subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 ((~(subset(A!4, union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[143, 20])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))) | member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(146,plain,
% 0.20/0.40 (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 ((member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)) | (~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[149, 144])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 ((~(member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))) | member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) | (~(member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(152,plain,
% 0.20/0.41 (~(member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[151, 150, 148])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(154,plain,
% 0.20/0.41 ((member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3) | member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4))) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(155,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3) | member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.41 tff(156,plain,
% 0.20/0.41 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3) | member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.41 tff(157,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3) | member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(158,plain,
% 0.20/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(A!4, B!3), A!4), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), A!4), A!4) | member(tptp_fun_X_0(union(A!4, B!3), A!4), B!3)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.41 tff(159,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[158, 37, 152])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------