%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET015+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:24:48 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET015+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 04:01:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(member_type, type, (
% 0.11/0.37 member: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_B_3_type, type, (
% 0.11/0.37 tptp_fun_B_3: $i)).
% 0.11/0.37 tff(tptp_fun_X_0_type, type, (
% 0.11/0.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.11/0.37 tff(union_type, type, (
% 0.11/0.37 union: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_A_4_type, type, (
% 0.11/0.37 tptp_fun_A_4: $i)).
% 0.11/0.37 tff(subset_type, type, (
% 0.11/0.37 subset: ( $i * $i ) > $o)).
% 0.11/0.37 tff(equal_set_type, type, (
% 0.11/0.37 equal_set: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.37 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,(
% 0.11/0.37 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![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), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[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))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (^[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))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (^[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)))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.37 tff(23,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')).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.11/0.37 tff(26,plain,(
% 0.11/0.37 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[25])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (~((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (((~((~subset(union(B!3, A!4), union(A!4, B!3))) | ![X: $i] : ((~member(X, union(B!3, A!4))) | member(X, union(A!4, B!3))))) | (~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))))) | (subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.37 tff(33,assumption,((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))), introduced(assumption)).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.19/0.37 tff(36,plain,(~((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (((~((~subset(union(A!4, B!3), union(B!3, A!4))) | ![X: $i] : ((~member(X, union(A!4, B!3))) | member(X, union(B!3, A!4))))) | (~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))))) | (subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, 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(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4))) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, 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(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, 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(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.19/0.38 tff(48,assumption,(~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))), introduced(assumption)).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))) | (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) | (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[54, 48])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 ((~(member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3)))) | (member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), A!4) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[57, 53, 45])).
% 0.19/0.38 tff(59,plain,((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))) | subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((~(subset(union(A!4, B!3), union(B!3, A!4)) | (~((~member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(A!4, B!3))) | member(tptp_fun_X_0(union(B!3, A!4), union(A!4, B!3)), union(B!3, A!4)))))) | subset(union(A!4, B!3), union(B!3, A!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (subset(union(A!4, B!3), union(B!3, A!4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[61, 38])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 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')).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.38 tff(70,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[69])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))) <=> equal_set(union(A!4, B!3), union(B!3, A!4))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (~(((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))) <=> equal_set(union(A!4, B!3), union(B!3, A!4)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))) <=> (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(76,axiom,(~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI07')).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (~![A: $i, B: $i] : equal_set(union(A, B), union(B, A))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.39 tff(81,plain,(
% 0.19/0.39 ~equal_set(union(A!4, B!3), union(B!3, A!4))),
% 0.19/0.39 inference(skolemize,[status(sab)],[80])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 ((((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))) <=> equal_set(union(A!4, B!3), union(B!3, A!4))) | ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))) | equal_set(union(A!4, B!3), union(B!3, A!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 ((((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))) <=> equal_set(union(A!4, B!3), union(B!3, A!4))) | ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[83, 74])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3))))) | (~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~subset(union(A!4, B!3), union(B!3, A!4))) | (~subset(union(B!3, A!4), union(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 (~subset(union(B!3, A!4), union(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 62])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))) | subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~(subset(union(B!3, A!4), union(A!4, B!3)) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (~((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[89, 32])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)))) | (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[94, 12])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 ((~![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), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[96, 10])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (((~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(B!3, A!4))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[98, 90])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) | (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), union(A!4, B!3)) <=> (member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))) | (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 ((member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (~member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ((~(member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3))) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), A!4) | member(tptp_fun_X_0(union(A!4, B!3), union(B!3, A!4)), B!3)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[107, 106, 104, 95])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------