%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET703+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:26:11 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET703+4 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:38:07 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(tptp_fun_A_4_type, type, (
% 0.21/0.38 tptp_fun_A_4: $i)).
% 0.21/0.38 tff(tptp_fun_X_0_type, type, (
% 0.21/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.38 tff(unordered_pair_type, type, (
% 0.21/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_B_3_type, type, (
% 0.21/0.38 tptp_fun_B_3: $i)).
% 0.21/0.38 tff(union_type, type, (
% 0.21/0.38 union: ( $i * $i ) > $i)).
% 0.21/0.38 tff(singleton_type, type, (
% 0.21/0.38 singleton: $i > $i)).
% 0.21/0.38 tff(member_type, type, (
% 0.21/0.38 member: ( $i * $i ) > $o)).
% 0.21/0.38 tff(subset_type, type, (
% 0.21/0.38 subset: ( $i * $i ) > $o)).
% 0.21/0.38 tff(equal_set_type, type, (
% 0.21/0.38 equal_set: ( $i * $i ) > $o)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 (^[X: $i, A: $i, B: $i] : refl((member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (^[X: $i, A: $i, B: $i] : rewrite((member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B))) <=> (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B))) <=> ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.38 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','unordered_pair')).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.38 tff(9,plain,(
% 0.21/0.38 ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[8])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (^[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))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (^[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))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (^[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)))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![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)))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (^[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))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (![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)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.38 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.39 tff(26,plain,(
% 0.21/0.39 ![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)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![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)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![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)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~![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(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!4, B!3))) | member(X, union(singleton(A!4), singleton(B!3)))))) | (~(subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (~((~((~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!4, B!3))) | member(X, union(singleton(A!4), singleton(B!3)))))) | (~(subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (((~((~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!4, B!3))) | member(X, union(singleton(A!4), singleton(B!3)))))) | (~(subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))))))) | (subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,assumption,((~((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ![X: $i] : ((~member(X, union(singleton(A!4), singleton(B!3)))) | member(X, unordered_pair(A!4, B!3))))) | (~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))))))), introduced(assumption)).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![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(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ![X: $i] : ((~member(X, union(singleton(A!4), singleton(B!3)))) | member(X, unordered_pair(A!4, B!3))))) | (~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.21/0.39 tff(36,plain,(~((~((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ![X: $i] : ((~member(X, union(singleton(A!4), singleton(B!3)))) | member(X, unordered_pair(A!4, B!3))))) | (~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (((~((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ![X: $i] : ((~member(X, union(singleton(A!4), singleton(B!3)))) | member(X, unordered_pair(A!4, B!3))))) | (~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))))))) | (subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (^[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))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![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)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.39 tff(44,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','union')).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.39 tff(47,plain,(
% 0.21/0.39 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[46])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.39 tff(51,assumption,(~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))), introduced(assumption)).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))))) | (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[55, 50])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[57, 10])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))) | (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[59, 51])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)) | (~((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)))) | (~((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (~((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)) | (~(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (~(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.21/0.40 tff(66,assumption,(~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3))), introduced(assumption)).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','singleton')).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.40 tff(72,plain,(
% 0.21/0.40 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.40 inference(skolemize,[status(sab)],[71])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 73, 66])).
% 0.21/0.40 tff(76,plain,(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3))) | (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3))) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3))) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[78, 65])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = B!3) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)) | (~(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (~(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[80, 63])).
% 0.21/0.40 tff(82,assumption,(~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))), introduced(assumption)).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[83, 73, 82])).
% 0.21/0.40 tff(85,plain,(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)) <=> (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4))) | (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 ((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))) | (tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) = A!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[87, 81])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ((~(member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(B!3)) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), singleton(A!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[89, 88, 79, 56])).
% 0.21/0.40 tff(91,plain,((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 ((~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))))) | subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 ((~(subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) | (~((~member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))), unordered_pair(A!4, B!3)))))) | subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[93, 38])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(100,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.40 tff(102,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[101])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))) <=> equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (~(((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))) <=> equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))) <=> (~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(108,axiom,(~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI41')).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[109, 107])).
% 0.21/0.40 tff(111,plain,
% 0.21/0.40 (~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 (~![A: $i, B: $i] : equal_set(union(singleton(A), singleton(B)), unordered_pair(A, B))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.21/0.40 tff(113,plain,(
% 0.21/0.40 ~equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.40 inference(skolemize,[status(sab)],[112])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 ((((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))) <=> equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))) | equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 ((((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))) <=> equal_set(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | ((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 ((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 106])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 ((~((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))))) | (~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((~subset(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3))) | (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (~subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[118, 94])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 ((~(subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))))) | subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~(subset(unordered_pair(A!4, B!3), union(singleton(A!4), singleton(B!3))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))))) | (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 (~((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[121, 32])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)))) | (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3)) <=> ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)))) | ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 ((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[126, 12])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[128, 73])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[130, 48])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (((~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))) | (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[132, 122])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))) | (~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), union(singleton(A!4), singleton(B!3))) <=> (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))))) | (~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[135, 131])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ((member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))) | (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)) | (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))) | (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[140, 129])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 (member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[142, 73])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(A!4))) | (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (~member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[144, 136])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3))) | member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) | (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 ((~(member(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)), singleton(B!3)) <=> (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3))) | (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 (~(tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[147, 143])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 ((~((tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4))) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_X_0(union(singleton(A!4), singleton(B!3)), unordered_pair(A!4, B!3)) = A!4)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[149, 148, 141, 127])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------