%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET018+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:24:50 AM UTC 2025
% Result : Theorem 16.38s 16.54s
% Output : Proof 16.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET018+4 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:02:41 EDT 2025
% 0.13/0.35 % CPUTime :
% 16.38/16.54 % SZS status Theorem
% 16.38/16.54 % SZS output start Proof
% 16.38/16.54 tff(member_type, type, (
% 16.38/16.54 member: ( $i * $i ) > $o)).
% 16.38/16.54 tff(unordered_pair_type, type, (
% 16.38/16.54 unordered_pair: ( $i * $i ) > $i)).
% 16.38/16.54 tff(tptp_fun_A_6_type, type, (
% 16.38/16.54 tptp_fun_A_6: $i)).
% 16.38/16.54 tff(tptp_fun_V_3_type, type, (
% 16.38/16.54 tptp_fun_V_3: $i)).
% 16.38/16.54 tff(tptp_fun_B_5_type, type, (
% 16.38/16.54 tptp_fun_B_5: $i)).
% 16.38/16.54 tff(tptp_fun_U_4_type, type, (
% 16.38/16.54 tptp_fun_U_4: $i)).
% 16.38/16.54 tff(singleton_type, type, (
% 16.38/16.54 singleton: $i > $i)).
% 16.38/16.54 tff(subset_type, type, (
% 16.38/16.54 subset: ( $i * $i ) > $o)).
% 16.38/16.54 tff(tptp_fun_X_0_type, type, (
% 16.38/16.54 tptp_fun_X_0: ( $i * $i ) > $i)).
% 16.38/16.54 tff(equal_set_type, type, (
% 16.38/16.54 equal_set: ( $i * $i ) > $o)).
% 16.38/16.54 tff(power_set_type, type, (
% 16.38/16.54 power_set: $i > $i)).
% 16.38/16.54 tff(intersection_type, type, (
% 16.38/16.54 intersection: ( $i * $i ) > $i)).
% 16.38/16.54 tff(difference_type, type, (
% 16.38/16.54 difference: ( $i * $i ) > $i)).
% 16.38/16.54 tff(1,assumption,(~(singleton(U!4) = singleton(A!6))), introduced(assumption)).
% 16.38/16.54 tff(2,plain,
% 16.38/16.54 (^[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))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(3,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[2])).
% 16.38/16.54 tff(4,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(5,plain,
% 16.38/16.54 (^[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))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(6,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[5])).
% 16.38/16.54 tff(7,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')).
% 16.38/16.54 tff(8,plain,
% 16.38/16.54 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[7, 6])).
% 16.38/16.54 tff(9,plain,
% 16.38/16.54 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[8, 4])).
% 16.38/16.54 tff(10,plain,(
% 16.38/16.54 ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 16.38/16.54 inference(skolemize,[status(sab)],[9])).
% 16.38/16.54 tff(11,plain,
% 16.38/16.54 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[10, 3])).
% 16.38/16.54 tff(12,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(13,plain,
% 16.38/16.54 ((member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = unordered_pair(A!6, B!5)) | (singleton(U!4) = singleton(A!6)))) <=> (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(14,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = unordered_pair(A!6, B!5)) | (singleton(U!4) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))))),
% 16.38/16.54 inference(monotonicity,[status(thm)],[13])).
% 16.38/16.54 tff(15,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = unordered_pair(A!6, B!5)) | (singleton(U!4) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))))),
% 16.38/16.54 inference(transitivity,[status(thm)],[14, 12])).
% 16.38/16.54 tff(16,plain,
% 16.38/16.54 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = unordered_pair(A!6, B!5)) | (singleton(U!4) = singleton(A!6))))),
% 16.38/16.54 inference(quant_inst,[status(thm)],[])).
% 16.38/16.54 tff(17,plain,
% 16.38/16.54 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[16, 15])).
% 16.38/16.54 tff(18,plain,
% 16.38/16.54 (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))),
% 16.38/16.54 inference(unit_resolution,[status(thm)],[17, 11])).
% 16.38/16.54 tff(19,assumption,(~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.38/16.54 tff(20,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(21,plain,
% 16.38/16.54 ((member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> $true) <=> member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(22,plain,
% 16.38/16.54 (((singleton(U!4) = unordered_pair(U!4, V!3)) | $true) <=> $true),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(23,plain,
% 16.38/16.54 ((singleton(U!4) = singleton(U!4)) <=> $true),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(24,plain,
% 16.38/16.54 (((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | $true)),
% 16.38/16.54 inference(monotonicity,[status(thm)],[23])).
% 16.38/16.54 tff(25,plain,
% 16.38/16.54 (((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))) <=> $true),
% 16.38/16.54 inference(transitivity,[status(thm)],[24, 22])).
% 16.38/16.54 tff(26,plain,
% 16.38/16.54 ((member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4)))) <=> (member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> $true)),
% 16.38/16.54 inference(monotonicity,[status(thm)],[25])).
% 16.38/16.54 tff(27,plain,
% 16.38/16.54 ((member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4)))) <=> member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.54 inference(transitivity,[status(thm)],[26, 21])).
% 16.38/16.54 tff(28,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.54 inference(monotonicity,[status(thm)],[27])).
% 16.38/16.54 tff(29,plain,
% 16.38/16.54 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.54 inference(transitivity,[status(thm)],[28, 20])).
% 16.38/16.54 tff(30,plain,
% 16.38/16.54 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))))),
% 16.38/16.54 inference(quant_inst,[status(thm)],[])).
% 16.38/16.54 tff(31,plain,
% 16.38/16.54 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[30, 29])).
% 16.38/16.54 tff(32,plain,
% 16.38/16.54 ($false),
% 16.38/16.54 inference(unit_resolution,[status(thm)],[31, 11, 19])).
% 16.38/16.54 tff(33,plain,(member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.54 tff(34,plain,
% 16.38/16.54 (^[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))))))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(35,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[34])).
% 16.38/16.54 tff(36,plain,
% 16.38/16.54 (^[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))))))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(37,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[36])).
% 16.38/16.54 tff(38,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(transitivity,[status(thm)],[37, 35])).
% 16.38/16.54 tff(39,plain,
% 16.38/16.54 (^[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)))))))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(40,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[39])).
% 16.38/16.54 tff(41,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(42,plain,
% 16.38/16.54 (^[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))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(43,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[42])).
% 16.38/16.54 tff(44,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')).
% 16.38/16.54 tff(45,plain,
% 16.38/16.54 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[44, 43])).
% 16.38/16.54 tff(46,plain,
% 16.38/16.54 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[45, 41])).
% 16.38/16.54 tff(47,plain,(
% 16.38/16.54 ![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)))))),
% 16.38/16.54 inference(skolemize,[status(sab)],[46])).
% 16.38/16.54 tff(48,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[47, 40])).
% 16.38/16.54 tff(49,plain,
% 16.38/16.54 (![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)))))))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[48, 38])).
% 16.38/16.54 tff(50,plain,
% 16.38/16.54 ((~![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(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))))))),
% 16.38/16.54 inference(quant_inst,[status(thm)],[])).
% 16.38/16.54 tff(51,plain,
% 16.38/16.54 (~((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))))))),
% 16.38/16.54 inference(unit_resolution,[status(thm)],[50, 49])).
% 16.38/16.54 tff(52,plain,
% 16.38/16.54 (((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))))) | ((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))),
% 16.38/16.54 inference(tautology,[status(thm)],[])).
% 16.38/16.54 tff(53,plain,
% 16.38/16.54 ((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.54 inference(unit_resolution,[status(thm)],[52, 51])).
% 16.38/16.54 tff(54,plain,
% 16.38/16.54 (^[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))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(55,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[54])).
% 16.38/16.54 tff(56,plain,
% 16.38/16.54 (^[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)))))),
% 16.38/16.54 inference(bind,[status(th)],[])).
% 16.38/16.54 tff(57,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(quant_intro,[status(thm)],[56])).
% 16.38/16.54 tff(58,plain,
% 16.38/16.54 (![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)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(59,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')).
% 16.38/16.54 tff(60,plain,
% 16.38/16.54 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[59, 58])).
% 16.38/16.54 tff(61,plain,(
% 16.38/16.54 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 16.38/16.54 inference(skolemize,[status(sab)],[60])).
% 16.38/16.54 tff(62,plain,
% 16.38/16.54 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[61, 57])).
% 16.38/16.54 tff(63,plain,
% 16.38/16.54 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 16.38/16.54 inference(modus_ponens,[status(thm)],[62, 55])).
% 16.38/16.54 tff(64,plain,
% 16.38/16.54 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.54 inference(quant_inst,[status(thm)],[])).
% 16.38/16.54 tff(65,plain,
% 16.38/16.54 (~(((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.54 inference(unit_resolution,[status(thm)],[64, 63])).
% 16.38/16.54 tff(66,plain,
% 16.38/16.54 ((~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V))) <=> (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(67,plain,
% 16.38/16.54 ((~![A: $i, B: $i, U: $i, V: $i] : (equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V))) => (B = V))) <=> (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V)))),
% 16.38/16.54 inference(rewrite,[status(thm)],[])).
% 16.38/16.54 tff(68,axiom,(~![A: $i, B: $i, U: $i, V: $i] : (equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V))) => (B = V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI50b')).
% 16.38/16.55 tff(69,plain,
% 16.38/16.55 (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[68, 67])).
% 16.38/16.55 tff(70,plain,
% 16.38/16.55 (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[69, 66])).
% 16.38/16.55 tff(71,plain,
% 16.38/16.55 (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[70, 66])).
% 16.38/16.55 tff(72,plain,
% 16.38/16.55 (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (B = V))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[71, 66])).
% 16.38/16.55 tff(73,plain,(
% 16.38/16.55 ~((~equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (B!5 = V!3))),
% 16.38/16.55 inference(skolemize,[status(sab)],[72])).
% 16.38/16.55 tff(74,plain,
% 16.38/16.55 (equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(or_elim,[status(thm)],[73])).
% 16.38/16.55 tff(75,plain,
% 16.38/16.55 ((((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | (~equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(76,plain,
% 16.38/16.55 ((((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[75, 74])).
% 16.38/16.55 tff(77,plain,
% 16.38/16.55 (~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[76, 65])).
% 16.38/16.55 tff(78,plain,
% 16.38/16.55 (((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(79,plain,
% 16.38/16.55 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[78, 77])).
% 16.38/16.55 tff(80,plain,
% 16.38/16.55 ((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(81,plain,
% 16.38/16.55 ((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[80, 79])).
% 16.38/16.55 tff(82,plain,
% 16.38/16.55 (![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[81, 53])).
% 16.38/16.55 tff(83,plain,
% 16.38/16.55 (((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | ((~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | (~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(84,plain,
% 16.38/16.55 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | ((~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(85,plain,
% 16.38/16.55 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | (~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[84, 83])).
% 16.38/16.55 tff(86,plain,
% 16.38/16.55 (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[85, 82, 33])).
% 16.38/16.55 tff(87,plain,
% 16.38/16.55 ((~(member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))))) | (~member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(88,plain,
% 16.38/16.55 ((~(member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))))) | ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[87, 86])).
% 16.38/16.55 tff(89,plain,
% 16.38/16.55 ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[88, 18])).
% 16.38/16.55 tff(90,plain,
% 16.38/16.55 ((~((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5)))) | (singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(91,plain,
% 16.38/16.55 ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[90, 89])).
% 16.38/16.55 tff(92,plain,
% 16.38/16.55 (singleton(U!4) = unordered_pair(A!6, B!5)),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[91, 1])).
% 16.38/16.55 tff(93,plain,
% 16.38/16.55 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 16.38/16.55 inference(bind,[status(th)],[])).
% 16.38/16.55 tff(94,plain,
% 16.38/16.55 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 16.38/16.55 inference(quant_intro,[status(thm)],[93])).
% 16.38/16.55 tff(95,plain,
% 16.38/16.55 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(96,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','singleton')).
% 16.38/16.55 tff(97,plain,
% 16.38/16.55 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[96, 95])).
% 16.38/16.55 tff(98,plain,(
% 16.38/16.55 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 16.38/16.55 inference(skolemize,[status(sab)],[97])).
% 16.38/16.55 tff(99,plain,
% 16.38/16.55 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[98, 94])).
% 16.38/16.55 tff(100,plain,
% 16.38/16.55 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!6, singleton(U!4)) <=> (A!6 = U!4))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(101,plain,
% 16.38/16.55 (member(A!6, singleton(U!4)) <=> (A!6 = U!4)),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[100, 99])).
% 16.38/16.55 tff(102,plain,
% 16.38/16.55 (member(A!6, singleton(U!4)) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(monotonicity,[status(thm)],[92])).
% 16.38/16.55 tff(103,plain,
% 16.38/16.55 (member(A!6, unordered_pair(A!6, B!5)) <=> member(A!6, singleton(U!4))),
% 16.38/16.55 inference(symmetry,[status(thm)],[102])).
% 16.38/16.55 tff(104,assumption,(~member(A!6, unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.55 tff(105,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!6, unordered_pair(A!6, B!5))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!6, unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(106,plain,
% 16.38/16.55 ((member(A!6, unordered_pair(A!6, B!5)) <=> $true) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(107,plain,
% 16.38/16.55 (((A!6 = B!5) | $true) <=> $true),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(108,plain,
% 16.38/16.55 ((A!6 = A!6) <=> $true),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(109,plain,
% 16.38/16.55 (((A!6 = B!5) | (A!6 = A!6)) <=> ((A!6 = B!5) | $true)),
% 16.38/16.55 inference(monotonicity,[status(thm)],[108])).
% 16.38/16.55 tff(110,plain,
% 16.38/16.55 (((A!6 = B!5) | (A!6 = A!6)) <=> $true),
% 16.38/16.55 inference(transitivity,[status(thm)],[109, 107])).
% 16.38/16.55 tff(111,plain,
% 16.38/16.55 ((member(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))) <=> (member(A!6, unordered_pair(A!6, B!5)) <=> $true)),
% 16.38/16.55 inference(monotonicity,[status(thm)],[110])).
% 16.38/16.55 tff(112,plain,
% 16.38/16.55 ((member(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(transitivity,[status(thm)],[111, 106])).
% 16.38/16.55 tff(113,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!6, unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(monotonicity,[status(thm)],[112])).
% 16.38/16.55 tff(114,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!6, unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(transitivity,[status(thm)],[113, 105])).
% 16.38/16.55 tff(115,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6)))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(116,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[115, 114])).
% 16.38/16.55 tff(117,plain,
% 16.38/16.55 ($false),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[116, 11, 104])).
% 16.38/16.55 tff(118,plain,(member(A!6, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.55 tff(119,plain,
% 16.38/16.55 (member(A!6, singleton(U!4))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[118, 103])).
% 16.38/16.55 tff(120,plain,
% 16.38/16.55 ((~(member(A!6, singleton(U!4)) <=> (A!6 = U!4))) | (~member(A!6, singleton(U!4))) | (A!6 = U!4)),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(121,plain,
% 16.38/16.55 (A!6 = U!4),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[120, 119, 101])).
% 16.38/16.55 tff(122,plain,
% 16.38/16.55 (singleton(A!6) = singleton(U!4)),
% 16.38/16.55 inference(monotonicity,[status(thm)],[121])).
% 16.38/16.55 tff(123,plain,
% 16.38/16.55 ((singleton(A!6) = singleton(U!4)) <=> (singleton(U!4) = singleton(A!6))),
% 16.38/16.55 inference(commutativity,[status(thm)],[])).
% 16.38/16.55 tff(124,assumption,(singleton(A!6) = singleton(U!4)), introduced(assumption)).
% 16.38/16.55 tff(125,plain,
% 16.38/16.55 (singleton(U!4) = singleton(A!6)),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[124, 123])).
% 16.38/16.55 tff(126,plain,
% 16.38/16.55 ($false),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[1, 125])).
% 16.38/16.55 tff(127,plain,((~(singleton(A!6) = singleton(U!4))) | (singleton(U!4) = singleton(A!6))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.55 tff(128,plain,
% 16.38/16.55 (~(singleton(A!6) = singleton(U!4))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[127, 1])).
% 16.38/16.55 tff(129,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(130,plain,
% 16.38/16.55 ((member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = singleton(U!4)))) <=> (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(131,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = singleton(U!4))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))))),
% 16.38/16.55 inference(monotonicity,[status(thm)],[130])).
% 16.38/16.55 tff(132,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = singleton(U!4))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))))),
% 16.38/16.55 inference(transitivity,[status(thm)],[131, 129])).
% 16.38/16.55 tff(133,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = singleton(U!4))))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(134,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[133, 132])).
% 16.38/16.55 tff(135,plain,
% 16.38/16.55 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[134, 11])).
% 16.38/16.55 tff(136,assumption,(~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), introduced(assumption)).
% 16.38/16.55 tff(137,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(138,plain,
% 16.38/16.55 ((member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> $true) <=> member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(139,plain,
% 16.38/16.55 (((singleton(A!6) = unordered_pair(A!6, B!5)) | $true) <=> $true),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(140,plain,
% 16.38/16.55 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(141,plain,
% 16.38/16.55 (((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | $true)),
% 16.38/16.55 inference(monotonicity,[status(thm)],[140])).
% 16.38/16.55 tff(142,plain,
% 16.38/16.55 (((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))) <=> $true),
% 16.38/16.55 inference(transitivity,[status(thm)],[141, 139])).
% 16.38/16.55 tff(143,plain,
% 16.38/16.55 ((member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6)))) <=> (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> $true)),
% 16.38/16.55 inference(monotonicity,[status(thm)],[142])).
% 16.38/16.55 tff(144,plain,
% 16.38/16.55 ((member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6)))) <=> member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(transitivity,[status(thm)],[143, 138])).
% 16.38/16.55 tff(145,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(monotonicity,[status(thm)],[144])).
% 16.38/16.55 tff(146,plain,
% 16.38/16.55 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.55 inference(transitivity,[status(thm)],[145, 137])).
% 16.38/16.55 tff(147,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(148,plain,
% 16.38/16.55 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[147, 146])).
% 16.38/16.55 tff(149,plain,
% 16.38/16.55 ($false),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[148, 11, 136])).
% 16.38/16.55 tff(150,plain,(member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.55 tff(151,plain,
% 16.38/16.55 ((~![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(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(152,plain,
% 16.38/16.55 (~((~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[151, 49])).
% 16.38/16.55 tff(153,plain,
% 16.38/16.55 (((~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | ((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(154,plain,
% 16.38/16.55 ((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[153, 152])).
% 16.38/16.55 tff(155,plain,
% 16.38/16.55 (((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(156,plain,
% 16.38/16.55 (subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[155, 77])).
% 16.38/16.55 tff(157,plain,
% 16.38/16.55 ((~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(158,plain,
% 16.38/16.55 ((~((~subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[157, 156])).
% 16.38/16.55 tff(159,plain,
% 16.38/16.55 (![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[158, 154])).
% 16.38/16.55 tff(160,plain,
% 16.38/16.55 (((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(rewrite,[status(thm)],[])).
% 16.38/16.55 tff(161,plain,
% 16.38/16.55 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.55 inference(quant_inst,[status(thm)],[])).
% 16.38/16.55 tff(162,plain,
% 16.38/16.55 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(modus_ponens,[status(thm)],[161, 160])).
% 16.38/16.55 tff(163,plain,
% 16.38/16.55 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[162, 159, 150])).
% 16.38/16.55 tff(164,plain,
% 16.38/16.55 ((~(member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(165,plain,
% 16.38/16.55 ((~(member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))))) | ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[164, 163])).
% 16.38/16.55 tff(166,plain,
% 16.38/16.55 ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[165, 135])).
% 16.38/16.55 tff(167,plain,
% 16.38/16.55 ((~((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3)))) | (singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))),
% 16.38/16.55 inference(tautology,[status(thm)],[])).
% 16.38/16.55 tff(168,plain,
% 16.38/16.55 ((singleton(A!6) = singleton(U!4)) | (singleton(A!6) = unordered_pair(U!4, V!3))),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[167, 166])).
% 16.38/16.55 tff(169,plain,
% 16.38/16.55 (singleton(A!6) = unordered_pair(U!4, V!3)),
% 16.38/16.55 inference(unit_resolution,[status(thm)],[168, 128])).
% 16.38/16.55 tff(170,plain,
% 16.38/16.55 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 16.38/16.55 inference(symmetry,[status(thm)],[169])).
% 16.38/16.55 tff(171,plain,
% 16.38/16.55 (unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)),
% 16.38/16.56 inference(transitivity,[status(thm)],[170, 122, 92])).
% 16.38/16.56 tff(172,plain,
% 16.38/16.56 (unordered_pair(A!6, B!5) = singleton(U!4)),
% 16.38/16.56 inference(symmetry,[status(thm)],[92])).
% 16.38/16.56 tff(173,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) <=> (singleton(A!6) = singleton(U!4))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[170, 172])).
% 16.38/16.56 tff(174,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) <=> (singleton(U!4) = singleton(A!6))),
% 16.38/16.56 inference(transitivity,[status(thm)],[173, 123])).
% 16.38/16.56 tff(175,plain,
% 16.38/16.56 ((singleton(U!4) = singleton(A!6)) <=> (unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(symmetry,[status(thm)],[174])).
% 16.38/16.56 tff(176,plain,
% 16.38/16.56 ((~(singleton(U!4) = singleton(A!6))) <=> (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[175])).
% 16.38/16.56 tff(177,plain,
% 16.38/16.56 (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[1, 176])).
% 16.38/16.56 tff(178,plain,
% 16.38/16.56 ($false),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[177, 171])).
% 16.38/16.56 tff(179,plain,(singleton(U!4) = singleton(A!6)), inference(lemma,lemma(discharge,[]))).
% 16.38/16.56 tff(180,plain,
% 16.38/16.56 (singleton(A!6) = singleton(U!4)),
% 16.38/16.56 inference(symmetry,[status(thm)],[179])).
% 16.38/16.56 tff(181,assumption,(~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.56 tff(182,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(183,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[182, 11])).
% 16.38/16.56 tff(184,plain,
% 16.38/16.56 (unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)) = unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[179])).
% 16.38/16.56 tff(185,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[184])).
% 16.38/16.56 tff(186,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(symmetry,[status(thm)],[185])).
% 16.38/16.56 tff(187,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(188,plain,
% 16.38/16.56 ((member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> $true) <=> member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(189,plain,
% 16.38/16.56 (($true | (unordered_pair(U!4, V!3) = singleton(A!6))) <=> $true),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(190,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) <=> $true),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(191,plain,
% 16.38/16.56 (((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6))) <=> ($true | (unordered_pair(U!4, V!3) = singleton(A!6)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[190])).
% 16.38/16.56 tff(192,plain,
% 16.38/16.56 (((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6))) <=> $true),
% 16.38/16.56 inference(transitivity,[status(thm)],[191, 189])).
% 16.38/16.56 tff(193,plain,
% 16.38/16.56 ((member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6)))) <=> (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> $true)),
% 16.38/16.56 inference(monotonicity,[status(thm)],[192])).
% 16.38/16.56 tff(194,plain,
% 16.38/16.56 ((member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6)))) <=> member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(transitivity,[status(thm)],[193, 188])).
% 16.38/16.56 tff(195,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[194])).
% 16.38/16.56 tff(196,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(transitivity,[status(thm)],[195, 187])).
% 16.38/16.56 tff(197,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) | (unordered_pair(U!4, V!3) = singleton(A!6))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(198,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[197, 196])).
% 16.38/16.56 tff(199,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[198, 11])).
% 16.38/16.56 tff(200,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[199, 186])).
% 16.38/16.56 tff(201,plain,
% 16.38/16.56 (((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | ((~member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | (~member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(202,plain,
% 16.38/16.56 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | ((~member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(203,plain,
% 16.38/16.56 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))) | (~member(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[202, 201])).
% 16.38/16.56 tff(204,plain,
% 16.38/16.56 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[203, 82, 200])).
% 16.38/16.56 tff(205,plain,
% 16.38/16.56 ((~(member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))))) | (~member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6)))),
% 16.38/16.56 inference(tautology,[status(thm)],[])).
% 16.38/16.56 tff(206,plain,
% 16.38/16.56 ((~(member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))))) | ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[205, 204])).
% 16.38/16.56 tff(207,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[206, 183])).
% 16.38/16.56 tff(208,plain,
% 16.38/16.56 ((~((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6)))) | (unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))),
% 16.38/16.56 inference(tautology,[status(thm)],[])).
% 16.38/16.56 tff(209,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) | (unordered_pair(U!4, V!3) = singleton(A!6))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[208, 207])).
% 16.38/16.56 tff(210,plain,
% 16.38/16.56 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[209, 181])).
% 16.38/16.56 tff(211,plain,
% 16.38/16.56 (unordered_pair(U!4, V!3) = singleton(U!4)),
% 16.38/16.56 inference(transitivity,[status(thm)],[210, 180])).
% 16.38/16.56 tff(212,plain,
% 16.38/16.56 ((unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)) <=> (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[211])).
% 16.38/16.56 tff(213,plain,
% 16.38/16.56 ((singleton(U!4) = unordered_pair(A!6, B!5)) <=> (unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(symmetry,[status(thm)],[212])).
% 16.38/16.56 tff(214,assumption,(~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.38/16.56 tff(215,assumption,(~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), introduced(assumption)).
% 16.38/16.56 tff(216,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(217,plain,
% 16.38/16.56 ((member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> $true) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(218,plain,
% 16.38/16.56 (($true | (unordered_pair(A!6, B!5) = singleton(A!6))) <=> $true),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(219,plain,
% 16.38/16.56 ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) <=> $true),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(220,plain,
% 16.38/16.56 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6))) <=> ($true | (unordered_pair(A!6, B!5) = singleton(A!6)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[219])).
% 16.38/16.56 tff(221,plain,
% 16.38/16.56 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6))) <=> $true),
% 16.38/16.56 inference(transitivity,[status(thm)],[220, 218])).
% 16.38/16.56 tff(222,plain,
% 16.38/16.56 ((member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6)))) <=> (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> $true)),
% 16.38/16.56 inference(monotonicity,[status(thm)],[221])).
% 16.38/16.56 tff(223,plain,
% 16.38/16.56 ((member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6)))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(transitivity,[status(thm)],[222, 217])).
% 16.38/16.56 tff(224,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[223])).
% 16.38/16.56 tff(225,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 16.38/16.56 inference(transitivity,[status(thm)],[224, 216])).
% 16.38/16.56 tff(226,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | (unordered_pair(A!6, B!5) = singleton(A!6))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(227,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[226, 225])).
% 16.38/16.56 tff(228,plain,
% 16.38/16.56 ($false),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[227, 11, 215])).
% 16.38/16.56 tff(229,plain,(member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.56 tff(230,plain,
% 16.38/16.56 (((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(231,plain,
% 16.38/16.56 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(232,plain,
% 16.38/16.56 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[231, 230])).
% 16.38/16.56 tff(233,plain,
% 16.38/16.56 ($false),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[232, 159, 229, 214])).
% 16.38/16.56 tff(234,plain,(member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.56 tff(235,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[184])).
% 16.38/16.56 tff(236,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(symmetry,[status(thm)],[235])).
% 16.38/16.56 tff(237,plain,
% 16.38/16.56 ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[236])).
% 16.38/16.56 tff(238,assumption,(~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.38/16.56 tff(239,plain,
% 16.38/16.56 (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 16.38/16.56 tff(240,assumption,(member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.38/16.56 tff(241,plain,
% 16.38/16.56 ($false),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[240, 239])).
% 16.38/16.56 tff(242,plain,((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.56 tff(243,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[242, 234])).
% 16.38/16.56 tff(244,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6))))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(245,plain,
% 16.38/16.56 ((member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((unordered_pair(A!6, B!5) = singleton(A!6)) | (unordered_pair(A!6, B!5) = singleton(A!6)))) <=> (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6)))),
% 16.38/16.56 inference(rewrite,[status(thm)],[])).
% 16.38/16.56 tff(246,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((unordered_pair(A!6, B!5) = singleton(A!6)) | (unordered_pair(A!6, B!5) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6))))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[245])).
% 16.38/16.56 tff(247,plain,
% 16.38/16.56 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((unordered_pair(A!6, B!5) = singleton(A!6)) | (unordered_pair(A!6, B!5) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6))))),
% 16.38/16.56 inference(transitivity,[status(thm)],[246, 244])).
% 16.38/16.56 tff(248,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((unordered_pair(A!6, B!5) = singleton(A!6)) | (unordered_pair(A!6, B!5) = singleton(A!6))))),
% 16.38/16.56 inference(quant_inst,[status(thm)],[])).
% 16.38/16.56 tff(249,plain,
% 16.38/16.56 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[248, 247])).
% 16.38/16.56 tff(250,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[249, 11])).
% 16.38/16.56 tff(251,assumption,(unordered_pair(U!4, V!3) = singleton(A!6)), introduced(assumption)).
% 16.38/16.56 tff(252,plain,
% 16.38/16.56 (singleton(A!6) = unordered_pair(U!4, V!3)),
% 16.38/16.56 inference(symmetry,[status(thm)],[251])).
% 16.38/16.56 tff(253,plain,
% 16.38/16.56 (unordered_pair(singleton(A!6), singleton(A!6)) = unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[252])).
% 16.38/16.56 tff(254,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[253])).
% 16.38/16.56 tff(255,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.38/16.56 inference(symmetry,[status(thm)],[254])).
% 16.38/16.56 tff(256,assumption,(member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.38/16.56 tff(257,plain,
% 16.38/16.56 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[256, 255])).
% 16.38/16.56 tff(258,plain,
% 16.38/16.56 ((unordered_pair(A!6, B!5) = singleton(U!4)) <=> (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(commutativity,[status(thm)],[])).
% 16.38/16.56 tff(259,plain,
% 16.38/16.56 ((unordered_pair(A!6, B!5) = singleton(A!6)) <=> (unordered_pair(A!6, B!5) = singleton(U!4))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[180])).
% 16.38/16.56 tff(260,plain,
% 16.38/16.56 ((unordered_pair(A!6, B!5) = singleton(A!6)) <=> (singleton(U!4) = unordered_pair(A!6, B!5))),
% 16.38/16.56 inference(transitivity,[status(thm)],[259, 258])).
% 16.38/16.56 tff(261,plain,
% 16.38/16.56 ((singleton(U!4) = unordered_pair(A!6, B!5)) <=> (unordered_pair(A!6, B!5) = singleton(A!6))),
% 16.38/16.56 inference(symmetry,[status(thm)],[260])).
% 16.38/16.56 tff(262,plain,
% 16.38/16.56 ((~(singleton(U!4) = unordered_pair(A!6, B!5))) <=> (~(unordered_pair(A!6, B!5) = singleton(A!6)))),
% 16.38/16.56 inference(monotonicity,[status(thm)],[261])).
% 16.38/16.56 tff(263,assumption,(~(singleton(U!4) = unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.56 tff(264,plain,
% 16.38/16.56 (~(unordered_pair(A!6, B!5) = singleton(A!6))),
% 16.38/16.56 inference(modus_ponens,[status(thm)],[263, 262])).
% 16.38/16.56 tff(265,plain,
% 16.38/16.56 ((~(member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6))) <=> (unordered_pair(A!6, B!5) = singleton(A!6)))) | (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), singleton(A!6)))) | (unordered_pair(A!6, B!5) = singleton(A!6))),
% 16.38/16.56 inference(tautology,[status(thm)],[])).
% 16.38/16.56 tff(266,plain,
% 16.38/16.56 ($false),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[265, 264, 257, 250])).
% 16.38/16.56 tff(267,plain,((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | (singleton(U!4) = unordered_pair(A!6, B!5)) | (~(unordered_pair(U!4, V!3) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.56 tff(268,plain,
% 16.38/16.56 ((singleton(U!4) = unordered_pair(A!6, B!5)) | (~(unordered_pair(U!4, V!3) = singleton(A!6)))),
% 16.38/16.56 inference(unit_resolution,[status(thm)],[267, 243])).
% 16.38/16.56 tff(269,plain,
% 16.38/16.56 (singleton(U!4) = unordered_pair(A!6, B!5)),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[268, 210])).
% 16.38/16.57 tff(270,plain,
% 16.38/16.57 (unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[269, 213])).
% 16.38/16.57 tff(271,plain,
% 16.38/16.57 ($false),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[181, 270])).
% 16.38/16.57 tff(272,plain,(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)), inference(lemma,lemma(discharge,[]))).
% 16.38/16.57 tff(273,plain,
% 16.38/16.57 (member(B!5, unordered_pair(U!4, V!3)) <=> member(B!5, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[272])).
% 16.38/16.57 tff(274,plain,
% 16.38/16.57 (member(B!5, unordered_pair(A!6, B!5)) <=> member(B!5, unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(symmetry,[status(thm)],[273])).
% 16.38/16.57 tff(275,assumption,(~member(B!5, unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.57 tff(276,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!5, unordered_pair(A!6, B!5))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!5, unordered_pair(A!6, B!5)))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(277,plain,
% 16.38/16.57 ((member(B!5, unordered_pair(A!6, B!5)) <=> $true) <=> member(B!5, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(278,plain,
% 16.38/16.57 (($true | (B!5 = A!6)) <=> $true),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(279,plain,
% 16.38/16.57 ((B!5 = B!5) <=> $true),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(280,plain,
% 16.38/16.57 (((B!5 = B!5) | (B!5 = A!6)) <=> ($true | (B!5 = A!6))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[279])).
% 16.38/16.57 tff(281,plain,
% 16.38/16.57 (((B!5 = B!5) | (B!5 = A!6)) <=> $true),
% 16.38/16.57 inference(transitivity,[status(thm)],[280, 278])).
% 16.38/16.57 tff(282,plain,
% 16.38/16.57 ((member(B!5, unordered_pair(A!6, B!5)) <=> ((B!5 = B!5) | (B!5 = A!6))) <=> (member(B!5, unordered_pair(A!6, B!5)) <=> $true)),
% 16.38/16.57 inference(monotonicity,[status(thm)],[281])).
% 16.38/16.57 tff(283,plain,
% 16.38/16.57 ((member(B!5, unordered_pair(A!6, B!5)) <=> ((B!5 = B!5) | (B!5 = A!6))) <=> member(B!5, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(transitivity,[status(thm)],[282, 277])).
% 16.38/16.57 tff(284,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!5, unordered_pair(A!6, B!5)) <=> ((B!5 = B!5) | (B!5 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!5, unordered_pair(A!6, B!5)))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[283])).
% 16.38/16.57 tff(285,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!5, unordered_pair(A!6, B!5)) <=> ((B!5 = B!5) | (B!5 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!5, unordered_pair(A!6, B!5)))),
% 16.38/16.57 inference(transitivity,[status(thm)],[284, 276])).
% 16.38/16.57 tff(286,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!5, unordered_pair(A!6, B!5)) <=> ((B!5 = B!5) | (B!5 = A!6)))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(287,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(B!5, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[286, 285])).
% 16.38/16.57 tff(288,plain,
% 16.38/16.57 ($false),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[287, 11, 275])).
% 16.38/16.57 tff(289,plain,(member(B!5, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.57 tff(290,plain,
% 16.38/16.57 (member(B!5, unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[289, 274])).
% 16.38/16.57 tff(291,assumption,(~(member(B!5, unordered_pair(U!4, V!3)) <=> ((B!5 = V!3) | (B!5 = U!4)))), introduced(assumption)).
% 16.38/16.57 tff(292,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!5, unordered_pair(U!4, V!3)) <=> ((B!5 = V!3) | (B!5 = U!4)))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(293,plain,
% 16.38/16.57 ($false),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[292, 11, 291])).
% 16.38/16.57 tff(294,plain,(member(B!5, unordered_pair(U!4, V!3)) <=> ((B!5 = V!3) | (B!5 = U!4))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.57 tff(295,plain,
% 16.38/16.57 ((~(member(B!5, unordered_pair(U!4, V!3)) <=> ((B!5 = V!3) | (B!5 = U!4)))) | (~member(B!5, unordered_pair(U!4, V!3))) | ((B!5 = V!3) | (B!5 = U!4))),
% 16.38/16.57 inference(tautology,[status(thm)],[])).
% 16.38/16.57 tff(296,plain,
% 16.38/16.57 ((~member(B!5, unordered_pair(U!4, V!3))) | ((B!5 = V!3) | (B!5 = U!4))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[295, 294])).
% 16.38/16.57 tff(297,plain,
% 16.38/16.57 ((B!5 = V!3) | (B!5 = U!4)),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[296, 290])).
% 16.38/16.57 tff(298,plain,
% 16.38/16.57 (~(B!5 = V!3)),
% 16.38/16.57 inference(or_elim,[status(thm)],[73])).
% 16.38/16.57 tff(299,plain,
% 16.38/16.57 ((~((B!5 = V!3) | (B!5 = U!4))) | (B!5 = V!3) | (B!5 = U!4)),
% 16.38/16.57 inference(tautology,[status(thm)],[])).
% 16.38/16.57 tff(300,plain,
% 16.38/16.57 ((~((B!5 = V!3) | (B!5 = U!4))) | (B!5 = U!4)),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[299, 298])).
% 16.38/16.57 tff(301,plain,
% 16.38/16.57 (B!5 = U!4),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[300, 297])).
% 16.38/16.57 tff(302,plain,
% 16.38/16.57 (U!4 = B!5),
% 16.38/16.57 inference(symmetry,[status(thm)],[301])).
% 16.38/16.57 tff(303,assumption,(~member(A!6, singleton(A!6))), introduced(assumption)).
% 16.38/16.57 tff(304,plain,
% 16.38/16.57 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!6, singleton(A!6))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!6, singleton(A!6)))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(305,plain,
% 16.38/16.57 ((member(A!6, singleton(A!6)) <=> $true) <=> member(A!6, singleton(A!6))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(306,plain,
% 16.38/16.57 ((member(A!6, singleton(A!6)) <=> (A!6 = A!6)) <=> (member(A!6, singleton(A!6)) <=> $true)),
% 16.38/16.57 inference(monotonicity,[status(thm)],[108])).
% 16.38/16.57 tff(307,plain,
% 16.38/16.57 ((member(A!6, singleton(A!6)) <=> (A!6 = A!6)) <=> member(A!6, singleton(A!6))),
% 16.38/16.57 inference(transitivity,[status(thm)],[306, 305])).
% 16.38/16.57 tff(308,plain,
% 16.38/16.57 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!6, singleton(A!6)) <=> (A!6 = A!6))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!6, singleton(A!6)))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[307])).
% 16.38/16.57 tff(309,plain,
% 16.38/16.57 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!6, singleton(A!6)) <=> (A!6 = A!6))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!6, singleton(A!6)))),
% 16.38/16.57 inference(transitivity,[status(thm)],[308, 304])).
% 16.38/16.57 tff(310,plain,
% 16.38/16.57 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(A!6, singleton(A!6)) <=> (A!6 = A!6))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(311,plain,
% 16.38/16.57 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(A!6, singleton(A!6))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[310, 309])).
% 16.38/16.57 tff(312,plain,
% 16.38/16.57 ($false),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[311, 99, 303])).
% 16.38/16.57 tff(313,plain,(member(A!6, singleton(A!6))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.57 tff(314,assumption,(~(U!4 = A!6)), introduced(assumption)).
% 16.38/16.57 tff(315,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(U!4, V!3)) <=> ((A!6 = V!3) | (A!6 = U!4)))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(316,plain,
% 16.38/16.57 (member(A!6, unordered_pair(U!4, V!3)) <=> ((A!6 = V!3) | (A!6 = U!4))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[315, 11])).
% 16.38/16.57 tff(317,assumption,(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)), introduced(assumption)).
% 16.38/16.57 tff(318,plain,
% 16.38/16.57 (member(A!6, unordered_pair(U!4, V!3)) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[317])).
% 16.38/16.57 tff(319,plain,
% 16.38/16.57 (member(A!6, unordered_pair(A!6, B!5)) <=> member(A!6, unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(symmetry,[status(thm)],[318])).
% 16.38/16.57 tff(320,plain,
% 16.38/16.57 (member(A!6, unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[118, 319])).
% 16.38/16.57 tff(321,plain,
% 16.38/16.57 ((~(member(A!6, unordered_pair(U!4, V!3)) <=> ((A!6 = V!3) | (A!6 = U!4)))) | (~member(A!6, unordered_pair(U!4, V!3))) | ((A!6 = V!3) | (A!6 = U!4))),
% 16.38/16.57 inference(tautology,[status(thm)],[])).
% 16.38/16.57 tff(322,plain,
% 16.38/16.57 ((A!6 = V!3) | (A!6 = U!4)),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[321, 320, 316])).
% 16.38/16.57 tff(323,plain,
% 16.38/16.57 ((A!6 = U!4) <=> (U!4 = A!6)),
% 16.38/16.57 inference(commutativity,[status(thm)],[])).
% 16.38/16.57 tff(324,assumption,(A!6 = U!4), introduced(assumption)).
% 16.38/16.57 tff(325,plain,
% 16.38/16.57 (U!4 = A!6),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[324, 323])).
% 16.38/16.57 tff(326,plain,
% 16.38/16.57 ($false),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[314, 325])).
% 16.38/16.57 tff(327,plain,((~(A!6 = U!4)) | (U!4 = A!6)), inference(lemma,lemma(discharge,[]))).
% 16.38/16.57 tff(328,plain,
% 16.38/16.57 (~(A!6 = U!4)),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[327, 314])).
% 16.38/16.57 tff(329,plain,
% 16.38/16.57 ((~((A!6 = V!3) | (A!6 = U!4))) | (A!6 = V!3) | (A!6 = U!4)),
% 16.38/16.57 inference(tautology,[status(thm)],[])).
% 16.38/16.57 tff(330,plain,
% 16.38/16.57 (A!6 = V!3),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[329, 328, 322])).
% 16.38/16.57 tff(331,plain,
% 16.38/16.57 (V!3 = A!6),
% 16.38/16.57 inference(symmetry,[status(thm)],[330])).
% 16.38/16.57 tff(332,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(333,plain,
% 16.38/16.57 ((member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = unordered_pair(A!6, B!5)) | (V!3 = singleton(A!6)))) <=> (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(334,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = unordered_pair(A!6, B!5)) | (V!3 = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[333])).
% 16.38/16.57 tff(335,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = unordered_pair(A!6, B!5)) | (V!3 = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))))),
% 16.38/16.57 inference(transitivity,[status(thm)],[334, 332])).
% 16.38/16.57 tff(336,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = unordered_pair(A!6, B!5)) | (V!3 = singleton(A!6))))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(337,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[336, 335])).
% 16.38/16.57 tff(338,plain,
% 16.38/16.57 (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[337, 11])).
% 16.38/16.57 tff(339,plain,
% 16.38/16.57 (unordered_pair(A!6, B!5) = unordered_pair(U!4, V!3)),
% 16.38/16.57 inference(symmetry,[status(thm)],[317])).
% 16.38/16.57 tff(340,plain,
% 16.38/16.57 (unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)) = unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[339])).
% 16.38/16.57 tff(341,plain,
% 16.38/16.57 (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[340])).
% 16.38/16.57 tff(342,plain,
% 16.38/16.57 (member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.57 inference(symmetry,[status(thm)],[341])).
% 16.38/16.57 tff(343,plain,
% 16.38/16.57 (member(V!3, unordered_pair(A!6, B!5)) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[331])).
% 16.38/16.57 tff(344,plain,
% 16.38/16.57 (member(A!6, unordered_pair(A!6, B!5)) <=> member(V!3, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(symmetry,[status(thm)],[343])).
% 16.38/16.57 tff(345,plain,
% 16.38/16.57 (member(V!3, unordered_pair(A!6, B!5))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[118, 344])).
% 16.38/16.57 tff(346,plain,
% 16.38/16.57 ((~![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!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(347,plain,
% 16.38/16.57 (~((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[346, 49])).
% 16.38/16.57 tff(348,plain,
% 16.38/16.57 (((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))) | ((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.38/16.57 inference(tautology,[status(thm)],[])).
% 16.38/16.57 tff(349,plain,
% 16.38/16.57 ((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[348, 347])).
% 16.38/16.57 tff(350,plain,
% 16.38/16.57 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 16.38/16.57 inference(bind,[status(th)],[])).
% 16.38/16.57 tff(351,plain,
% 16.38/16.57 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 16.38/16.57 inference(quant_intro,[status(thm)],[350])).
% 16.38/16.57 tff(352,plain,
% 16.38/16.57 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(353,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','power_set')).
% 16.38/16.57 tff(354,plain,
% 16.38/16.57 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[353, 352])).
% 16.38/16.57 tff(355,plain,(
% 16.38/16.57 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 16.38/16.57 inference(skolemize,[status(sab)],[354])).
% 16.38/16.57 tff(356,plain,
% 16.38/16.57 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[355, 351])).
% 16.38/16.57 tff(357,plain,
% 16.38/16.57 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(358,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[357, 356])).
% 16.38/16.57 tff(359,plain,
% 16.38/16.57 (unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 16.38/16.57 inference(symmetry,[status(thm)],[184])).
% 16.38/16.57 tff(360,plain,
% 16.38/16.57 (power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[359])).
% 16.38/16.57 tff(361,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[360])).
% 16.38/16.57 tff(362,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.57 inference(symmetry,[status(thm)],[361])).
% 16.38/16.57 tff(363,plain,
% 16.38/16.57 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 16.38/16.57 inference(bind,[status(th)],[])).
% 16.38/16.57 tff(364,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 16.38/16.57 inference(quant_intro,[status(thm)],[363])).
% 16.38/16.57 tff(365,plain,
% 16.38/16.57 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 16.38/16.57 inference(bind,[status(th)],[])).
% 16.38/16.57 tff(366,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 16.38/16.57 inference(quant_intro,[status(thm)],[365])).
% 16.38/16.57 tff(367,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(368,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 16.38/16.57 tff(369,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[368, 367])).
% 16.38/16.57 tff(370,plain,(
% 16.38/16.57 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 16.38/16.57 inference(skolemize,[status(sab)],[369])).
% 16.38/16.57 tff(371,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[370, 366])).
% 16.38/16.57 tff(372,plain,
% 16.38/16.57 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[371, 364])).
% 16.38/16.57 tff(373,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(374,plain,
% 16.38/16.57 ((~(~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(375,plain,
% 16.38/16.57 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(376,plain,
% 16.38/16.57 (((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(377,plain,
% 16.38/16.57 (((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.57 inference(rewrite,[status(thm)],[])).
% 16.38/16.57 tff(378,plain,
% 16.38/16.57 ((((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> ((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[377])).
% 16.38/16.57 tff(379,plain,
% 16.38/16.57 ((((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(transitivity,[status(thm)],[378, 376])).
% 16.38/16.57 tff(380,plain,
% 16.38/16.57 ((((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(transitivity,[status(thm)],[379, 375])).
% 16.38/16.57 tff(381,plain,
% 16.38/16.57 ((~(((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[380])).
% 16.38/16.57 tff(382,plain,
% 16.38/16.57 ((~(((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.57 inference(transitivity,[status(thm)],[381, 374])).
% 16.38/16.57 tff(383,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[382])).
% 16.38/16.57 tff(384,plain,
% 16.38/16.57 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(transitivity,[status(thm)],[383, 373])).
% 16.38/16.57 tff(385,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.57 inference(quant_inst,[status(thm)],[])).
% 16.38/16.57 tff(386,plain,
% 16.38/16.57 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[385, 384])).
% 16.38/16.57 tff(387,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.57 inference(unit_resolution,[status(thm)],[386, 372])).
% 16.38/16.57 tff(388,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(monotonicity,[status(thm)],[339, 184])).
% 16.38/16.57 tff(389,plain,
% 16.38/16.57 (member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(symmetry,[status(thm)],[388])).
% 16.38/16.57 tff(390,plain,
% 16.38/16.57 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.57 inference(modus_ponens,[status(thm)],[199, 389])).
% 16.38/16.57 tff(391,assumption,(A!6 = V!3), introduced(assumption)).
% 16.38/16.57 tff(392,plain,
% 16.38/16.57 (V!3 = A!6),
% 16.38/16.57 inference(symmetry,[status(thm)],[391])).
% 16.38/16.57 tff(393,plain,
% 16.38/16.57 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = V!3))),
% 16.38/16.58 inference(quant_inst,[status(thm)],[])).
% 16.38/16.58 tff(394,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = V!3)),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[393, 99])).
% 16.38/16.58 tff(395,plain,
% 16.38/16.58 (singleton(V!3) = singleton(A!6)),
% 16.38/16.58 inference(monotonicity,[status(thm)],[392])).
% 16.38/16.58 tff(396,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[395])).
% 16.38/16.58 tff(397,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3))),
% 16.38/16.58 inference(symmetry,[status(thm)],[396])).
% 16.38/16.58 tff(398,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), introduced(assumption)).
% 16.38/16.58 tff(399,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3))),
% 16.38/16.58 inference(modus_ponens,[status(thm)],[398, 397])).
% 16.38/16.58 tff(400,plain,
% 16.38/16.58 ((~(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = V!3))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(V!3))) | (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = V!3)),
% 16.38/16.58 inference(tautology,[status(thm)],[])).
% 16.38/16.58 tff(401,plain,
% 16.38/16.58 (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = V!3),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[400, 399, 394])).
% 16.38/16.58 tff(402,plain,
% 16.38/16.58 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = U!4))),
% 16.38/16.58 inference(quant_inst,[status(thm)],[])).
% 16.38/16.58 tff(403,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = U!4)),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[402, 99])).
% 16.38/16.58 tff(404,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[179])).
% 16.38/16.58 tff(405,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4))),
% 16.38/16.58 inference(symmetry,[status(thm)],[404])).
% 16.38/16.58 tff(406,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4))),
% 16.38/16.58 inference(modus_ponens,[status(thm)],[398, 405])).
% 16.38/16.58 tff(407,plain,
% 16.38/16.58 ((~(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = U!4))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(U!4))) | (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = U!4)),
% 16.38/16.58 inference(tautology,[status(thm)],[])).
% 16.38/16.58 tff(408,plain,
% 16.38/16.58 (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) = U!4),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[407, 406, 403])).
% 16.38/16.58 tff(409,plain,
% 16.38/16.58 (U!4 = tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.58 inference(symmetry,[status(thm)],[408])).
% 16.38/16.58 tff(410,plain,
% 16.38/16.58 (U!4 = A!6),
% 16.38/16.58 inference(transitivity,[status(thm)],[409, 401, 392])).
% 16.38/16.58 tff(411,plain,
% 16.38/16.58 ($false),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[314, 410])).
% 16.38/16.58 tff(412,plain,((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) | (U!4 = A!6) | (~(A!6 = V!3))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.58 tff(413,plain,
% 16.38/16.58 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[412, 314, 330])).
% 16.38/16.58 tff(414,plain,
% 16.38/16.58 (difference(unordered_pair(A!6, B!5), singleton(A!6)) = difference(unordered_pair(U!4, V!3), singleton(U!4))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[339, 180])).
% 16.38/16.58 tff(415,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[414])).
% 16.38/16.58 tff(416,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.58 inference(symmetry,[status(thm)],[415])).
% 16.38/16.58 tff(417,plain,
% 16.38/16.58 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) <=> (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6))))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[416])).
% 16.38/16.58 tff(418,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[184])).
% 16.38/16.58 tff(419,plain,
% 16.38/16.58 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.58 inference(symmetry,[status(thm)],[418])).
% 16.38/16.58 tff(420,plain,
% 16.38/16.58 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[419])).
% 16.38/16.58 tff(421,plain,
% 16.38/16.58 ((~![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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))))),
% 16.38/16.58 inference(quant_inst,[status(thm)],[])).
% 16.38/16.58 tff(422,plain,
% 16.38/16.58 (~((~((~subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))))),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[421, 49])).
% 16.38/16.58 tff(423,plain,
% 16.38/16.58 (((~((~subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))) | (subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))),
% 16.38/16.58 inference(tautology,[status(thm)],[])).
% 16.38/16.58 tff(424,plain,
% 16.38/16.58 (subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[423, 422])).
% 16.38/16.58 tff(425,plain,
% 16.38/16.58 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.58 inference(quant_inst,[status(thm)],[])).
% 16.38/16.58 tff(426,plain,
% 16.38/16.58 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.58 inference(unit_resolution,[status(thm)],[425, 356])).
% 16.38/16.58 tff(427,plain,
% 16.38/16.58 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[360])).
% 16.38/16.58 tff(428,plain,
% 16.38/16.58 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.58 inference(symmetry,[status(thm)],[427])).
% 16.38/16.58 tff(429,plain,
% 16.38/16.58 ((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.38/16.58 inference(monotonicity,[status(thm)],[428])).
% 16.38/16.58 tff(430,plain,
% 16.38/16.58 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(rewrite,[status(thm)],[])).
% 16.38/16.59 tff(431,plain,
% 16.38/16.59 ((~(~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.59 inference(rewrite,[status(thm)],[])).
% 16.38/16.59 tff(432,plain,
% 16.38/16.59 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(rewrite,[status(thm)],[])).
% 16.38/16.59 tff(433,plain,
% 16.38/16.59 (((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(rewrite,[status(thm)],[])).
% 16.38/16.59 tff(434,plain,
% 16.38/16.59 (((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.59 inference(rewrite,[status(thm)],[])).
% 16.38/16.59 tff(435,plain,
% 16.38/16.59 ((((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> ((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.59 inference(monotonicity,[status(thm)],[434])).
% 16.38/16.59 tff(436,plain,
% 16.38/16.59 ((((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(transitivity,[status(thm)],[435, 433])).
% 16.38/16.59 tff(437,plain,
% 16.38/16.59 ((((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(transitivity,[status(thm)],[436, 432])).
% 16.38/16.59 tff(438,plain,
% 16.38/16.59 ((~(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.38/16.59 inference(monotonicity,[status(thm)],[437])).
% 16.38/16.59 tff(439,plain,
% 16.38/16.59 ((~(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.59 inference(transitivity,[status(thm)],[438, 431])).
% 16.38/16.59 tff(440,plain,
% 16.38/16.59 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(monotonicity,[status(thm)],[439])).
% 16.38/16.59 tff(441,plain,
% 16.38/16.59 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(transitivity,[status(thm)],[440, 430])).
% 16.38/16.59 tff(442,plain,
% 16.38/16.59 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.59 inference(quant_inst,[status(thm)],[])).
% 16.38/16.59 tff(443,plain,
% 16.38/16.59 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.59 inference(modus_ponens,[status(thm)],[442, 441])).
% 16.38/16.59 tff(444,plain,
% 16.38/16.59 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.59 inference(unit_resolution,[status(thm)],[443, 372])).
% 16.38/16.59 tff(445,assumption,(~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))), introduced(assumption)).
% 16.38/16.59 tff(446,plain,
% 16.38/16.59 (((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.59 inference(tautology,[status(thm)],[])).
% 16.38/16.59 tff(447,plain,
% 16.38/16.59 (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.59 inference(unit_resolution,[status(thm)],[446, 445])).
% 16.38/16.59 tff(448,plain,
% 16.38/16.59 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.59 inference(tautology,[status(thm)],[])).
% 16.38/16.59 tff(449,plain,
% 16.38/16.59 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.59 inference(unit_resolution,[status(thm)],[448, 447])).
% 16.38/16.59 tff(450,plain,
% 16.38/16.59 (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.59 inference(unit_resolution,[status(thm)],[449, 444])).
% 16.38/16.59 tff(451,plain,
% 16.38/16.59 (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.59 inference(modus_ponens,[status(thm)],[450, 429])).
% 16.38/16.59 tff(452,plain,
% 16.38/16.59 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | (~subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(453,plain,
% 16.38/16.60 (~subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[452, 451, 426])).
% 16.38/16.60 tff(454,plain,
% 16.38/16.60 ((~(subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))) | subset(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(455,plain,
% 16.38/16.60 (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[454, 453, 424])).
% 16.38/16.60 tff(456,plain,
% 16.38/16.60 (((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(457,plain,
% 16.38/16.60 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[456, 455])).
% 16.38/16.60 tff(458,plain,
% 16.38/16.60 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[457, 420])).
% 16.38/16.60 tff(459,plain,
% 16.38/16.60 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)))),
% 16.38/16.60 inference(quant_inst,[status(thm)],[])).
% 16.38/16.60 tff(460,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[459, 11])).
% 16.38/16.60 tff(461,assumption,(singleton(U!4) = singleton(A!6)), introduced(assumption)).
% 16.38/16.60 tff(462,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))), introduced(assumption)).
% 16.38/16.60 tff(463,plain,
% 16.38/16.60 (singleton(A!6) = singleton(U!4)),
% 16.38/16.60 inference(symmetry,[status(thm)],[461])).
% 16.38/16.60 tff(464,plain,
% 16.38/16.60 (difference(unordered_pair(U!4, V!3), singleton(A!6)) = difference(unordered_pair(U!4, V!3), singleton(U!4))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[463])).
% 16.38/16.60 tff(465,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[464])).
% 16.38/16.60 tff(466,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.38/16.60 inference(symmetry,[status(thm)],[465])).
% 16.38/16.60 tff(467,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[462, 466])).
% 16.38/16.60 tff(468,plain,
% 16.38/16.60 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 16.38/16.60 inference(bind,[status(th)],[])).
% 16.38/16.60 tff(469,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 16.38/16.60 inference(quant_intro,[status(thm)],[468])).
% 16.38/16.60 tff(470,plain,
% 16.38/16.60 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 16.38/16.60 inference(bind,[status(th)],[])).
% 16.38/16.60 tff(471,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 16.38/16.60 inference(quant_intro,[status(thm)],[470])).
% 16.38/16.60 tff(472,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 16.38/16.60 inference(rewrite,[status(thm)],[])).
% 16.38/16.60 tff(473,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','difference')).
% 16.38/16.60 tff(474,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[473, 472])).
% 16.38/16.60 tff(475,plain,(
% 16.38/16.60 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 16.38/16.60 inference(skolemize,[status(sab)],[474])).
% 16.38/16.60 tff(476,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[475, 471])).
% 16.38/16.60 tff(477,plain,
% 16.38/16.60 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[476, 469])).
% 16.38/16.60 tff(478,plain,
% 16.38/16.60 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))))),
% 16.38/16.60 inference(quant_inst,[status(thm)],[])).
% 16.38/16.60 tff(479,plain,
% 16.38/16.60 (~(((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[478, 477])).
% 16.38/16.60 tff(480,assumption,(~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))), introduced(assumption)).
% 16.38/16.60 tff(481,plain,
% 16.38/16.60 (((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(482,plain,
% 16.38/16.60 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[481, 480])).
% 16.38/16.60 tff(483,plain,
% 16.38/16.60 ((((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(484,plain,
% 16.38/16.60 ((((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[483, 482])).
% 16.38/16.60 tff(485,plain,
% 16.38/16.60 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[484, 479])).
% 16.38/16.60 tff(486,plain,
% 16.38/16.60 ($false),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[485, 467])).
% 16.38/16.60 tff(487,plain,((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | (~(singleton(U!4) = singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.60 tff(488,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[487, 462, 461])).
% 16.38/16.60 tff(489,plain,
% 16.38/16.60 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))) | ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(490,plain,
% 16.38/16.60 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)))) | ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[489, 488])).
% 16.38/16.60 tff(491,plain,
% 16.38/16.60 ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[490, 460])).
% 16.38/16.60 tff(492,plain,
% 16.38/16.60 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(quant_inst,[status(thm)],[])).
% 16.38/16.60 tff(493,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[492, 99])).
% 16.38/16.60 tff(494,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[463])).
% 16.38/16.60 tff(495,plain,
% 16.38/16.60 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[494])).
% 16.38/16.60 tff(496,plain,
% 16.38/16.60 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6)))))),
% 16.38/16.60 inference(quant_inst,[status(thm)],[])).
% 16.38/16.60 tff(497,plain,
% 16.38/16.60 (~(((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6))))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[496, 477])).
% 16.38/16.60 tff(498,plain,
% 16.38/16.60 (difference(unordered_pair(A!6, B!5), singleton(A!6)) = difference(unordered_pair(U!4, V!3), singleton(U!4))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[339, 463])).
% 16.38/16.60 tff(499,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.60 inference(monotonicity,[status(thm)],[498])).
% 16.38/16.60 tff(500,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.60 inference(symmetry,[status(thm)],[499])).
% 16.38/16.60 tff(501,plain,
% 16.38/16.60 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[462, 500])).
% 16.38/16.60 tff(502,plain,
% 16.38/16.60 ((((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6)))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(A!6, B!5), singleton(A!6))))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(503,plain,
% 16.38/16.60 (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[502, 501, 497])).
% 16.38/16.60 tff(504,plain,
% 16.38/16.60 (((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(505,plain,
% 16.38/16.60 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[504, 503])).
% 16.38/16.60 tff(506,plain,
% 16.38/16.60 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4))),
% 16.38/16.60 inference(modus_ponens,[status(thm)],[505, 495])).
% 16.38/16.60 tff(507,plain,
% 16.38/16.60 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)) | (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(508,plain,
% 16.38/16.60 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))) | (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[507, 506])).
% 16.38/16.60 tff(509,plain,
% 16.38/16.60 (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[508, 493])).
% 16.38/16.60 tff(510,plain,
% 16.38/16.60 ((~((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4))) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = U!4)),
% 16.38/16.60 inference(tautology,[status(thm)],[])).
% 16.38/16.60 tff(511,plain,
% 16.38/16.60 (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = V!3),
% 16.38/16.60 inference(unit_resolution,[status(thm)],[510, 509, 491])).
% 16.38/16.60 tff(512,plain,
% 16.38/16.60 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))))),
% 16.38/16.61 inference(rewrite,[status(thm)],[])).
% 16.38/16.61 tff(513,plain,
% 16.38/16.61 ((member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))) <=> (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)))),
% 16.38/16.61 inference(rewrite,[status(thm)],[])).
% 16.38/16.61 tff(514,plain,
% 16.38/16.61 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))))),
% 16.38/16.61 inference(monotonicity,[status(thm)],[513])).
% 16.38/16.61 tff(515,plain,
% 16.38/16.61 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))))),
% 16.38/16.61 inference(transitivity,[status(thm)],[514, 512])).
% 16.38/16.61 tff(516,plain,
% 16.38/16.61 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6)))),
% 16.38/16.61 inference(quant_inst,[status(thm)],[])).
% 16.38/16.61 tff(517,plain,
% 16.38/16.61 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)))),
% 16.38/16.61 inference(modus_ponens,[status(thm)],[516, 515])).
% 16.38/16.61 tff(518,plain,
% 16.38/16.61 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[517, 11])).
% 16.38/16.61 tff(519,plain,
% 16.38/16.61 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3))),
% 16.38/16.61 inference(monotonicity,[status(thm)],[339])).
% 16.38/16.61 tff(520,plain,
% 16.38/16.61 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(U!4, V!3)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))),
% 16.38/16.61 inference(symmetry,[status(thm)],[519])).
% 16.38/16.61 tff(521,plain,
% 16.38/16.61 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))),
% 16.38/16.61 inference(modus_ponens,[status(thm)],[488, 520])).
% 16.38/16.61 tff(522,plain,
% 16.38/16.61 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5))) | ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(523,plain,
% 16.38/16.61 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(A!6, B!5)) <=> ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)))) | ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[522, 521])).
% 16.38/16.61 tff(524,plain,
% 16.38/16.61 ((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[523, 518])).
% 16.38/16.61 tff(525,plain,
% 16.38/16.61 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))),
% 16.38/16.61 inference(quant_inst,[status(thm)],[])).
% 16.38/16.61 tff(526,plain,
% 16.38/16.61 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6)),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[525, 99])).
% 16.38/16.61 tff(527,plain,
% 16.38/16.61 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) | (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(528,plain,
% 16.38/16.61 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))) | (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[527, 505])).
% 16.38/16.61 tff(529,plain,
% 16.38/16.61 (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6)),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[528, 526])).
% 16.38/16.61 tff(530,plain,
% 16.38/16.61 ((~((tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5))) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = A!6) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5)),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(531,plain,
% 16.38/16.61 (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) = B!5),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[530, 529, 524])).
% 16.38/16.61 tff(532,plain,
% 16.38/16.61 (B!5 = tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.61 inference(symmetry,[status(thm)],[531])).
% 16.38/16.61 tff(533,plain,
% 16.38/16.61 (B!5 = V!3),
% 16.38/16.61 inference(transitivity,[status(thm)],[532, 511])).
% 16.38/16.61 tff(534,plain,
% 16.38/16.61 ($false),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[298, 533])).
% 16.38/16.61 tff(535,plain,((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | (~(singleton(U!4) = singleton(A!6))) | (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.61 tff(536,plain,
% 16.38/16.61 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[535, 179])).
% 16.38/16.61 tff(537,plain,
% 16.38/16.61 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[536, 317])).
% 16.38/16.61 tff(538,plain,
% 16.38/16.61 (((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(539,plain,
% 16.38/16.61 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[538, 537])).
% 16.38/16.61 tff(540,plain,
% 16.38/16.61 ((~![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(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 16.38/16.61 inference(quant_inst,[status(thm)],[])).
% 16.38/16.61 tff(541,plain,
% 16.38/16.61 (~((~((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[540, 49])).
% 16.38/16.61 tff(542,plain,
% 16.38/16.61 (((~((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(543,plain,
% 16.38/16.61 (subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[542, 541])).
% 16.38/16.61 tff(544,plain,
% 16.38/16.61 ((~(subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(545,plain,
% 16.38/16.61 (subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[544, 543])).
% 16.38/16.61 tff(546,plain,
% 16.38/16.61 (subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[545, 539])).
% 16.38/16.61 tff(547,plain,
% 16.38/16.61 (((~((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | ((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(548,plain,
% 16.38/16.61 ((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[547, 541])).
% 16.38/16.61 tff(549,plain,
% 16.38/16.61 ((~((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(tautology,[status(thm)],[])).
% 16.38/16.61 tff(550,plain,
% 16.38/16.61 ((~subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[549, 548])).
% 16.38/16.61 tff(551,plain,
% 16.38/16.61 (![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[550, 546])).
% 16.38/16.61 tff(552,plain,
% 16.38/16.61 (((~![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(rewrite,[status(thm)],[])).
% 16.38/16.61 tff(553,plain,
% 16.38/16.61 ((~![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.61 inference(quant_inst,[status(thm)],[])).
% 16.38/16.61 tff(554,plain,
% 16.38/16.61 ((~![X: $i] : ((~member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.61 inference(modus_ponens,[status(thm)],[553, 552])).
% 16.38/16.61 tff(555,plain,
% 16.38/16.61 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[554, 551])).
% 16.38/16.61 tff(556,plain,
% 16.38/16.61 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.38/16.61 inference(unit_resolution,[status(thm)],[555, 458])).
% 16.38/16.61 tff(557,plain,
% 16.38/16.61 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.61 inference(modus_ponens,[status(thm)],[556, 417])).
% 16.38/16.61 tff(558,plain,
% 16.38/16.61 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))))),
% 16.38/16.62 inference(quant_inst,[status(thm)],[])).
% 16.38/16.62 tff(559,plain,
% 16.38/16.62 (~(((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6))))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[558, 477])).
% 16.38/16.62 tff(560,plain,
% 16.38/16.62 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))))),
% 16.38/16.62 inference(rewrite,[status(thm)],[])).
% 16.38/16.62 tff(561,plain,
% 16.38/16.62 ((member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))) <=> (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))))),
% 16.38/16.62 inference(rewrite,[status(thm)],[])).
% 16.38/16.62 tff(562,plain,
% 16.38/16.62 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))))),
% 16.38/16.62 inference(monotonicity,[status(thm)],[561])).
% 16.38/16.62 tff(563,plain,
% 16.38/16.62 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))))),
% 16.38/16.62 inference(transitivity,[status(thm)],[562, 560])).
% 16.38/16.62 tff(564,plain,
% 16.38/16.62 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.38/16.62 inference(quant_inst,[status(thm)],[])).
% 16.38/16.62 tff(565,plain,
% 16.38/16.62 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))))),
% 16.38/16.62 inference(modus_ponens,[status(thm)],[564, 563])).
% 16.38/16.62 tff(566,plain,
% 16.38/16.62 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[565, 11])).
% 16.38/16.62 tff(567,plain,
% 16.38/16.62 (unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 16.38/16.62 inference(transitivity,[status(thm)],[340, 359])).
% 16.38/16.62 tff(568,plain,
% 16.38/16.62 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.62 inference(monotonicity,[status(thm)],[567])).
% 16.38/16.62 tff(569,plain,
% 16.38/16.62 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.62 inference(symmetry,[status(thm)],[568])).
% 16.38/16.62 tff(570,plain,
% 16.38/16.62 (((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.62 inference(tautology,[status(thm)],[])).
% 16.38/16.62 tff(571,plain,
% 16.38/16.62 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[570, 445])).
% 16.38/16.62 tff(572,plain,
% 16.38/16.62 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.38/16.62 inference(modus_ponens,[status(thm)],[571, 569])).
% 16.38/16.62 tff(573,plain,
% 16.38/16.62 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))),
% 16.38/16.62 inference(tautology,[status(thm)],[])).
% 16.38/16.62 tff(574,plain,
% 16.38/16.62 ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[573, 572, 566])).
% 16.38/16.62 tff(575,assumption,(~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), introduced(assumption)).
% 16.38/16.62 tff(576,plain,
% 16.38/16.62 (((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.62 inference(tautology,[status(thm)],[])).
% 16.38/16.62 tff(577,plain,
% 16.38/16.62 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[576, 455])).
% 16.38/16.62 tff(578,assumption,((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.62 tff(579,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))), introduced(assumption)).
% 16.38/16.62 tff(580,assumption,((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), introduced(assumption)).
% 16.38/16.62 tff(581,plain,
% 16.38/16.62 ((~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))),
% 16.38/16.62 inference(tautology,[status(thm)],[])).
% 16.38/16.62 tff(582,plain,
% 16.38/16.62 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[581, 575, 580])).
% 16.38/16.62 tff(583,assumption,(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)), introduced(assumption)).
% 16.38/16.62 tff(584,plain,
% 16.38/16.62 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))),
% 16.38/16.62 inference(monotonicity,[status(thm)],[583])).
% 16.38/16.62 tff(585,plain,
% 16.38/16.62 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.62 inference(symmetry,[status(thm)],[584])).
% 16.38/16.62 tff(586,plain,
% 16.38/16.62 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) <=> (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.62 inference(monotonicity,[status(thm)],[585])).
% 16.38/16.62 tff(587,assumption,(~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.38/16.62 tff(588,plain,
% 16.38/16.62 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.62 inference(modus_ponens,[status(thm)],[587, 586])).
% 16.38/16.62 tff(589,plain,
% 16.38/16.62 ($false),
% 16.38/16.62 inference(unit_resolution,[status(thm)],[579, 588])).
% 16.38/16.62 tff(590,plain,((~(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.62 tff(591,plain,
% 16.38/16.62 (~(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[590, 582, 579])).
% 16.38/16.63 tff(592,plain,
% 16.38/16.63 ((~((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(593,plain,
% 16.38/16.63 (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[592, 591, 578])).
% 16.38/16.63 tff(594,plain,
% 16.38/16.63 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))),
% 16.38/16.63 inference(monotonicity,[status(thm)],[593])).
% 16.38/16.63 tff(595,plain,
% 16.38/16.63 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.63 inference(symmetry,[status(thm)],[594])).
% 16.38/16.63 tff(596,plain,
% 16.38/16.63 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) <=> (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.63 inference(monotonicity,[status(thm)],[595])).
% 16.38/16.63 tff(597,plain,
% 16.38/16.63 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.63 inference(modus_ponens,[status(thm)],[575, 596])).
% 16.38/16.63 tff(598,plain,
% 16.38/16.63 ($false),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[579, 597])).
% 16.38/16.63 tff(599,plain,(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(A!6, B!5)))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.63 tff(600,plain,
% 16.38/16.63 (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[599, 577, 575, 574])).
% 16.38/16.63 tff(601,plain,
% 16.38/16.63 ((((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))) | ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(602,plain,
% 16.38/16.63 ((((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[601, 600])).
% 16.38/16.63 tff(603,plain,
% 16.38/16.63 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), difference(unordered_pair(A!6, B!5), singleton(A!6)))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[602, 559])).
% 16.38/16.63 tff(604,plain,
% 16.38/16.63 ($false),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[603, 557])).
% 16.38/16.63 tff(605,plain,(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), inference(lemma,lemma(discharge,[]))).
% 16.38/16.63 tff(606,plain,
% 16.38/16.63 ((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[605, 413, 317])).
% 16.38/16.63 tff(607,plain,
% 16.38/16.63 ((~![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(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))))),
% 16.38/16.63 inference(quant_inst,[status(thm)],[])).
% 16.38/16.63 tff(608,plain,
% 16.38/16.63 (~((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[607, 49])).
% 16.38/16.63 tff(609,plain,
% 16.38/16.63 (((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) | (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(610,plain,
% 16.38/16.63 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[609, 608])).
% 16.38/16.63 tff(611,plain,
% 16.38/16.63 ((~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))) | subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(612,plain,
% 16.38/16.63 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[611, 610])).
% 16.38/16.63 tff(613,plain,
% 16.38/16.63 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[612, 606])).
% 16.38/16.63 tff(614,plain,
% 16.38/16.63 (((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (~(subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) | ((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(615,plain,
% 16.38/16.63 ((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[614, 608])).
% 16.38/16.63 tff(616,plain,
% 16.38/16.63 ((~((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.63 inference(tautology,[status(thm)],[])).
% 16.38/16.63 tff(617,plain,
% 16.38/16.63 ((~subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[616, 615])).
% 16.38/16.63 tff(618,plain,
% 16.38/16.63 (![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.63 inference(unit_resolution,[status(thm)],[617, 613])).
% 16.38/16.63 tff(619,plain,
% 16.38/16.63 (((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.64 inference(rewrite,[status(thm)],[])).
% 16.38/16.64 tff(620,plain,
% 16.38/16.64 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.64 inference(quant_inst,[status(thm)],[])).
% 16.38/16.64 tff(621,plain,
% 16.38/16.64 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.64 inference(modus_ponens,[status(thm)],[620, 619])).
% 16.38/16.64 tff(622,plain,
% 16.38/16.64 ((~member(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.64 inference(unit_resolution,[status(thm)],[621, 618])).
% 16.38/16.64 tff(623,plain,
% 16.38/16.64 (member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.38/16.64 inference(unit_resolution,[status(thm)],[622, 390])).
% 16.38/16.64 tff(624,plain,
% 16.38/16.64 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.38/16.64 inference(tautology,[status(thm)],[])).
% 16.38/16.64 tff(625,plain,
% 16.38/16.64 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(A!6, B!5), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.64 inference(unit_resolution,[status(thm)],[624, 623])).
% 16.38/16.64 tff(626,plain,
% 16.38/16.64 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.38/16.64 inference(unit_resolution,[status(thm)],[625, 387])).
% 16.38/16.64 tff(627,plain,
% 16.38/16.64 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.38/16.64 inference(modus_ponens,[status(thm)],[626, 362])).
% 16.38/16.64 tff(628,plain,
% 16.38/16.64 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(629,plain,
% 16.48/16.64 (subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[628, 627, 358])).
% 16.48/16.64 tff(630,plain,
% 16.48/16.64 ((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(631,plain,
% 16.48/16.64 (![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[630, 629, 349])).
% 16.48/16.64 tff(632,plain,
% 16.48/16.64 (((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | ((~member(V!3, unordered_pair(A!6, B!5))) | member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(V!3, unordered_pair(A!6, B!5))) | member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(633,plain,
% 16.48/16.64 ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | ((~member(V!3, unordered_pair(A!6, B!5))) | member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(634,plain,
% 16.48/16.64 ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(V!3, unordered_pair(A!6, B!5))) | member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[633, 632])).
% 16.48/16.64 tff(635,plain,
% 16.48/16.64 ((~member(V!3, unordered_pair(A!6, B!5))) | member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[634, 631])).
% 16.48/16.64 tff(636,plain,
% 16.48/16.64 (member(V!3, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[635, 345])).
% 16.48/16.64 tff(637,plain,
% 16.48/16.64 (member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[636, 342])).
% 16.48/16.64 tff(638,plain,
% 16.48/16.64 ((~(member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))))) | (~member(V!3, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(639,plain,
% 16.48/16.64 ((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[638, 637, 338])).
% 16.48/16.64 tff(640,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(U!4)) <=> member(singleton(A!6), singleton(A!6))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[179])).
% 16.48/16.64 tff(641,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(A!6)) <=> member(singleton(A!6), singleton(U!4))),
% 16.48/16.64 inference(symmetry,[status(thm)],[640])).
% 16.48/16.64 tff(642,assumption,(V!3 = singleton(A!6)), introduced(assumption)).
% 16.48/16.64 tff(643,plain,
% 16.48/16.64 (singleton(A!6) = V!3),
% 16.48/16.64 inference(symmetry,[status(thm)],[642])).
% 16.48/16.64 tff(644,plain,
% 16.48/16.64 (singleton(A!6) = A!6),
% 16.48/16.64 inference(transitivity,[status(thm)],[643, 392])).
% 16.48/16.64 tff(645,plain,
% 16.48/16.64 (singleton(singleton(A!6)) = singleton(A!6)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[644])).
% 16.48/16.64 tff(646,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(singleton(A!6))) <=> member(singleton(A!6), singleton(A!6))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[645])).
% 16.48/16.64 tff(647,plain,
% 16.48/16.64 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(singleton(A!6), singleton(singleton(A!6)))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(singleton(A!6), singleton(singleton(A!6))))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(648,plain,
% 16.48/16.64 ((member(singleton(A!6), singleton(singleton(A!6))) <=> $true) <=> member(singleton(A!6), singleton(singleton(A!6)))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(649,plain,
% 16.48/16.64 ((member(singleton(A!6), singleton(singleton(A!6))) <=> (singleton(A!6) = singleton(A!6))) <=> (member(singleton(A!6), singleton(singleton(A!6))) <=> $true)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[140])).
% 16.48/16.64 tff(650,plain,
% 16.48/16.64 ((member(singleton(A!6), singleton(singleton(A!6))) <=> (singleton(A!6) = singleton(A!6))) <=> member(singleton(A!6), singleton(singleton(A!6)))),
% 16.48/16.64 inference(transitivity,[status(thm)],[649, 648])).
% 16.48/16.64 tff(651,plain,
% 16.48/16.64 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(singleton(A!6), singleton(singleton(A!6))) <=> (singleton(A!6) = singleton(A!6)))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(singleton(A!6), singleton(singleton(A!6))))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[650])).
% 16.48/16.64 tff(652,plain,
% 16.48/16.64 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(singleton(A!6), singleton(singleton(A!6))) <=> (singleton(A!6) = singleton(A!6)))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(singleton(A!6), singleton(singleton(A!6))))),
% 16.48/16.64 inference(transitivity,[status(thm)],[651, 647])).
% 16.48/16.64 tff(653,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(singleton(A!6), singleton(singleton(A!6))) <=> (singleton(A!6) = singleton(A!6)))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(654,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(singleton(A!6), singleton(singleton(A!6)))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[653, 652])).
% 16.48/16.64 tff(655,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(singleton(A!6)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[654, 99])).
% 16.48/16.64 tff(656,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(A!6))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[655, 646])).
% 16.48/16.64 tff(657,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(U!4))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[656, 641])).
% 16.48/16.64 tff(658,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(singleton(A!6), singleton(U!4)) <=> (singleton(A!6) = U!4))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(659,plain,
% 16.48/16.64 (member(singleton(A!6), singleton(U!4)) <=> (singleton(A!6) = U!4)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[658, 99])).
% 16.48/16.64 tff(660,plain,
% 16.48/16.64 ((singleton(A!6) = U!4) <=> (A!6 = U!4)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[644])).
% 16.48/16.64 tff(661,plain,
% 16.48/16.64 ((singleton(A!6) = U!4) <=> (U!4 = A!6)),
% 16.48/16.64 inference(transitivity,[status(thm)],[660, 323])).
% 16.48/16.64 tff(662,plain,
% 16.48/16.64 ((U!4 = A!6) <=> (singleton(A!6) = U!4)),
% 16.48/16.64 inference(symmetry,[status(thm)],[661])).
% 16.48/16.64 tff(663,plain,
% 16.48/16.64 ((~(U!4 = A!6)) <=> (~(singleton(A!6) = U!4))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[662])).
% 16.48/16.64 tff(664,plain,
% 16.48/16.64 (~(singleton(A!6) = U!4)),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[314, 663])).
% 16.48/16.64 tff(665,plain,
% 16.48/16.64 ((~(member(singleton(A!6), singleton(U!4)) <=> (singleton(A!6) = U!4))) | (~member(singleton(A!6), singleton(U!4))) | (singleton(A!6) = U!4)),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(666,plain,
% 16.48/16.64 ((~(member(singleton(A!6), singleton(U!4)) <=> (singleton(A!6) = U!4))) | (~member(singleton(A!6), singleton(U!4)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[665, 664])).
% 16.48/16.64 tff(667,plain,
% 16.48/16.64 (~member(singleton(A!6), singleton(U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[666, 659])).
% 16.48/16.64 tff(668,plain,
% 16.48/16.64 ($false),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[667, 657])).
% 16.48/16.64 tff(669,plain,((~(V!3 = singleton(A!6))) | (~(A!6 = V!3)) | (U!4 = A!6)), inference(lemma,lemma(discharge,[]))).
% 16.48/16.64 tff(670,plain,
% 16.48/16.64 (~(V!3 = singleton(A!6))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[669, 330, 314])).
% 16.48/16.64 tff(671,plain,
% 16.48/16.64 ((~((V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5)))) | (V!3 = singleton(A!6)) | (V!3 = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(672,plain,
% 16.48/16.64 (V!3 = unordered_pair(A!6, B!5)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[671, 670, 639])).
% 16.48/16.64 tff(673,plain,
% 16.48/16.64 (unordered_pair(A!6, B!5) = V!3),
% 16.48/16.64 inference(symmetry,[status(thm)],[672])).
% 16.48/16.64 tff(674,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(unordered_pair(A!6, B!5), singleton(U!4)) <=> (unordered_pair(A!6, B!5) = U!4))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(675,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), singleton(U!4)) <=> (unordered_pair(A!6, B!5) = U!4)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[674, 99])).
% 16.48/16.64 tff(676,plain,
% 16.48/16.64 (A!6 = unordered_pair(A!6, B!5)),
% 16.48/16.64 inference(transitivity,[status(thm)],[330, 672])).
% 16.48/16.64 tff(677,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), A!6) <=> member(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[676])).
% 16.48/16.64 tff(678,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5)) <=> member(unordered_pair(A!6, B!5), A!6)),
% 16.48/16.64 inference(symmetry,[status(thm)],[677])).
% 16.48/16.64 tff(679,plain,
% 16.48/16.64 (unordered_pair(A!6, B!5) = A!6),
% 16.48/16.64 inference(transitivity,[status(thm)],[673, 331])).
% 16.48/16.64 tff(680,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5)) <=> member(A!6, unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[679])).
% 16.48/16.64 tff(681,plain,
% 16.48/16.64 (member(A!6, unordered_pair(A!6, B!5)) <=> member(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(symmetry,[status(thm)],[680])).
% 16.48/16.64 tff(682,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[118, 681])).
% 16.48/16.64 tff(683,plain,
% 16.48/16.64 (member(unordered_pair(A!6, B!5), A!6)),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[682, 678])).
% 16.48/16.64 tff(684,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) <=> (tptp_fun_X_0(singleton(U!4), A!6) = U!4))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(685,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) <=> (tptp_fun_X_0(singleton(U!4), A!6) = U!4)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[684, 99])).
% 16.48/16.64 tff(686,assumption,(~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)))), introduced(assumption)).
% 16.48/16.64 tff(687,plain,
% 16.48/16.64 (((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))) | (~member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(688,plain,
% 16.48/16.64 (~member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[687, 686])).
% 16.48/16.64 tff(689,plain,
% 16.48/16.64 ((~(member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) <=> (tptp_fun_X_0(singleton(U!4), A!6) = U!4))) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) | (~(tptp_fun_X_0(singleton(U!4), A!6) = U!4))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(690,plain,
% 16.48/16.64 ((~(member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) <=> (tptp_fun_X_0(singleton(U!4), A!6) = U!4))) | (~(tptp_fun_X_0(singleton(U!4), A!6) = U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[689, 688])).
% 16.48/16.64 tff(691,plain,
% 16.48/16.64 (~(tptp_fun_X_0(singleton(U!4), A!6) = U!4)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[690, 685])).
% 16.48/16.64 tff(692,plain,
% 16.48/16.64 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))) <=> (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(693,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))) <=> (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[692, 99])).
% 16.48/16.64 tff(694,assumption,(V!3 = unordered_pair(A!6, B!5)), introduced(assumption)).
% 16.48/16.64 tff(695,plain,
% 16.48/16.64 (unordered_pair(A!6, B!5) = V!3),
% 16.48/16.64 inference(symmetry,[status(thm)],[694])).
% 16.48/16.64 tff(696,plain,
% 16.48/16.64 (unordered_pair(A!6, B!5) = A!6),
% 16.48/16.64 inference(transitivity,[status(thm)],[695, 392])).
% 16.48/16.64 tff(697,plain,
% 16.48/16.64 (singleton(unordered_pair(A!6, B!5)) = singleton(A!6)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[696])).
% 16.48/16.64 tff(698,plain,
% 16.48/16.64 (singleton(unordered_pair(A!6, B!5)) = singleton(U!4)),
% 16.48/16.64 inference(transitivity,[status(thm)],[697, 180])).
% 16.48/16.64 tff(699,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))) <=> member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[698])).
% 16.48/16.64 tff(700,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)) <=> member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(symmetry,[status(thm)],[699])).
% 16.48/16.64 tff(701,plain,
% 16.48/16.64 ((~member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))) <=> (~member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[700])).
% 16.48/16.64 tff(702,plain,
% 16.48/16.64 (~member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[688, 701])).
% 16.48/16.64 tff(703,plain,
% 16.48/16.64 ((~(member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))) <=> (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(unordered_pair(A!6, B!5))) | (~(tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(704,plain,
% 16.48/16.64 (~(tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[703, 702, 693])).
% 16.48/16.64 tff(705,plain,
% 16.48/16.64 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(706,plain,
% 16.48/16.64 ((member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(singleton(U!4), A!6) = U!4))) <=> (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(707,plain,
% 16.48/16.64 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(singleton(U!4), A!6) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))))),
% 16.48/16.64 inference(monotonicity,[status(thm)],[706])).
% 16.48/16.64 tff(708,plain,
% 16.48/16.64 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(singleton(U!4), A!6) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))))),
% 16.48/16.64 inference(transitivity,[status(thm)],[707, 705])).
% 16.48/16.64 tff(709,plain,
% 16.48/16.64 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)) | (tptp_fun_X_0(singleton(U!4), A!6) = U!4)))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(710,plain,
% 16.48/16.64 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[709, 708])).
% 16.48/16.64 tff(711,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[710, 11])).
% 16.48/16.64 tff(712,plain,
% 16.48/16.64 (unordered_pair(U!4, unordered_pair(A!6, B!5)) = unordered_pair(U!4, V!3)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[695])).
% 16.48/16.64 tff(713,plain,
% 16.48/16.64 (unordered_pair(U!4, unordered_pair(A!6, B!5)) = A!6),
% 16.48/16.64 inference(transitivity,[status(thm)],[712, 317, 695, 392])).
% 16.48/16.64 tff(714,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> member(tptp_fun_X_0(singleton(U!4), A!6), A!6)),
% 16.48/16.64 inference(monotonicity,[status(thm)],[713])).
% 16.48/16.64 tff(715,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), A!6) <=> member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(symmetry,[status(thm)],[714])).
% 16.48/16.64 tff(716,plain,
% 16.48/16.64 (((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))) | member(tptp_fun_X_0(singleton(U!4), A!6), A!6)),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(717,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), A!6)),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[716, 686])).
% 16.48/16.64 tff(718,plain,
% 16.48/16.64 (member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[717, 715])).
% 16.48/16.64 tff(719,plain,
% 16.48/16.64 ((~(member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5))) <=> ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))))) | (~member(tptp_fun_X_0(singleton(U!4), A!6), unordered_pair(U!4, unordered_pair(A!6, B!5)))) | ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(720,plain,
% 16.48/16.64 ((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[719, 718, 711])).
% 16.48/16.64 tff(721,plain,
% 16.48/16.64 ((~((tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5)))) | (tptp_fun_X_0(singleton(U!4), A!6) = U!4) | (tptp_fun_X_0(singleton(U!4), A!6) = unordered_pair(A!6, B!5))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(722,plain,
% 16.48/16.64 ($false),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[721, 720, 704, 691])).
% 16.48/16.64 tff(723,plain,(((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))) | (~(A!6 = V!3)) | (~(V!3 = unordered_pair(A!6, B!5))) | (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.64 tff(724,plain,
% 16.48/16.64 ((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[723, 330, 672, 317])).
% 16.48/16.64 tff(725,plain,
% 16.48/16.64 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))) | (~(subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))))))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(726,plain,
% 16.48/16.64 (~((~((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))) | (~(subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)))))))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[725, 49])).
% 16.48/16.64 tff(727,plain,
% 16.48/16.64 (((~((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))) | (~(subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))))) | (subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)))))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(728,plain,
% 16.48/16.64 (subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[727, 726])).
% 16.48/16.64 tff(729,plain,
% 16.48/16.64 ((~(subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4)))))) | subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(730,plain,
% 16.48/16.64 (subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[729, 728])).
% 16.48/16.64 tff(731,plain,
% 16.48/16.64 (subset(A!6, singleton(U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[730, 724])).
% 16.48/16.64 tff(732,plain,
% 16.48/16.64 (((~((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))) | (~(subset(A!6, singleton(U!4)) | (~((~member(tptp_fun_X_0(singleton(U!4), A!6), A!6)) | member(tptp_fun_X_0(singleton(U!4), A!6), singleton(U!4))))))) | ((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(733,plain,
% 16.48/16.64 ((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[732, 726])).
% 16.48/16.64 tff(734,plain,
% 16.48/16.64 ((~((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4))))) | (~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))),
% 16.48/16.64 inference(tautology,[status(thm)],[])).
% 16.48/16.64 tff(735,plain,
% 16.48/16.64 ((~subset(A!6, singleton(U!4))) | ![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[734, 733])).
% 16.48/16.64 tff(736,plain,
% 16.48/16.64 (![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[735, 731])).
% 16.48/16.64 tff(737,plain,
% 16.48/16.64 (((~![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))) | ((~member(unordered_pair(A!6, B!5), A!6)) | member(unordered_pair(A!6, B!5), singleton(U!4)))) <=> ((~![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))) | (~member(unordered_pair(A!6, B!5), A!6)) | member(unordered_pair(A!6, B!5), singleton(U!4)))),
% 16.48/16.64 inference(rewrite,[status(thm)],[])).
% 16.48/16.64 tff(738,plain,
% 16.48/16.64 ((~![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))) | ((~member(unordered_pair(A!6, B!5), A!6)) | member(unordered_pair(A!6, B!5), singleton(U!4)))),
% 16.48/16.64 inference(quant_inst,[status(thm)],[])).
% 16.48/16.64 tff(739,plain,
% 16.48/16.64 ((~![X: $i] : ((~member(X, A!6)) | member(X, singleton(U!4)))) | (~member(unordered_pair(A!6, B!5), A!6)) | member(unordered_pair(A!6, B!5), singleton(U!4))),
% 16.48/16.64 inference(modus_ponens,[status(thm)],[738, 737])).
% 16.48/16.64 tff(740,plain,
% 16.48/16.64 ((~member(unordered_pair(A!6, B!5), A!6)) | member(unordered_pair(A!6, B!5), singleton(U!4))),
% 16.48/16.64 inference(unit_resolution,[status(thm)],[739, 736])).
% 16.48/16.65 tff(741,plain,
% 16.48/16.65 (member(unordered_pair(A!6, B!5), singleton(U!4))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[740, 683])).
% 16.48/16.65 tff(742,plain,
% 16.48/16.65 ((~(member(unordered_pair(A!6, B!5), singleton(U!4)) <=> (unordered_pair(A!6, B!5) = U!4))) | (~member(unordered_pair(A!6, B!5), singleton(U!4))) | (unordered_pair(A!6, B!5) = U!4)),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(743,plain,
% 16.48/16.65 ((~(member(unordered_pair(A!6, B!5), singleton(U!4)) <=> (unordered_pair(A!6, B!5) = U!4))) | (unordered_pair(A!6, B!5) = U!4)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[742, 741])).
% 16.48/16.65 tff(744,plain,
% 16.48/16.65 (unordered_pair(A!6, B!5) = U!4),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[743, 675])).
% 16.48/16.65 tff(745,plain,
% 16.48/16.65 (U!4 = unordered_pair(A!6, B!5)),
% 16.48/16.65 inference(symmetry,[status(thm)],[744])).
% 16.48/16.65 tff(746,plain,
% 16.48/16.65 (U!4 = A!6),
% 16.48/16.65 inference(transitivity,[status(thm)],[745, 673, 331])).
% 16.48/16.65 tff(747,plain,
% 16.48/16.65 ($false),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[314, 746])).
% 16.48/16.65 tff(748,plain,((U!4 = A!6) | (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.65 tff(749,plain,
% 16.48/16.65 (~(unordered_pair(U!4, V!3) = unordered_pair(A!6, B!5))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[748, 314])).
% 16.48/16.65 tff(750,plain,
% 16.48/16.65 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[209, 749])).
% 16.48/16.65 tff(751,plain,
% 16.48/16.65 (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[184])).
% 16.48/16.65 tff(752,plain,
% 16.48/16.65 (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(symmetry,[status(thm)],[751])).
% 16.48/16.65 tff(753,plain,
% 16.48/16.65 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[752])).
% 16.48/16.65 tff(754,plain,
% 16.48/16.65 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.65 inference(symmetry,[status(thm)],[753])).
% 16.48/16.65 tff(755,plain,
% 16.48/16.65 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[251])).
% 16.48/16.65 tff(756,plain,
% 16.48/16.65 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[752])).
% 16.48/16.65 tff(757,plain,
% 16.48/16.65 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.65 inference(transitivity,[status(thm)],[756, 755, 754])).
% 16.48/16.65 tff(758,assumption,(~(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))), introduced(assumption)).
% 16.48/16.65 tff(759,plain,
% 16.48/16.65 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(760,plain,
% 16.48/16.65 (member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[759, 11])).
% 16.48/16.65 tff(761,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(762,plain,
% 16.48/16.65 ((member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = V!3) | (singleton(A!6) = U!4))) <=> (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(763,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = V!3) | (singleton(A!6) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[762])).
% 16.48/16.65 tff(764,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = V!3) | (singleton(A!6) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))))),
% 16.48/16.65 inference(transitivity,[status(thm)],[763, 761])).
% 16.48/16.65 tff(765,plain,
% 16.48/16.65 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = V!3) | (singleton(A!6) = U!4)))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(766,plain,
% 16.48/16.65 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[765, 764])).
% 16.48/16.65 tff(767,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[766, 11])).
% 16.48/16.65 tff(768,plain,
% 16.48/16.65 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6))) <=> member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6)))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(769,plain,
% 16.48/16.65 (~(((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6))) <=> member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[768, 477])).
% 16.48/16.65 tff(770,plain,
% 16.48/16.65 (member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[464])).
% 16.48/16.65 tff(771,plain,
% 16.48/16.65 (member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4))) <=> member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(symmetry,[status(thm)],[770])).
% 16.48/16.65 tff(772,plain,
% 16.48/16.65 (unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)) = unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[461])).
% 16.48/16.65 tff(773,plain,
% 16.48/16.65 (unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(symmetry,[status(thm)],[772])).
% 16.48/16.65 tff(774,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[773])).
% 16.48/16.65 tff(775,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(symmetry,[status(thm)],[774])).
% 16.48/16.65 tff(776,plain,
% 16.48/16.65 (member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[461])).
% 16.48/16.65 tff(777,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[33, 776])).
% 16.48/16.65 tff(778,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[777, 775])).
% 16.48/16.65 tff(779,assumption,(![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))), introduced(assumption)).
% 16.48/16.65 tff(780,plain,
% 16.48/16.65 (((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | ((~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | (~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(781,plain,
% 16.48/16.65 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | ((~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(782,plain,
% 16.48/16.65 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | (~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[781, 780])).
% 16.48/16.65 tff(783,plain,
% 16.48/16.65 ((~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[782, 779])).
% 16.48/16.65 tff(784,plain,
% 16.48/16.65 (member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[783, 778])).
% 16.48/16.65 tff(785,plain,
% 16.48/16.65 (member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[784, 771])).
% 16.48/16.65 tff(786,plain,
% 16.48/16.65 ((((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6))) <=> member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6)))) | (~((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6)))) | (~member(singleton(A!6), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(787,plain,
% 16.48/16.65 (~((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[786, 785, 769])).
% 16.48/16.65 tff(788,plain,
% 16.48/16.65 (((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6))) | member(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(789,plain,
% 16.48/16.65 (member(singleton(A!6), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[788, 787])).
% 16.48/16.65 tff(790,plain,
% 16.48/16.65 ((~(member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)))) | (~member(singleton(A!6), unordered_pair(U!4, V!3))) | ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(791,plain,
% 16.48/16.65 ((~(member(singleton(A!6), unordered_pair(U!4, V!3)) <=> ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)))) | ((singleton(A!6) = U!4) | (singleton(A!6) = V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[790, 789])).
% 16.48/16.65 tff(792,plain,
% 16.48/16.65 ((singleton(A!6) = U!4) | (singleton(A!6) = V!3)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[791, 767])).
% 16.48/16.65 tff(793,plain,
% 16.48/16.65 (member(singleton(A!6), singleton(U!4)) <=> member(singleton(A!6), singleton(A!6))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[461])).
% 16.48/16.65 tff(794,plain,
% 16.48/16.65 (member(singleton(A!6), singleton(A!6)) <=> member(singleton(A!6), singleton(U!4))),
% 16.48/16.65 inference(symmetry,[status(thm)],[793])).
% 16.48/16.65 tff(795,plain,
% 16.48/16.65 ((~member(singleton(A!6), singleton(A!6))) <=> (~member(singleton(A!6), singleton(U!4)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[794])).
% 16.48/16.65 tff(796,plain,
% 16.48/16.65 (((~member(singleton(A!6), unordered_pair(U!4, V!3))) | member(singleton(A!6), singleton(A!6))) | (~member(singleton(A!6), singleton(A!6)))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(797,plain,
% 16.48/16.65 (~member(singleton(A!6), singleton(A!6))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[796, 787])).
% 16.48/16.65 tff(798,plain,
% 16.48/16.65 (~member(singleton(A!6), singleton(U!4))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[797, 795])).
% 16.48/16.65 tff(799,plain,
% 16.48/16.65 ((~(member(singleton(A!6), singleton(U!4)) <=> (singleton(A!6) = U!4))) | member(singleton(A!6), singleton(U!4)) | (~(singleton(A!6) = U!4))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(800,plain,
% 16.48/16.65 (~(singleton(A!6) = U!4)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[799, 798, 659])).
% 16.48/16.65 tff(801,plain,
% 16.48/16.65 ((~((singleton(A!6) = U!4) | (singleton(A!6) = V!3))) | (singleton(A!6) = U!4) | (singleton(A!6) = V!3)),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(802,plain,
% 16.48/16.65 (singleton(A!6) = V!3),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[801, 800, 792])).
% 16.48/16.65 tff(803,plain,
% 16.48/16.65 (V!3 = singleton(A!6)),
% 16.48/16.65 inference(symmetry,[status(thm)],[802])).
% 16.48/16.65 tff(804,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(805,plain,
% 16.48/16.65 ((member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = U!4))) <=> (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(806,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[805])).
% 16.48/16.65 tff(807,plain,
% 16.48/16.65 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = U!4)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))))),
% 16.48/16.65 inference(transitivity,[status(thm)],[806, 804])).
% 16.48/16.65 tff(808,plain,
% 16.48/16.65 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = U!4)))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(809,plain,
% 16.48/16.65 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[808, 807])).
% 16.48/16.65 tff(810,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[809, 11])).
% 16.48/16.65 tff(811,plain,
% 16.48/16.65 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6)))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(812,plain,
% 16.48/16.65 (~(((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[811, 477])).
% 16.48/16.65 tff(813,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[464])).
% 16.48/16.65 tff(814,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4))) <=> member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(symmetry,[status(thm)],[813])).
% 16.48/16.65 tff(815,plain,
% 16.48/16.65 (((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | ((~member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | (~member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.65 inference(rewrite,[status(thm)],[])).
% 16.48/16.65 tff(816,plain,
% 16.48/16.65 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | ((~member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(817,plain,
% 16.48/16.65 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | (~member(unordered_pair(U!4, V!3), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[816, 815])).
% 16.48/16.65 tff(818,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[817, 199, 779])).
% 16.48/16.65 tff(819,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[818, 814])).
% 16.48/16.65 tff(820,plain,
% 16.48/16.65 ((((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6))) <=> member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6)))) | (~((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6)))) | (~member(unordered_pair(U!4, V!3), difference(unordered_pair(U!4, V!3), singleton(A!6))))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(821,plain,
% 16.48/16.65 (~((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[820, 819, 812])).
% 16.48/16.65 tff(822,plain,
% 16.48/16.65 (((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6))) | member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(823,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[822, 821])).
% 16.48/16.65 tff(824,plain,
% 16.48/16.65 ((~(member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)))) | (~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(825,plain,
% 16.48/16.65 ((~(member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)))) | ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[824, 823])).
% 16.48/16.65 tff(826,plain,
% 16.48/16.65 ((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[825, 810])).
% 16.48/16.65 tff(827,plain,
% 16.48/16.65 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(unordered_pair(U!4, V!3), singleton(U!4)) <=> (unordered_pair(U!4, V!3) = U!4))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(828,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), singleton(U!4)) <=> (unordered_pair(U!4, V!3) = U!4)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[827, 99])).
% 16.48/16.65 tff(829,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), singleton(U!4)) <=> member(unordered_pair(U!4, V!3), singleton(A!6))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[461])).
% 16.48/16.65 tff(830,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), singleton(A!6)) <=> member(unordered_pair(U!4, V!3), singleton(U!4))),
% 16.48/16.65 inference(symmetry,[status(thm)],[829])).
% 16.48/16.65 tff(831,plain,
% 16.48/16.65 ((~member(unordered_pair(U!4, V!3), singleton(A!6))) <=> (~member(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[830])).
% 16.48/16.65 tff(832,plain,
% 16.48/16.65 (((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) | member(unordered_pair(U!4, V!3), singleton(A!6))) | (~member(unordered_pair(U!4, V!3), singleton(A!6)))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(833,plain,
% 16.48/16.65 (~member(unordered_pair(U!4, V!3), singleton(A!6))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[832, 821])).
% 16.48/16.65 tff(834,plain,
% 16.48/16.65 (~member(unordered_pair(U!4, V!3), singleton(U!4))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[833, 831])).
% 16.48/16.65 tff(835,plain,
% 16.48/16.65 ((~(member(unordered_pair(U!4, V!3), singleton(U!4)) <=> (unordered_pair(U!4, V!3) = U!4))) | member(unordered_pair(U!4, V!3), singleton(U!4)) | (~(unordered_pair(U!4, V!3) = U!4))),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(836,plain,
% 16.48/16.65 (~(unordered_pair(U!4, V!3) = U!4)),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[835, 834, 828])).
% 16.48/16.65 tff(837,plain,
% 16.48/16.65 ((~((unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3))) | (unordered_pair(U!4, V!3) = U!4) | (unordered_pair(U!4, V!3) = V!3)),
% 16.48/16.65 inference(tautology,[status(thm)],[])).
% 16.48/16.65 tff(838,plain,
% 16.48/16.65 (unordered_pair(U!4, V!3) = V!3),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[837, 836, 826])).
% 16.48/16.65 tff(839,plain,
% 16.48/16.65 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 16.48/16.65 inference(transitivity,[status(thm)],[838, 803])).
% 16.48/16.65 tff(840,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> member(unordered_pair(U!4, V!3), singleton(A!6))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[839])).
% 16.48/16.65 tff(841,plain,
% 16.48/16.65 (member(unordered_pair(U!4, V!3), singleton(A!6)) <=> member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(symmetry,[status(thm)],[840])).
% 16.48/16.65 tff(842,plain,
% 16.48/16.65 ((~member(unordered_pair(U!4, V!3), singleton(A!6))) <=> (~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)))),
% 16.48/16.65 inference(monotonicity,[status(thm)],[841])).
% 16.48/16.65 tff(843,plain,
% 16.48/16.65 (~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 16.48/16.65 inference(modus_ponens,[status(thm)],[833, 842])).
% 16.48/16.65 tff(844,plain,
% 16.48/16.65 ($false),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[823, 843])).
% 16.48/16.65 tff(845,plain,((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))) | (~(singleton(U!4) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.65 tff(846,plain,
% 16.48/16.65 (~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[845, 179])).
% 16.48/16.65 tff(847,assumption,((~((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))))), introduced(assumption)).
% 16.48/16.65 tff(848,plain,
% 16.48/16.65 ((~![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(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))))))),
% 16.48/16.65 inference(quant_inst,[status(thm)],[])).
% 16.48/16.65 tff(849,plain,
% 16.48/16.65 ($false),
% 16.48/16.65 inference(unit_resolution,[status(thm)],[848, 49, 847])).
% 16.48/16.65 tff(850,plain,(~((~((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4))))))))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.66 tff(851,plain,
% 16.48/16.66 (((~((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))))) | ((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(852,plain,
% 16.48/16.66 ((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[851, 850])).
% 16.48/16.66 tff(853,plain,
% 16.48/16.66 ((~((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(854,plain,
% 16.48/16.66 ((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[853, 852])).
% 16.48/16.66 tff(855,plain,
% 16.48/16.66 (~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[854, 846])).
% 16.48/16.66 tff(856,plain,
% 16.48/16.66 (((~((~subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | ![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(X, difference(unordered_pair(U!4, V!3), singleton(U!4)))))) | (~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))))) | (subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4))))))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(857,plain,
% 16.48/16.66 (subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[856, 850])).
% 16.48/16.66 tff(858,plain,
% 16.48/16.66 ((~(subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4))))))) | subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(859,plain,
% 16.48/16.66 (subset(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), difference(unordered_pair(U!4, V!3), singleton(U!4))) | (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[858, 857])).
% 16.48/16.66 tff(860,plain,
% 16.48/16.66 (~((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[859, 855])).
% 16.48/16.66 tff(861,plain,
% 16.48/16.66 (((~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), difference(unordered_pair(U!4, V!3), singleton(U!4)))) | member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(862,plain,
% 16.48/16.66 (member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[861, 860])).
% 16.48/16.66 tff(863,plain,
% 16.48/16.66 ((~(member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))))) | (~member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(864,plain,
% 16.48/16.66 ((~(member(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))))) | ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[863, 862])).
% 16.48/16.66 tff(865,plain,
% 16.48/16.66 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[864, 760])).
% 16.48/16.66 tff(866,plain,
% 16.48/16.66 ((~((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)))) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(867,plain,
% 16.48/16.66 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)) | (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[866, 865])).
% 16.48/16.66 tff(868,plain,
% 16.48/16.66 (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = unordered_pair(U!4, V!3)),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[867, 758])).
% 16.48/16.66 tff(869,plain,
% 16.48/16.66 (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[868, 757])).
% 16.48/16.66 tff(870,plain,
% 16.48/16.66 ($false),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[758, 869])).
% 16.48/16.66 tff(871,plain,((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)) | (~(unordered_pair(U!4, V!3) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.66 tff(872,plain,
% 16.48/16.66 (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[871, 750])).
% 16.48/16.66 tff(873,assumption,(member(singleton(A!6), singleton(A!6))), introduced(assumption)).
% 16.48/16.66 tff(874,plain,
% 16.48/16.66 (member(singleton(A!6), singleton(U!4))),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[873, 641])).
% 16.48/16.66 tff(875,assumption,(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)), introduced(assumption)).
% 16.48/16.66 tff(876,plain,
% 16.48/16.66 (singleton(A!6) = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(symmetry,[status(thm)],[875])).
% 16.48/16.66 tff(877,plain,
% 16.48/16.66 (singleton(A!6) = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(transitivity,[status(thm)],[876, 752])).
% 16.48/16.66 tff(878,plain,
% 16.48/16.66 ((singleton(A!6) = U!4) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = U!4)),
% 16.48/16.66 inference(monotonicity,[status(thm)],[877])).
% 16.48/16.66 tff(879,plain,
% 16.48/16.66 ((tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = U!4) <=> (singleton(A!6) = U!4)),
% 16.48/16.66 inference(symmetry,[status(thm)],[878])).
% 16.48/16.66 tff(880,plain,
% 16.48/16.66 ((U!4 = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = U!4)),
% 16.48/16.66 inference(commutativity,[status(thm)],[])).
% 16.48/16.66 tff(881,assumption,(~(member(singleton(A!6), singleton(A!6)) <=> (singleton(A!6) = A!6))), introduced(assumption)).
% 16.48/16.66 tff(882,plain,
% 16.48/16.66 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(singleton(A!6), singleton(A!6)) <=> (singleton(A!6) = A!6))),
% 16.48/16.66 inference(quant_inst,[status(thm)],[])).
% 16.48/16.66 tff(883,plain,
% 16.48/16.66 ($false),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[882, 99, 881])).
% 16.48/16.66 tff(884,plain,(member(singleton(A!6), singleton(A!6)) <=> (singleton(A!6) = A!6)), inference(lemma,lemma(discharge,[]))).
% 16.48/16.66 tff(885,plain,
% 16.48/16.66 ((~(member(singleton(A!6), singleton(A!6)) <=> (singleton(A!6) = A!6))) | (~member(singleton(A!6), singleton(A!6))) | (singleton(A!6) = A!6)),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(886,plain,
% 16.48/16.66 ((~member(singleton(A!6), singleton(A!6))) | (singleton(A!6) = A!6)),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[885, 884])).
% 16.48/16.66 tff(887,plain,
% 16.48/16.66 (singleton(A!6) = A!6),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[886, 873])).
% 16.48/16.66 tff(888,plain,
% 16.48/16.66 (A!6 = singleton(A!6)),
% 16.48/16.66 inference(symmetry,[status(thm)],[887])).
% 16.48/16.66 tff(889,plain,
% 16.48/16.66 (A!6 = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(transitivity,[status(thm)],[888, 876, 752])).
% 16.48/16.66 tff(890,plain,
% 16.48/16.66 ((U!4 = A!6) <=> (U!4 = tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[889])).
% 16.48/16.66 tff(891,plain,
% 16.48/16.66 ((U!4 = A!6) <=> (tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = U!4)),
% 16.48/16.66 inference(transitivity,[status(thm)],[890, 880])).
% 16.48/16.66 tff(892,plain,
% 16.48/16.66 ((U!4 = A!6) <=> (singleton(A!6) = U!4)),
% 16.48/16.66 inference(transitivity,[status(thm)],[891, 879])).
% 16.48/16.66 tff(893,plain,
% 16.48/16.66 ((~(U!4 = A!6)) <=> (~(singleton(A!6) = U!4))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[892])).
% 16.48/16.66 tff(894,plain,
% 16.48/16.66 (~(singleton(A!6) = U!4)),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[314, 893])).
% 16.48/16.66 tff(895,plain,
% 16.48/16.66 ($false),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[665, 894, 874, 659])).
% 16.48/16.66 tff(896,plain,((~member(singleton(A!6), singleton(A!6))) | (U!4 = A!6) | (~(tptp_fun_X_0(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.66 tff(897,plain,
% 16.48/16.66 (~member(singleton(A!6), singleton(A!6))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[896, 872, 314])).
% 16.48/16.66 tff(898,plain,
% 16.48/16.66 ((~(member(singleton(A!6), singleton(A!6)) <=> (singleton(A!6) = A!6))) | member(singleton(A!6), singleton(A!6)) | (~(singleton(A!6) = A!6))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(899,plain,
% 16.48/16.66 (member(singleton(A!6), singleton(A!6)) | (~(singleton(A!6) = A!6))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[898, 884])).
% 16.48/16.66 tff(900,plain,
% 16.48/16.66 (~(singleton(A!6) = A!6)),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[899, 897])).
% 16.48/16.66 tff(901,plain,
% 16.48/16.66 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(902,plain,
% 16.48/16.66 ((member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> ((A!6 = singleton(A!6)) | (A!6 = singleton(A!6)))) <=> (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6)))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(903,plain,
% 16.48/16.66 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> ((A!6 = singleton(A!6)) | (A!6 = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6))))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[902])).
% 16.48/16.66 tff(904,plain,
% 16.48/16.66 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> ((A!6 = singleton(A!6)) | (A!6 = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6))))),
% 16.48/16.66 inference(transitivity,[status(thm)],[903, 901])).
% 16.48/16.66 tff(905,plain,
% 16.48/16.66 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> ((A!6 = singleton(A!6)) | (A!6 = singleton(A!6))))),
% 16.48/16.66 inference(quant_inst,[status(thm)],[])).
% 16.48/16.66 tff(906,plain,
% 16.48/16.66 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6)))),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[905, 904])).
% 16.48/16.66 tff(907,plain,
% 16.48/16.66 (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[906, 11])).
% 16.48/16.66 tff(908,plain,
% 16.48/16.66 (member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[253])).
% 16.48/16.66 tff(909,plain,
% 16.48/16.66 (member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) <=> member(A!6, unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.48/16.66 inference(symmetry,[status(thm)],[908])).
% 16.48/16.66 tff(910,assumption,(member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 16.48/16.66 tff(911,plain,
% 16.48/16.66 (member(A!6, unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[910, 909])).
% 16.48/16.66 tff(912,plain,
% 16.48/16.66 ((A!6 = singleton(A!6)) <=> (singleton(A!6) = A!6)),
% 16.48/16.66 inference(commutativity,[status(thm)],[])).
% 16.48/16.66 tff(913,plain,
% 16.48/16.66 ((singleton(A!6) = A!6) <=> (A!6 = singleton(A!6))),
% 16.48/16.66 inference(symmetry,[status(thm)],[912])).
% 16.48/16.66 tff(914,plain,
% 16.48/16.66 ((~(singleton(A!6) = A!6)) <=> (~(A!6 = singleton(A!6)))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[913])).
% 16.48/16.66 tff(915,assumption,(~(singleton(A!6) = A!6)), introduced(assumption)).
% 16.48/16.66 tff(916,plain,
% 16.48/16.66 (~(A!6 = singleton(A!6))),
% 16.48/16.66 inference(modus_ponens,[status(thm)],[915, 914])).
% 16.48/16.66 tff(917,plain,
% 16.48/16.66 ((~(member(A!6, unordered_pair(singleton(A!6), singleton(A!6))) <=> (A!6 = singleton(A!6)))) | (~member(A!6, unordered_pair(singleton(A!6), singleton(A!6)))) | (A!6 = singleton(A!6))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(918,plain,
% 16.48/16.66 ($false),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[917, 916, 911, 907])).
% 16.48/16.66 tff(919,plain,((~member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | (singleton(A!6) = A!6) | (~(unordered_pair(U!4, V!3) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.66 tff(920,plain,
% 16.48/16.66 (~member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[919, 900, 750])).
% 16.48/16.66 tff(921,plain,
% 16.48/16.66 ((~![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(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))))),
% 16.48/16.66 inference(quant_inst,[status(thm)],[])).
% 16.48/16.66 tff(922,plain,
% 16.48/16.66 (~((~((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[921, 49])).
% 16.48/16.66 tff(923,plain,
% 16.48/16.66 (((~((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))) | ((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.48/16.66 inference(tautology,[status(thm)],[])).
% 16.48/16.66 tff(924,plain,
% 16.48/16.66 ((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[923, 922])).
% 16.48/16.66 tff(925,plain,
% 16.48/16.66 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.66 inference(quant_inst,[status(thm)],[])).
% 16.48/16.66 tff(926,plain,
% 16.48/16.66 (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.66 inference(unit_resolution,[status(thm)],[925, 356])).
% 16.48/16.66 tff(927,plain,
% 16.48/16.66 (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.48/16.66 inference(monotonicity,[status(thm)],[360])).
% 16.48/16.66 tff(928,plain,
% 16.48/16.66 (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.66 inference(symmetry,[status(thm)],[927])).
% 16.48/16.66 tff(929,plain,
% 16.48/16.66 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(930,plain,
% 16.48/16.66 ((~(~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(931,plain,
% 16.48/16.66 ((~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(932,plain,
% 16.48/16.66 (((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(933,plain,
% 16.48/16.66 (((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.66 inference(rewrite,[status(thm)],[])).
% 16.48/16.66 tff(934,plain,
% 16.48/16.66 ((((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> ((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[933])).
% 16.48/16.67 tff(935,plain,
% 16.48/16.67 ((((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.67 inference(transitivity,[status(thm)],[934, 932])).
% 16.48/16.67 tff(936,plain,
% 16.48/16.67 ((((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.67 inference(transitivity,[status(thm)],[935, 931])).
% 16.48/16.67 tff(937,plain,
% 16.48/16.67 ((~(((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (~(~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[936])).
% 16.48/16.67 tff(938,plain,
% 16.48/16.67 ((~(((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.67 inference(transitivity,[status(thm)],[937, 930])).
% 16.48/16.67 tff(939,plain,
% 16.48/16.67 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[938])).
% 16.48/16.67 tff(940,plain,
% 16.48/16.67 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.67 inference(transitivity,[status(thm)],[939, 929])).
% 16.48/16.67 tff(941,plain,
% 16.48/16.67 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 16.48/16.67 inference(quant_inst,[status(thm)],[])).
% 16.48/16.67 tff(942,plain,
% 16.48/16.67 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[941, 940])).
% 16.48/16.67 tff(943,plain,
% 16.48/16.67 (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[942, 372])).
% 16.48/16.67 tff(944,plain,
% 16.48/16.67 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))),
% 16.48/16.67 inference(quant_inst,[status(thm)],[])).
% 16.48/16.67 tff(945,plain,
% 16.48/16.67 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[944, 99])).
% 16.48/16.67 tff(946,plain,
% 16.48/16.67 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[179])).
% 16.48/16.67 tff(947,plain,
% 16.48/16.67 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))),
% 16.48/16.67 inference(symmetry,[status(thm)],[946])).
% 16.48/16.67 tff(948,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))), introduced(assumption)).
% 16.48/16.67 tff(949,plain,
% 16.48/16.67 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[948, 947])).
% 16.48/16.67 tff(950,plain,
% 16.48/16.67 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))),
% 16.48/16.67 inference(quant_inst,[status(thm)],[])).
% 16.48/16.67 tff(951,plain,
% 16.48/16.67 (member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[950, 99])).
% 16.48/16.67 tff(952,plain,
% 16.48/16.67 ((~(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(953,plain,
% 16.48/16.67 ((~(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))) | (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[952, 948])).
% 16.48/16.67 tff(954,plain,
% 16.48/16.67 (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[953, 951])).
% 16.48/16.67 tff(955,plain,
% 16.48/16.67 ((tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4) <=> (A!6 = U!4)),
% 16.48/16.67 inference(monotonicity,[status(thm)],[954])).
% 16.48/16.67 tff(956,plain,
% 16.48/16.67 ((tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4) <=> (U!4 = A!6)),
% 16.48/16.67 inference(transitivity,[status(thm)],[955, 323])).
% 16.48/16.67 tff(957,plain,
% 16.48/16.67 ((U!4 = A!6) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 16.48/16.67 inference(symmetry,[status(thm)],[956])).
% 16.48/16.67 tff(958,plain,
% 16.48/16.67 ((~(U!4 = A!6)) <=> (~(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[957])).
% 16.48/16.67 tff(959,plain,
% 16.48/16.67 (~(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[314, 958])).
% 16.48/16.67 tff(960,plain,
% 16.48/16.67 ((~(member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))) | (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))) | (tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(961,plain,
% 16.48/16.67 ($false),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[960, 959, 949, 945])).
% 16.48/16.67 tff(962,plain,((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | (U!4 = A!6)), inference(lemma,lemma(discharge,[]))).
% 16.48/16.67 tff(963,plain,
% 16.48/16.67 (~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[962, 314])).
% 16.48/16.67 tff(964,plain,
% 16.48/16.67 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.48/16.67 inference(rewrite,[status(thm)],[])).
% 16.48/16.67 tff(965,plain,
% 16.48/16.67 ((member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))) <=> (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))),
% 16.48/16.67 inference(rewrite,[status(thm)],[])).
% 16.48/16.67 tff(966,plain,
% 16.48/16.67 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[965])).
% 16.48/16.67 tff(967,plain,
% 16.48/16.67 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.48/16.67 inference(transitivity,[status(thm)],[966, 964])).
% 16.48/16.67 tff(968,plain,
% 16.48/16.67 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))))),
% 16.48/16.67 inference(quant_inst,[status(thm)],[])).
% 16.48/16.67 tff(969,plain,
% 16.48/16.67 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[968, 967])).
% 16.48/16.67 tff(970,plain,
% 16.48/16.67 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[969, 11])).
% 16.48/16.67 tff(971,plain,
% 16.48/16.67 (unordered_pair(singleton(A!6), singleton(A!6)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 16.48/16.67 inference(transitivity,[status(thm)],[253, 359])).
% 16.48/16.67 tff(972,plain,
% 16.48/16.67 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[971])).
% 16.48/16.67 tff(973,plain,
% 16.48/16.67 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.48/16.67 inference(symmetry,[status(thm)],[972])).
% 16.48/16.67 tff(974,plain,
% 16.48/16.67 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6)))),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[571, 973])).
% 16.48/16.67 tff(975,plain,
% 16.48/16.67 ((~(member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6))) <=> (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)))) | (~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(A!6), singleton(A!6)))) | (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6))),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(976,plain,
% 16.48/16.67 (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) = singleton(A!6)),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[975, 974, 970])).
% 16.48/16.67 tff(977,plain,
% 16.48/16.67 (singleton(A!6) = tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 16.48/16.67 inference(symmetry,[status(thm)],[976])).
% 16.48/16.67 tff(978,plain,
% 16.48/16.67 (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[977, 360])).
% 16.48/16.67 tff(979,plain,
% 16.48/16.67 (member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.67 inference(symmetry,[status(thm)],[978])).
% 16.48/16.67 tff(980,plain,
% 16.48/16.67 ((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> (~member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(monotonicity,[status(thm)],[979])).
% 16.48/16.67 tff(981,plain,
% 16.48/16.67 (~member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.67 inference(modus_ponens,[status(thm)],[450, 980])).
% 16.48/16.67 tff(982,plain,
% 16.48/16.67 (((~((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))))) | (subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(983,plain,
% 16.48/16.67 (subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[982, 922])).
% 16.48/16.67 tff(984,assumption,(~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))), introduced(assumption)).
% 16.48/16.67 tff(985,plain,
% 16.48/16.67 (((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(986,plain,
% 16.48/16.67 ((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[985, 984])).
% 16.48/16.67 tff(987,plain,
% 16.48/16.67 ((~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))) | subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(988,plain,
% 16.48/16.67 ((~(subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))))) | subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[987, 986])).
% 16.48/16.67 tff(989,plain,
% 16.48/16.67 (subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[988, 983])).
% 16.48/16.67 tff(990,plain,
% 16.48/16.67 ((~(member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | (~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.67 inference(tautology,[status(thm)],[])).
% 16.48/16.67 tff(991,plain,
% 16.48/16.67 (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[990, 989, 926])).
% 16.48/16.67 tff(992,plain,
% 16.48/16.67 ($false),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[991, 981])).
% 16.48/16.67 tff(993,plain,(((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | member(tptp_fun_X_0(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) | (~(unordered_pair(U!4, V!3) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.67 tff(994,plain,
% 16.48/16.67 ((~member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[993, 750, 963])).
% 16.48/16.67 tff(995,plain,
% 16.48/16.67 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[612, 994])).
% 16.48/16.67 tff(996,plain,
% 16.48/16.67 (![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.67 inference(unit_resolution,[status(thm)],[617, 995])).
% 16.48/16.67 tff(997,plain,
% 16.48/16.67 (((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | ((~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(998,plain,
% 16.48/16.68 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | ((~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.68 inference(quant_inst,[status(thm)],[])).
% 16.48/16.68 tff(999,plain,
% 16.48/16.68 ((~![X: $i] : ((~member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(X, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | (~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[998, 997])).
% 16.48/16.68 tff(1000,plain,
% 16.48/16.68 (member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[999, 996, 163])).
% 16.48/16.68 tff(1001,plain,
% 16.48/16.68 ((~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 16.48/16.68 inference(tautology,[status(thm)],[])).
% 16.48/16.68 tff(1002,plain,
% 16.48/16.68 ((~(member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(singleton(A!6), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1001, 1000])).
% 16.48/16.68 tff(1003,plain,
% 16.48/16.68 (member(singleton(A!6), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1002, 943])).
% 16.48/16.68 tff(1004,plain,
% 16.48/16.68 (member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1003, 928])).
% 16.48/16.68 tff(1005,plain,
% 16.48/16.68 ((~(member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) <=> subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), power_set(unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.68 inference(tautology,[status(thm)],[])).
% 16.48/16.68 tff(1006,plain,
% 16.48/16.68 (subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1005, 1004, 926])).
% 16.48/16.68 tff(1007,plain,
% 16.48/16.68 ((~((~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))))) | (~subset(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(tautology,[status(thm)],[])).
% 16.48/16.68 tff(1008,plain,
% 16.48/16.68 (![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1007, 1006, 924])).
% 16.48/16.68 tff(1009,plain,
% 16.48/16.68 (((~![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | ((~member(A!6, singleton(A!6))) | member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(A!6, singleton(A!6))) | member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1010,plain,
% 16.48/16.68 ((~![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | ((~member(A!6, singleton(A!6))) | member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))),
% 16.48/16.68 inference(quant_inst,[status(thm)],[])).
% 16.48/16.68 tff(1011,plain,
% 16.48/16.68 ((~![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3))))) | (~member(A!6, singleton(A!6))) | member(A!6, unordered_pair(singleton(A!6), unordered_pair(U!4, V!3)))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 16.48/16.68 tff(1012,plain,
% 16.48/16.68 ($false),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1011, 1008, 920, 313])).
% 16.48/16.68 tff(1013,plain,(U!4 = A!6), inference(lemma,lemma(discharge,[]))).
% 16.48/16.68 tff(1014,plain,
% 16.48/16.68 (A!6 = U!4),
% 16.48/16.68 inference(symmetry,[status(thm)],[1013])).
% 16.48/16.68 tff(1015,plain,
% 16.48/16.68 (A!6 = B!5),
% 16.48/16.68 inference(transitivity,[status(thm)],[1014, 302])).
% 16.48/16.68 tff(1016,plain,
% 16.48/16.68 (unordered_pair(A!6, A!6) = unordered_pair(A!6, B!5)),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1015])).
% 16.48/16.68 tff(1017,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, A!6)) <=> member(V!3, unordered_pair(A!6, B!5))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1016])).
% 16.48/16.68 tff(1018,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, B!5)) <=> member(V!3, unordered_pair(A!6, A!6))),
% 16.48/16.68 inference(symmetry,[status(thm)],[1017])).
% 16.48/16.68 tff(1019,plain,
% 16.48/16.68 (unordered_pair(A!6, V!3) = unordered_pair(U!4, V!3)),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1014])).
% 16.48/16.68 tff(1020,plain,
% 16.48/16.68 (unordered_pair(A!6, V!3) = unordered_pair(A!6, B!5)),
% 16.48/16.68 inference(transitivity,[status(thm)],[1019, 272])).
% 16.48/16.68 tff(1021,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, V!3)) <=> member(V!3, unordered_pair(A!6, B!5))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1020])).
% 16.48/16.68 tff(1022,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, B!5)) <=> member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(symmetry,[status(thm)],[1021])).
% 16.48/16.68 tff(1023,plain,
% 16.48/16.68 ((~member(V!3, unordered_pair(A!6, B!5))) <=> (~member(V!3, unordered_pair(A!6, V!3)))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1022])).
% 16.48/16.68 tff(1024,assumption,(~member(V!3, unordered_pair(A!6, B!5))), introduced(assumption)).
% 16.48/16.68 tff(1025,plain,
% 16.48/16.68 (~member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 16.48/16.68 tff(1026,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(V!3, unordered_pair(A!6, V!3))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(V!3, unordered_pair(A!6, V!3)))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1027,plain,
% 16.48/16.68 ((member(V!3, unordered_pair(A!6, V!3)) <=> $true) <=> member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1028,plain,
% 16.48/16.68 (($true | (V!3 = A!6)) <=> $true),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1029,plain,
% 16.48/16.68 ((V!3 = V!3) <=> $true),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1030,plain,
% 16.48/16.68 (((V!3 = V!3) | (V!3 = A!6)) <=> ($true | (V!3 = A!6))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1029])).
% 16.48/16.68 tff(1031,plain,
% 16.48/16.68 (((V!3 = V!3) | (V!3 = A!6)) <=> $true),
% 16.48/16.68 inference(transitivity,[status(thm)],[1030, 1028])).
% 16.48/16.68 tff(1032,plain,
% 16.48/16.68 ((member(V!3, unordered_pair(A!6, V!3)) <=> ((V!3 = V!3) | (V!3 = A!6))) <=> (member(V!3, unordered_pair(A!6, V!3)) <=> $true)),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1031])).
% 16.48/16.68 tff(1033,plain,
% 16.48/16.68 ((member(V!3, unordered_pair(A!6, V!3)) <=> ((V!3 = V!3) | (V!3 = A!6))) <=> member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(transitivity,[status(thm)],[1032, 1027])).
% 16.48/16.68 tff(1034,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, V!3)) <=> ((V!3 = V!3) | (V!3 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(V!3, unordered_pair(A!6, V!3)))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1033])).
% 16.48/16.68 tff(1035,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, V!3)) <=> ((V!3 = V!3) | (V!3 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(V!3, unordered_pair(A!6, V!3)))),
% 16.48/16.68 inference(transitivity,[status(thm)],[1034, 1026])).
% 16.48/16.68 tff(1036,plain,
% 16.48/16.68 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, V!3)) <=> ((V!3 = V!3) | (V!3 = A!6)))),
% 16.48/16.68 inference(quant_inst,[status(thm)],[])).
% 16.48/16.68 tff(1037,plain,
% 16.48/16.68 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 16.48/16.68 tff(1038,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, V!3))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1037, 11])).
% 16.48/16.68 tff(1039,plain,
% 16.48/16.68 ($false),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1038, 1025])).
% 16.48/16.68 tff(1040,plain,(member(V!3, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 16.48/16.68 tff(1041,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, A!6))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1040, 1018])).
% 16.48/16.68 tff(1042,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6)))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1043,plain,
% 16.48/16.68 ((member(V!3, unordered_pair(A!6, A!6)) <=> ((V!3 = A!6) | (V!3 = A!6))) <=> (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6))),
% 16.48/16.68 inference(rewrite,[status(thm)],[])).
% 16.48/16.68 tff(1044,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> ((V!3 = A!6) | (V!3 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6)))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1043])).
% 16.48/16.68 tff(1045,plain,
% 16.48/16.68 (((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> ((V!3 = A!6) | (V!3 = A!6)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6)))),
% 16.48/16.68 inference(transitivity,[status(thm)],[1044, 1042])).
% 16.48/16.68 tff(1046,plain,
% 16.48/16.68 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> ((V!3 = A!6) | (V!3 = A!6)))),
% 16.48/16.68 inference(quant_inst,[status(thm)],[])).
% 16.48/16.68 tff(1047,plain,
% 16.48/16.68 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6))),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 16.48/16.68 tff(1048,plain,
% 16.48/16.68 (member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6)),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1047, 11])).
% 16.48/16.68 tff(1049,plain,
% 16.48/16.68 ((A!6 = V!3) <=> (V!3 = A!6)),
% 16.48/16.68 inference(commutativity,[status(thm)],[])).
% 16.48/16.68 tff(1050,plain,
% 16.48/16.68 (B!5 = A!6),
% 16.48/16.68 inference(transitivity,[status(thm)],[301, 1013])).
% 16.48/16.68 tff(1051,plain,
% 16.48/16.68 ((B!5 = V!3) <=> (A!6 = V!3)),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1050])).
% 16.48/16.68 tff(1052,plain,
% 16.48/16.68 ((B!5 = V!3) <=> (V!3 = A!6)),
% 16.48/16.68 inference(transitivity,[status(thm)],[1051, 1049])).
% 16.48/16.68 tff(1053,plain,
% 16.48/16.68 ((~(B!5 = V!3)) <=> (~(V!3 = A!6))),
% 16.48/16.68 inference(monotonicity,[status(thm)],[1052])).
% 16.48/16.68 tff(1054,plain,
% 16.48/16.68 (~(V!3 = A!6)),
% 16.48/16.68 inference(modus_ponens,[status(thm)],[298, 1053])).
% 16.48/16.68 tff(1055,plain,
% 16.48/16.68 ((~(member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6))) | (~member(V!3, unordered_pair(A!6, A!6))) | (V!3 = A!6)),
% 16.48/16.68 inference(tautology,[status(thm)],[])).
% 16.48/16.68 tff(1056,plain,
% 16.48/16.68 ((~(member(V!3, unordered_pair(A!6, A!6)) <=> (V!3 = A!6))) | (~member(V!3, unordered_pair(A!6, A!6)))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1055, 1054])).
% 16.48/16.68 tff(1057,plain,
% 16.48/16.68 (~member(V!3, unordered_pair(A!6, A!6))),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1056, 1048])).
% 16.48/16.68 tff(1058,plain,
% 16.48/16.68 ($false),
% 16.48/16.68 inference(unit_resolution,[status(thm)],[1057, 1041])).
% 16.48/16.68 % SZS output end Proof
% 16.48/16.69 % E exiting
%------------------------------------------------------------------------------