%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET016+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:48 AM UTC 2025
% Result : Theorem 4.94s 5.19s
% Output : Proof 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016+4 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:03:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.94/5.19 % SZS status Theorem
% 4.94/5.19 % SZS output start Proof
% 4.94/5.19 tff(member_type, type, (
% 4.94/5.19 member: ( $i * $i ) > $o)).
% 4.94/5.19 tff(unordered_pair_type, type, (
% 4.94/5.19 unordered_pair: ( $i * $i ) > $i)).
% 4.94/5.19 tff(tptp_fun_V_3_type, type, (
% 4.94/5.19 tptp_fun_V_3: $i)).
% 4.94/5.19 tff(tptp_fun_B_5_type, type, (
% 4.94/5.19 tptp_fun_B_5: $i)).
% 4.94/5.19 tff(tptp_fun_A_6_type, type, (
% 4.94/5.19 tptp_fun_A_6: $i)).
% 4.94/5.19 tff(tptp_fun_U_4_type, type, (
% 4.94/5.19 tptp_fun_U_4: $i)).
% 4.94/5.19 tff(singleton_type, type, (
% 4.94/5.19 singleton: $i > $i)).
% 4.94/5.19 tff(equal_set_type, type, (
% 4.94/5.19 equal_set: ( $i * $i ) > $o)).
% 4.94/5.19 tff(subset_type, type, (
% 4.94/5.19 subset: ( $i * $i ) > $o)).
% 4.94/5.19 tff(tptp_fun_X_0_type, type, (
% 4.94/5.19 tptp_fun_X_0: ( $i * $i ) > $i)).
% 4.94/5.19 tff(tptp_fun_Y_1_type, type, (
% 4.94/5.19 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 4.94/5.19 tff(intersection_type, type, (
% 4.94/5.19 intersection: ( $i * $i ) > $i)).
% 4.94/5.19 tff(power_set_type, type, (
% 4.94/5.19 power_set: $i > $i)).
% 4.94/5.19 tff(sum_type, type, (
% 4.94/5.19 sum: $i > $i)).
% 4.94/5.19 tff(difference_type, type, (
% 4.94/5.19 difference: ( $i * $i ) > $i)).
% 4.94/5.19 tff(1,plain,
% 4.94/5.19 (^[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))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(2,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[1])).
% 4.94/5.19 tff(3,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(4,plain,
% 4.94/5.19 (^[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))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(5,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[4])).
% 4.94/5.19 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = A) | (X = B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','unordered_pair')).
% 4.94/5.19 tff(7,plain,
% 4.94/5.19 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[6, 5])).
% 4.94/5.19 tff(8,plain,
% 4.94/5.19 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.94/5.19 tff(9,plain,(
% 4.94/5.19 ![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 4.94/5.19 inference(skolemize,[status(sab)],[8])).
% 4.94/5.19 tff(10,plain,
% 4.94/5.19 (![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[9, 2])).
% 4.94/5.19 tff(11,plain,
% 4.94/5.19 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(U!4, unordered_pair(A!6, B!5)) <=> ((U!4 = B!5) | (U!4 = A!6)))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(12,plain,
% 4.94/5.19 (member(U!4, unordered_pair(A!6, B!5)) <=> ((U!4 = B!5) | (U!4 = A!6))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[11, 10])).
% 4.94/5.19 tff(13,assumption,(~(member(U!4, singleton(A!6)) <=> (U!4 = A!6))), introduced(assumption)).
% 4.94/5.19 tff(14,plain,
% 4.94/5.19 (^[X: $i, A: $i] : refl((member(X, singleton(A)) <=> (X = A)) <=> (member(X, singleton(A)) <=> (X = A)))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(15,plain,
% 4.94/5.19 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[14])).
% 4.94/5.19 tff(16,plain,
% 4.94/5.19 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A)) <=> ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(17,axiom,(![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','singleton')).
% 4.94/5.19 tff(18,plain,
% 4.94/5.19 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[17, 16])).
% 4.94/5.19 tff(19,plain,(
% 4.94/5.19 ![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 4.94/5.19 inference(skolemize,[status(sab)],[18])).
% 4.94/5.19 tff(20,plain,
% 4.94/5.19 (![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[19, 15])).
% 4.94/5.19 tff(21,plain,
% 4.94/5.19 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(U!4, singleton(A!6)) <=> (U!4 = A!6))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(22,plain,
% 4.94/5.19 ($false),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 4.94/5.19 tff(23,plain,(member(U!4, singleton(A!6)) <=> (U!4 = A!6)), inference(lemma,lemma(discharge,[]))).
% 4.94/5.19 tff(24,assumption,(U!4 = A!6), introduced(assumption)).
% 4.94/5.19 tff(25,plain,
% 4.94/5.19 (A!6 = U!4),
% 4.94/5.19 inference(symmetry,[status(thm)],[24])).
% 4.94/5.19 tff(26,plain,
% 4.94/5.19 ((~![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)))) | (A = U))) <=> (~![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)))) | (A = U)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(27,plain,
% 4.94/5.19 ((~![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))) => (A = U))) <=> (~![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)))) | (A = U)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(28,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))) => (A = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI50a')).
% 4.94/5.19 tff(29,plain,
% 4.94/5.19 (~![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)))) | (A = U))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[28, 27])).
% 4.94/5.19 tff(30,plain,
% 4.94/5.19 (~![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)))) | (A = U))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[29, 26])).
% 4.94/5.19 tff(31,plain,
% 4.94/5.19 (~![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)))) | (A = U))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[30, 26])).
% 4.94/5.19 tff(32,plain,
% 4.94/5.19 (~![A: $i, B: $i, U: $i, V: $i] : ((~equal_set(unordered_pair(singleton(A), unordered_pair(A, B)), unordered_pair(singleton(U), unordered_pair(U, V)))) | (A = U))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[31, 26])).
% 4.94/5.19 tff(33,plain,(
% 4.94/5.19 ~((~equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (A!6 = U!4))),
% 4.94/5.19 inference(skolemize,[status(sab)],[32])).
% 4.94/5.19 tff(34,plain,
% 4.94/5.19 (~(A!6 = U!4)),
% 4.94/5.19 inference(or_elim,[status(thm)],[33])).
% 4.94/5.19 tff(35,plain,
% 4.94/5.19 ($false),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[34, 25])).
% 4.94/5.19 tff(36,plain,(~(U!4 = A!6)), inference(lemma,lemma(discharge,[]))).
% 4.94/5.19 tff(37,plain,
% 4.94/5.19 ((~(member(U!4, singleton(A!6)) <=> (U!4 = A!6))) | (~member(U!4, singleton(A!6))) | (U!4 = A!6)),
% 4.94/5.19 inference(tautology,[status(thm)],[])).
% 4.94/5.19 tff(38,plain,
% 4.94/5.19 ((~(member(U!4, singleton(A!6)) <=> (U!4 = A!6))) | (~member(U!4, singleton(A!6)))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[37, 36])).
% 4.94/5.19 tff(39,plain,
% 4.94/5.19 (~member(U!4, singleton(A!6))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[38, 23])).
% 4.94/5.19 tff(40,assumption,(singleton(U!4) = singleton(A!6)), introduced(assumption)).
% 4.94/5.19 tff(41,plain,
% 4.94/5.19 (member(U!4, singleton(U!4)) <=> member(U!4, singleton(A!6))),
% 4.94/5.19 inference(monotonicity,[status(thm)],[40])).
% 4.94/5.19 tff(42,plain,
% 4.94/5.19 (member(U!4, singleton(A!6)) <=> member(U!4, singleton(U!4))),
% 4.94/5.19 inference(symmetry,[status(thm)],[41])).
% 4.94/5.19 tff(43,plain,
% 4.94/5.19 ((~member(U!4, singleton(A!6))) <=> (~member(U!4, singleton(U!4)))),
% 4.94/5.19 inference(monotonicity,[status(thm)],[42])).
% 4.94/5.19 tff(44,assumption,(~member(U!4, singleton(A!6))), introduced(assumption)).
% 4.94/5.19 tff(45,plain,
% 4.94/5.19 (~member(U!4, singleton(U!4))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[44, 43])).
% 4.94/5.19 tff(46,plain,
% 4.94/5.19 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(U!4, singleton(U!4))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(U!4, singleton(U!4)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(47,plain,
% 4.94/5.19 ((member(U!4, singleton(U!4)) <=> $true) <=> member(U!4, singleton(U!4))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(48,plain,
% 4.94/5.19 ((U!4 = U!4) <=> $true),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(49,plain,
% 4.94/5.19 ((member(U!4, singleton(U!4)) <=> (U!4 = U!4)) <=> (member(U!4, singleton(U!4)) <=> $true)),
% 4.94/5.19 inference(monotonicity,[status(thm)],[48])).
% 4.94/5.19 tff(50,plain,
% 4.94/5.19 ((member(U!4, singleton(U!4)) <=> (U!4 = U!4)) <=> member(U!4, singleton(U!4))),
% 4.94/5.19 inference(transitivity,[status(thm)],[49, 47])).
% 4.94/5.19 tff(51,plain,
% 4.94/5.19 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(U!4, singleton(U!4)) <=> (U!4 = U!4))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(U!4, singleton(U!4)))),
% 4.94/5.19 inference(monotonicity,[status(thm)],[50])).
% 4.94/5.19 tff(52,plain,
% 4.94/5.19 (((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(U!4, singleton(U!4)) <=> (U!4 = U!4))) <=> ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(U!4, singleton(U!4)))),
% 4.94/5.19 inference(transitivity,[status(thm)],[51, 46])).
% 4.94/5.19 tff(53,plain,
% 4.94/5.19 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(U!4, singleton(U!4)) <=> (U!4 = U!4))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(54,plain,
% 4.94/5.19 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | member(U!4, singleton(U!4))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[53, 52])).
% 4.94/5.19 tff(55,plain,
% 4.94/5.19 (member(U!4, singleton(U!4))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[54, 20])).
% 4.94/5.19 tff(56,plain,
% 4.94/5.19 ($false),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[55, 45])).
% 4.94/5.19 tff(57,plain,(member(U!4, singleton(A!6)) | (~(singleton(U!4) = singleton(A!6)))), inference(lemma,lemma(discharge,[]))).
% 4.94/5.19 tff(58,plain,
% 4.94/5.19 (~(singleton(U!4) = singleton(A!6))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[57, 39])).
% 4.94/5.19 tff(59,plain,
% 4.94/5.19 (((~![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)))))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(60,plain,
% 4.94/5.19 ((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))))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(61,plain,
% 4.94/5.19 (((~![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)))))),
% 4.94/5.19 inference(monotonicity,[status(thm)],[60])).
% 4.94/5.19 tff(62,plain,
% 4.94/5.19 (((~![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)))))),
% 4.94/5.19 inference(transitivity,[status(thm)],[61, 59])).
% 4.94/5.19 tff(63,plain,
% 4.94/5.19 ((~![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))))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(64,plain,
% 4.94/5.19 ((~![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))))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.94/5.19 tff(65,plain,
% 4.94/5.19 (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)))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[64, 10])).
% 4.94/5.19 tff(66,assumption,(~member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 4.94/5.19 tff(67,plain,
% 4.94/5.19 (((~![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))))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(68,plain,
% 4.94/5.19 ((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)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(69,plain,
% 4.94/5.19 (((singleton(U!4) = unordered_pair(U!4, V!3)) | $true) <=> $true),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(70,plain,
% 4.94/5.19 ((singleton(U!4) = singleton(U!4)) <=> $true),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(71,plain,
% 4.94/5.19 (((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)),
% 4.94/5.19 inference(monotonicity,[status(thm)],[70])).
% 4.94/5.19 tff(72,plain,
% 4.94/5.19 (((singleton(U!4) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(U!4))) <=> $true),
% 4.94/5.19 inference(transitivity,[status(thm)],[71, 69])).
% 4.94/5.19 tff(73,plain,
% 4.94/5.19 ((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)),
% 4.94/5.19 inference(monotonicity,[status(thm)],[72])).
% 4.94/5.19 tff(74,plain,
% 4.94/5.19 ((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)))),
% 4.94/5.19 inference(transitivity,[status(thm)],[73, 68])).
% 4.94/5.19 tff(75,plain,
% 4.94/5.19 (((~![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))))),
% 4.94/5.19 inference(monotonicity,[status(thm)],[74])).
% 4.94/5.19 tff(76,plain,
% 4.94/5.19 (((~![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))))),
% 4.94/5.19 inference(transitivity,[status(thm)],[75, 67])).
% 4.94/5.19 tff(77,plain,
% 4.94/5.19 ((~![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))))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(78,plain,
% 4.94/5.19 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.94/5.19 tff(79,plain,
% 4.94/5.19 ($false),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[78, 10, 66])).
% 4.94/5.19 tff(80,plain,(member(singleton(U!4), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 4.94/5.19 tff(81,plain,
% 4.94/5.19 (^[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))))))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(82,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[81])).
% 4.94/5.19 tff(83,plain,
% 4.94/5.19 (^[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))))))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(84,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[83])).
% 4.94/5.19 tff(85,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(transitivity,[status(thm)],[84, 82])).
% 4.94/5.19 tff(86,plain,
% 4.94/5.19 (^[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)))))))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(87,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[86])).
% 4.94/5.19 tff(88,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(89,plain,
% 4.94/5.19 (^[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))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(90,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[89])).
% 4.94/5.19 tff(91,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 4.94/5.19 tff(92,plain,
% 4.94/5.19 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[91, 90])).
% 4.94/5.19 tff(93,plain,
% 4.94/5.19 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[92, 88])).
% 4.94/5.19 tff(94,plain,(
% 4.94/5.19 ![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)))))),
% 4.94/5.19 inference(skolemize,[status(sab)],[93])).
% 4.94/5.19 tff(95,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[94, 87])).
% 4.94/5.19 tff(96,plain,
% 4.94/5.19 (![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)))))))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[95, 85])).
% 4.94/5.19 tff(97,plain,
% 4.94/5.19 ((~![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)))))))))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(98,plain,
% 4.94/5.19 (~((~((~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))))))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[97, 96])).
% 4.94/5.19 tff(99,plain,
% 4.94/5.19 (((~((~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)))))),
% 4.94/5.19 inference(tautology,[status(thm)],[])).
% 4.94/5.19 tff(100,plain,
% 4.94/5.19 ((~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))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[99, 98])).
% 4.94/5.19 tff(101,plain,
% 4.94/5.19 (^[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))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(102,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[101])).
% 4.94/5.19 tff(103,plain,
% 4.94/5.19 (^[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)))))),
% 4.94/5.19 inference(bind,[status(th)],[])).
% 4.94/5.19 tff(104,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(quant_intro,[status(thm)],[103])).
% 4.94/5.19 tff(105,plain,
% 4.94/5.19 (![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)))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(106,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 4.94/5.19 tff(107,plain,
% 4.94/5.19 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[106, 105])).
% 4.94/5.19 tff(108,plain,(
% 4.94/5.19 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 4.94/5.19 inference(skolemize,[status(sab)],[107])).
% 4.94/5.19 tff(109,plain,
% 4.94/5.19 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[108, 104])).
% 4.94/5.19 tff(110,plain,
% 4.94/5.19 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 4.94/5.19 inference(modus_ponens,[status(thm)],[109, 102])).
% 4.94/5.19 tff(111,plain,
% 4.94/5.19 ((~![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)))))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(112,plain,
% 4.94/5.19 (~(((~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))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[111, 110])).
% 4.94/5.19 tff(113,plain,
% 4.94/5.19 (equal_set(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 4.94/5.19 inference(or_elim,[status(thm)],[33])).
% 4.94/5.19 tff(114,plain,
% 4.94/5.19 ((((~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))))),
% 4.94/5.19 inference(tautology,[status(thm)],[])).
% 4.94/5.19 tff(115,plain,
% 4.94/5.19 ((((~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))))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[114, 113])).
% 4.94/5.19 tff(116,plain,
% 4.94/5.19 (~((~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)))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[115, 112])).
% 4.94/5.19 tff(117,plain,
% 4.94/5.19 (((~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)))),
% 4.94/5.19 inference(tautology,[status(thm)],[])).
% 4.94/5.19 tff(118,plain,
% 4.94/5.19 (subset(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[117, 116])).
% 4.94/5.19 tff(119,plain,
% 4.94/5.19 ((~((~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))))),
% 4.94/5.19 inference(tautology,[status(thm)],[])).
% 4.94/5.19 tff(120,plain,
% 4.94/5.19 ((~((~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))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[119, 118])).
% 4.94/5.19 tff(121,plain,
% 4.94/5.19 (![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))))),
% 4.94/5.19 inference(unit_resolution,[status(thm)],[120, 100])).
% 4.94/5.19 tff(122,plain,
% 4.94/5.19 (((~![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))))),
% 4.94/5.19 inference(rewrite,[status(thm)],[])).
% 4.94/5.19 tff(123,plain,
% 4.94/5.19 ((~![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))))),
% 4.94/5.19 inference(quant_inst,[status(thm)],[])).
% 4.94/5.19 tff(124,plain,
% 4.94/5.19 ((~![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)))),
% 4.94/5.20 inference(modus_ponens,[status(thm)],[123, 122])).
% 4.94/5.20 tff(125,plain,
% 4.94/5.20 (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[124, 121, 80])).
% 4.94/5.20 tff(126,plain,
% 4.94/5.20 ((~(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)))),
% 4.94/5.20 inference(tautology,[status(thm)],[])).
% 4.94/5.20 tff(127,plain,
% 4.94/5.20 ((~(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)))),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[126, 125])).
% 4.94/5.20 tff(128,plain,
% 4.94/5.20 ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[127, 65])).
% 4.94/5.20 tff(129,plain,
% 4.94/5.20 ((~((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))),
% 4.94/5.20 inference(tautology,[status(thm)],[])).
% 4.94/5.20 tff(130,plain,
% 4.94/5.20 ((singleton(U!4) = singleton(A!6)) | (singleton(U!4) = unordered_pair(A!6, B!5))),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[129, 128])).
% 4.94/5.20 tff(131,plain,
% 4.94/5.20 (singleton(U!4) = unordered_pair(A!6, B!5)),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[130, 58])).
% 4.94/5.20 tff(132,plain,
% 4.94/5.20 (unordered_pair(A!6, B!5) = singleton(U!4)),
% 4.94/5.20 inference(symmetry,[status(thm)],[131])).
% 4.94/5.20 tff(133,plain,
% 4.94/5.20 (member(U!4, unordered_pair(A!6, B!5)) <=> member(U!4, singleton(U!4))),
% 4.94/5.20 inference(monotonicity,[status(thm)],[132])).
% 4.94/5.20 tff(134,plain,
% 4.94/5.20 (member(U!4, singleton(U!4)) <=> member(U!4, unordered_pair(A!6, B!5))),
% 4.94/5.20 inference(symmetry,[status(thm)],[133])).
% 4.94/5.20 tff(135,plain,
% 4.94/5.20 (member(U!4, unordered_pair(A!6, B!5))),
% 4.94/5.20 inference(modus_ponens,[status(thm)],[55, 134])).
% 4.94/5.20 tff(136,plain,
% 4.94/5.20 ((~(member(U!4, unordered_pair(A!6, B!5)) <=> ((U!4 = B!5) | (U!4 = A!6)))) | (~member(U!4, unordered_pair(A!6, B!5))) | ((U!4 = B!5) | (U!4 = A!6))),
% 4.94/5.20 inference(tautology,[status(thm)],[])).
% 4.94/5.20 tff(137,plain,
% 4.94/5.20 ((U!4 = B!5) | (U!4 = A!6)),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[136, 135, 12])).
% 4.94/5.20 tff(138,plain,
% 4.94/5.20 ((~((U!4 = B!5) | (U!4 = A!6))) | (U!4 = B!5) | (U!4 = A!6)),
% 4.94/5.20 inference(tautology,[status(thm)],[])).
% 4.94/5.20 tff(139,plain,
% 4.94/5.20 ((~((U!4 = B!5) | (U!4 = A!6))) | (U!4 = B!5)),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[138, 36])).
% 4.94/5.20 tff(140,plain,
% 4.94/5.20 (U!4 = B!5),
% 4.94/5.20 inference(unit_resolution,[status(thm)],[139, 137])).
% 4.94/5.20 tff(141,plain,
% 4.94/5.20 (B!5 = U!4),
% 4.94/5.20 inference(symmetry,[status(thm)],[140])).
% 4.94/5.20 tff(142,assumption,(B!5 = unordered_pair(U!4, V!3)), introduced(assumption)).
% 4.94/5.20 tff(143,plain,
% 4.94/5.20 (unordered_pair(U!4, V!3) = B!5),
% 4.94/5.20 inference(symmetry,[status(thm)],[142])).
% 4.94/5.20 tff(144,plain,
% 4.94/5.20 (unordered_pair(U!4, V!3) = U!4),
% 4.94/5.20 inference(transitivity,[status(thm)],[143, 141])).
% 4.94/5.20 tff(145,plain,
% 4.94/5.20 (unordered_pair(unordered_pair(U!4, V!3), V!3) = unordered_pair(U!4, V!3)),
% 4.94/5.20 inference(monotonicity,[status(thm)],[144])).
% 4.94/5.20 tff(146,plain,
% 4.94/5.20 (member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)) <=> member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 4.94/5.20 inference(monotonicity,[status(thm)],[145])).
% 4.94/5.20 tff(147,plain,
% 4.94/5.20 (member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)) <=> member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 4.94/5.20 inference(symmetry,[status(thm)],[146])).
% 4.94/5.20 tff(148,plain,
% 4.94/5.20 ((~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))) <=> (~member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)))),
% 4.94/5.20 inference(monotonicity,[status(thm)],[147])).
% 4.94/5.20 tff(149,assumption,(~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), introduced(assumption)).
% 5.02/5.20 tff(150,plain,
% 5.02/5.20 (((~![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))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(151,plain,
% 5.02/5.20 ((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)))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(152,plain,
% 5.02/5.20 (((singleton(A!6) = unordered_pair(A!6, B!5)) | $true) <=> $true),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(153,plain,
% 5.02/5.20 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(154,plain,
% 5.02/5.20 (((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)),
% 5.02/5.20 inference(monotonicity,[status(thm)],[153])).
% 5.02/5.20 tff(155,plain,
% 5.02/5.20 (((singleton(A!6) = unordered_pair(A!6, B!5)) | (singleton(A!6) = singleton(A!6))) <=> $true),
% 5.02/5.20 inference(transitivity,[status(thm)],[154, 152])).
% 5.02/5.20 tff(156,plain,
% 5.02/5.20 ((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)),
% 5.02/5.20 inference(monotonicity,[status(thm)],[155])).
% 5.02/5.20 tff(157,plain,
% 5.02/5.20 ((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)))),
% 5.02/5.20 inference(transitivity,[status(thm)],[156, 151])).
% 5.02/5.20 tff(158,plain,
% 5.02/5.20 (((~![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))))),
% 5.02/5.20 inference(monotonicity,[status(thm)],[157])).
% 5.02/5.20 tff(159,plain,
% 5.02/5.20 (((~![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))))),
% 5.02/5.20 inference(transitivity,[status(thm)],[158, 150])).
% 5.02/5.20 tff(160,plain,
% 5.02/5.20 ((~![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))))),
% 5.02/5.20 inference(quant_inst,[status(thm)],[])).
% 5.02/5.20 tff(161,plain,
% 5.02/5.20 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[160, 159])).
% 5.02/5.20 tff(162,plain,
% 5.02/5.20 ($false),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[161, 10, 149])).
% 5.02/5.20 tff(163,plain,(member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.20 tff(164,assumption,(![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))), introduced(assumption)).
% 5.02/5.20 tff(165,plain,
% 5.02/5.20 (^[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)))))),
% 5.02/5.20 inference(bind,[status(th)],[])).
% 5.02/5.20 tff(166,plain,
% 5.02/5.20 (![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))))),
% 5.02/5.20 inference(quant_intro,[status(thm)],[165])).
% 5.02/5.20 tff(167,plain,
% 5.02/5.20 (^[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))))))),
% 5.02/5.20 inference(bind,[status(th)],[])).
% 5.02/5.20 tff(168,plain,
% 5.02/5.20 (![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))))),
% 5.02/5.20 inference(quant_intro,[status(thm)],[167])).
% 5.02/5.20 tff(169,plain,
% 5.02/5.20 (![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)))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(170,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 5.02/5.20 tff(171,plain,
% 5.02/5.20 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[170, 169])).
% 5.02/5.20 tff(172,plain,(
% 5.02/5.20 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 5.02/5.20 inference(skolemize,[status(sab)],[171])).
% 5.02/5.20 tff(173,plain,
% 5.02/5.20 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[172, 168])).
% 5.02/5.20 tff(174,plain,
% 5.02/5.20 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[173, 166])).
% 5.02/5.20 tff(175,plain,
% 5.02/5.20 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(176,plain,
% 5.02/5.20 ((~(~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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))))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(177,plain,
% 5.02/5.20 ((~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(178,plain,
% 5.02/5.20 (((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(179,plain,
% 5.02/5.20 (((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(180,plain,
% 5.02/5.20 ((((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(unordered_pair(singleton(A!6), 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))))))),
% 5.02/5.20 inference(monotonicity,[status(thm)],[179])).
% 5.02/5.20 tff(181,plain,
% 5.02/5.20 ((((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(transitivity,[status(thm)],[180, 178])).
% 5.02/5.20 tff(182,plain,
% 5.02/5.20 ((((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(transitivity,[status(thm)],[181, 177])).
% 5.02/5.20 tff(183,plain,
% 5.02/5.20 ((~(((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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))))))))),
% 5.02/5.20 inference(monotonicity,[status(thm)],[182])).
% 5.02/5.20 tff(184,plain,
% 5.02/5.20 ((~(((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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))))))),
% 5.02/5.20 inference(transitivity,[status(thm)],[183, 176])).
% 5.02/5.20 tff(185,plain,
% 5.02/5.20 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(monotonicity,[status(thm)],[184])).
% 5.02/5.20 tff(186,plain,
% 5.02/5.20 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(transitivity,[status(thm)],[185, 175])).
% 5.02/5.20 tff(187,plain,
% 5.02/5.20 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(unordered_pair(singleton(A!6), 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)))))))),
% 5.02/5.20 inference(quant_inst,[status(thm)],[])).
% 5.02/5.20 tff(188,plain,
% 5.02/5.20 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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))))))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[187, 186])).
% 5.02/5.20 tff(189,plain,
% 5.02/5.20 (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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)))))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[188, 174])).
% 5.02/5.20 tff(190,plain,
% 5.02/5.20 (^[X: $i, A: $i] : refl((member(X, power_set(A)) <=> subset(X, A)) <=> (member(X, power_set(A)) <=> subset(X, A)))),
% 5.02/5.20 inference(bind,[status(th)],[])).
% 5.02/5.20 tff(191,plain,
% 5.02/5.20 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 5.02/5.20 inference(quant_intro,[status(thm)],[190])).
% 5.02/5.20 tff(192,plain,
% 5.02/5.20 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A)) <=> ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(193,axiom,(![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','power_set')).
% 5.02/5.20 tff(194,plain,
% 5.02/5.20 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[193, 192])).
% 5.02/5.20 tff(195,plain,(
% 5.02/5.20 ![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 5.02/5.20 inference(skolemize,[status(sab)],[194])).
% 5.02/5.20 tff(196,plain,
% 5.02/5.20 (![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[195, 191])).
% 5.02/5.20 tff(197,plain,
% 5.02/5.20 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(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))))),
% 5.02/5.20 inference(quant_inst,[status(thm)],[])).
% 5.02/5.20 tff(198,plain,
% 5.02/5.20 (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(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)))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[197, 196])).
% 5.02/5.20 tff(199,plain,
% 5.02/5.20 (((~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)))),
% 5.02/5.20 inference(tautology,[status(thm)],[])).
% 5.02/5.20 tff(200,plain,
% 5.02/5.20 (subset(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[199, 116])).
% 5.02/5.20 tff(201,plain,
% 5.02/5.20 ((~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(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(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(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))))),
% 5.02/5.20 inference(tautology,[status(thm)],[])).
% 5.02/5.20 tff(202,plain,
% 5.02/5.20 ((~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(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(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[201, 200])).
% 5.02/5.20 tff(203,plain,
% 5.02/5.20 (member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[202, 198])).
% 5.02/5.20 tff(204,plain,
% 5.02/5.20 ((~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(unordered_pair(singleton(A!6), 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)))))),
% 5.02/5.20 inference(tautology,[status(thm)],[])).
% 5.02/5.20 tff(205,plain,
% 5.02/5.20 ((~(member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(unordered_pair(singleton(A!6), 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(singleton(A!6), 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)))))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[204, 203])).
% 5.02/5.20 tff(206,plain,
% 5.02/5.20 (member(unordered_pair(singleton(A!6), 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)))))),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[205, 189])).
% 5.02/5.20 tff(207,plain,
% 5.02/5.20 (((~![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))) | ((~member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))) <=> ((~![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))) | (~member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))),
% 5.02/5.20 inference(rewrite,[status(thm)],[])).
% 5.02/5.20 tff(208,plain,
% 5.02/5.20 ((~![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))) | ((~member(unordered_pair(singleton(A!6), 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(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))))),
% 5.02/5.20 inference(quant_inst,[status(thm)],[])).
% 5.02/5.20 tff(209,plain,
% 5.02/5.20 ((~![Y: $i] : ((~member(Y, intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~member(singleton(A!6), Y)))) | (~member(unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~member(singleton(A!6), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))))),
% 5.02/5.20 inference(modus_ponens,[status(thm)],[208, 207])).
% 5.02/5.20 tff(210,plain,
% 5.02/5.20 ($false),
% 5.02/5.20 inference(unit_resolution,[status(thm)],[209, 206, 164, 163])).
% 5.02/5.20 tff(211,plain,(~![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.20 tff(212,plain,
% 5.02/5.20 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 5.02/5.20 inference(bind,[status(th)],[])).
% 5.02/5.20 tff(213,plain,
% 5.02/5.20 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.20 inference(quant_intro,[status(thm)],[212])).
% 5.02/5.20 tff(214,plain,
% 5.02/5.20 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 5.02/5.20 inference(bind,[status(th)],[])).
% 5.02/5.20 tff(215,plain,
% 5.02/5.20 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.20 inference(quant_intro,[status(thm)],[214])).
% 5.02/5.20 tff(216,plain,
% 5.02/5.20 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.21 inference(transitivity,[status(thm)],[215, 213])).
% 5.02/5.21 tff(217,plain,
% 5.02/5.21 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 5.02/5.21 inference(bind,[status(th)],[])).
% 5.02/5.21 tff(218,plain,
% 5.02/5.21 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.21 inference(quant_intro,[status(thm)],[217])).
% 5.02/5.21 tff(219,plain,
% 5.02/5.21 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 5.02/5.21 inference(rewrite,[status(thm)],[])).
% 5.02/5.21 tff(220,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','sum')).
% 5.02/5.21 tff(221,plain,
% 5.02/5.21 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 5.02/5.21 inference(modus_ponens,[status(thm)],[220, 219])).
% 5.02/5.21 tff(222,plain,(
% 5.02/5.21 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 5.02/5.21 inference(skolemize,[status(sab)],[221])).
% 5.02/5.21 tff(223,plain,
% 5.02/5.21 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.21 inference(modus_ponens,[status(thm)],[222, 218])).
% 5.02/5.21 tff(224,plain,
% 5.02/5.21 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 5.02/5.21 inference(modus_ponens,[status(thm)],[223, 216])).
% 5.02/5.21 tff(225,plain,
% 5.02/5.21 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))))))),
% 5.02/5.21 inference(rewrite,[status(thm)],[])).
% 5.02/5.21 tff(226,plain,
% 5.02/5.21 ((~((~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))) | (~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))))) <=> (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))))))),
% 5.02/5.21 inference(rewrite,[status(thm)],[])).
% 5.02/5.21 tff(227,plain,
% 5.02/5.21 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))) | (~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))))))),
% 5.02/5.21 inference(monotonicity,[status(thm)],[226])).
% 5.02/5.21 tff(228,plain,
% 5.02/5.21 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))) | (~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))))))),
% 5.02/5.21 inference(transitivity,[status(thm)],[227, 225])).
% 5.02/5.21 tff(229,plain,
% 5.02/5.21 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))) | (~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))))))),
% 5.02/5.21 inference(quant_inst,[status(thm)],[])).
% 5.02/5.21 tff(230,plain,
% 5.02/5.21 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))))))),
% 5.02/5.21 inference(modus_ponens,[status(thm)],[229, 228])).
% 5.02/5.21 tff(231,plain,
% 5.02/5.21 (~((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[230, 224])).
% 5.02/5.21 tff(232,plain,
% 5.02/5.21 (((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))))) | (member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))),
% 5.02/5.21 inference(tautology,[status(thm)],[])).
% 5.02/5.21 tff(233,plain,
% 5.02/5.21 (member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[232, 231])).
% 5.02/5.21 tff(234,plain,
% 5.02/5.21 ((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))),
% 5.02/5.21 inference(tautology,[status(thm)],[])).
% 5.02/5.21 tff(235,plain,
% 5.02/5.21 (member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y)))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[234, 233])).
% 5.02/5.21 tff(236,plain,
% 5.02/5.21 (member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[235, 211])).
% 5.02/5.21 tff(237,plain,
% 5.02/5.21 (((~(member(singleton(A!6), sum(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![Y: $i] : ((~member(Y, intersection(power_set(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), Y))))) | (~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))))) | ((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))),
% 5.02/5.21 inference(tautology,[status(thm)],[])).
% 5.02/5.21 tff(238,plain,
% 5.02/5.21 ((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[237, 231])).
% 5.02/5.21 tff(239,plain,
% 5.02/5.21 ((~((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))))) | (~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))),
% 5.02/5.21 inference(tautology,[status(thm)],[])).
% 5.02/5.21 tff(240,plain,
% 5.02/5.21 ((~member(singleton(A!6), sum(intersection(power_set(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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[239, 238])).
% 5.02/5.21 tff(241,plain,
% 5.02/5.21 (~((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))),
% 5.02/5.21 inference(unit_resolution,[status(thm)],[240, 236])).
% 5.02/5.21 tff(242,plain,
% 5.02/5.21 (((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.21 inference(rewrite,[status(thm)],[])).
% 5.02/5.21 tff(243,plain,
% 5.02/5.21 ((~((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))) <=> (~((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.02/5.21 inference(rewrite,[status(thm)],[])).
% 5.02/5.21 tff(244,plain,
% 5.02/5.21 (((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.22 inference(monotonicity,[status(thm)],[243])).
% 5.02/5.22 tff(245,plain,
% 5.02/5.22 (((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.22 inference(transitivity,[status(thm)],[244, 242])).
% 5.02/5.22 tff(246,plain,
% 5.02/5.22 ((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 5.02/5.22 inference(quant_inst,[status(thm)],[])).
% 5.02/5.22 tff(247,plain,
% 5.02/5.22 ((~![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_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.02/5.22 inference(modus_ponens,[status(thm)],[246, 245])).
% 5.02/5.22 tff(248,plain,
% 5.02/5.22 (~((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 5.02/5.22 inference(unit_resolution,[status(thm)],[247, 96])).
% 5.02/5.22 tff(249,plain,
% 5.02/5.22 (((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), 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)), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.22 inference(tautology,[status(thm)],[])).
% 5.02/5.22 tff(250,plain,
% 5.02/5.22 ((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.22 inference(unit_resolution,[status(thm)],[249, 248])).
% 5.02/5.22 tff(251,plain,
% 5.02/5.22 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.22 inference(quant_inst,[status(thm)],[])).
% 5.02/5.22 tff(252,plain,
% 5.02/5.22 (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.22 inference(unit_resolution,[status(thm)],[251, 196])).
% 5.02/5.22 tff(253,plain,
% 5.02/5.22 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(rewrite,[status(thm)],[])).
% 5.02/5.22 tff(254,plain,
% 5.02/5.22 ((~(~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))),
% 5.02/5.22 inference(rewrite,[status(thm)],[])).
% 5.02/5.22 tff(255,plain,
% 5.02/5.22 ((~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(rewrite,[status(thm)],[])).
% 5.02/5.22 tff(256,plain,
% 5.02/5.22 (((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(rewrite,[status(thm)],[])).
% 5.02/5.22 tff(257,plain,
% 5.02/5.22 (((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.22 inference(rewrite,[status(thm)],[])).
% 5.02/5.22 tff(258,plain,
% 5.02/5.22 ((((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))),
% 5.02/5.22 inference(monotonicity,[status(thm)],[257])).
% 5.02/5.22 tff(259,plain,
% 5.02/5.22 ((((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(transitivity,[status(thm)],[258, 256])).
% 5.02/5.22 tff(260,plain,
% 5.02/5.22 ((((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(transitivity,[status(thm)],[259, 255])).
% 5.02/5.22 tff(261,plain,
% 5.02/5.22 ((~(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))))),
% 5.02/5.22 inference(monotonicity,[status(thm)],[260])).
% 5.02/5.22 tff(262,plain,
% 5.02/5.22 ((~(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))),
% 5.02/5.22 inference(transitivity,[status(thm)],[261, 254])).
% 5.02/5.22 tff(263,plain,
% 5.02/5.22 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(monotonicity,[status(thm)],[262])).
% 5.02/5.22 tff(264,plain,
% 5.02/5.22 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.22 inference(transitivity,[status(thm)],[263, 253])).
% 5.02/5.22 tff(265,plain,
% 5.02/5.22 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(266,plain,
% 5.02/5.23 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[265, 264])).
% 5.02/5.23 tff(267,plain,
% 5.02/5.23 (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[266, 174])).
% 5.02/5.23 tff(268,assumption,(~((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))))), introduced(assumption)).
% 5.02/5.23 tff(269,plain,
% 5.02/5.23 (((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))) | member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(270,plain,
% 5.02/5.23 (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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)))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[269, 268])).
% 5.02/5.23 tff(271,plain,
% 5.02/5.23 ((~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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))))))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(272,plain,
% 5.02/5.23 ((~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[271, 270])).
% 5.02/5.23 tff(273,plain,
% 5.02/5.23 (member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[272, 267])).
% 5.02/5.23 tff(274,plain,
% 5.02/5.23 ((~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(275,plain,
% 5.02/5.23 ((~(member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[274, 273])).
% 5.02/5.23 tff(276,plain,
% 5.02/5.23 (subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[275, 252])).
% 5.02/5.23 tff(277,plain,
% 5.02/5.23 ((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(278,plain,
% 5.02/5.23 ((~((~subset(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[277, 276])).
% 5.02/5.23 tff(279,plain,
% 5.02/5.23 (![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[278, 250])).
% 5.02/5.23 tff(280,assumption,(~member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 5.02/5.23 tff(281,plain,
% 5.02/5.23 (((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))) | member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(282,plain,
% 5.02/5.23 (member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[281, 268])).
% 5.02/5.23 tff(283,plain,
% 5.02/5.23 (((~![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(284,plain,
% 5.02/5.23 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(285,plain,
% 5.02/5.23 ((~![X: $i] : ((~member(X, tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(singleton(A!6), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6)))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[284, 283])).
% 5.02/5.23 tff(286,plain,
% 5.02/5.23 ($false),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[285, 282, 280, 279])).
% 5.02/5.23 tff(287,plain,(((~member(tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), 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), tptp_fun_Y_1(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), singleton(A!6))))) | member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.23 tff(288,plain,
% 5.02/5.23 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[287, 241])).
% 5.02/5.23 tff(289,plain,
% 5.02/5.23 ((singleton(A!6) = singleton(U!4)) <=> (singleton(U!4) = singleton(A!6))),
% 5.02/5.23 inference(commutativity,[status(thm)],[])).
% 5.02/5.23 tff(290,assumption,(~(singleton(U!4) = singleton(A!6))), introduced(assumption)).
% 5.02/5.23 tff(291,plain,
% 5.02/5.23 (singleton(U!4) = unordered_pair(A!6, B!5)),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[130, 290])).
% 5.02/5.23 tff(292,plain,
% 5.02/5.23 (unordered_pair(A!6, B!5) = singleton(U!4)),
% 5.02/5.23 inference(symmetry,[status(thm)],[291])).
% 5.02/5.23 tff(293,plain,
% 5.02/5.23 ((singleton(A!6) = unordered_pair(A!6, B!5)) <=> (singleton(A!6) = singleton(U!4))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[292])).
% 5.02/5.23 tff(294,plain,
% 5.02/5.23 ((singleton(A!6) = unordered_pair(A!6, B!5)) <=> (singleton(U!4) = singleton(A!6))),
% 5.02/5.23 inference(transitivity,[status(thm)],[293, 289])).
% 5.02/5.23 tff(295,plain,
% 5.02/5.23 ((singleton(U!4) = singleton(A!6)) <=> (singleton(A!6) = unordered_pair(A!6, B!5))),
% 5.02/5.23 inference(symmetry,[status(thm)],[294])).
% 5.02/5.23 tff(296,plain,
% 5.02/5.23 ((~(singleton(U!4) = singleton(A!6))) <=> (~(singleton(A!6) = unordered_pair(A!6, B!5)))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[295])).
% 5.02/5.23 tff(297,plain,
% 5.02/5.23 (~(singleton(A!6) = unordered_pair(A!6, B!5))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[290, 296])).
% 5.02/5.23 tff(298,plain,
% 5.02/5.23 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(299,plain,
% 5.02/5.23 (member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[298, 10])).
% 5.02/5.23 tff(300,plain,
% 5.02/5.23 (unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[292])).
% 5.02/5.23 tff(301,plain,
% 5.02/5.23 (member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[300])).
% 5.02/5.23 tff(302,plain,
% 5.02/5.23 (member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(symmetry,[status(thm)],[301])).
% 5.02/5.23 tff(303,assumption,(member(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 5.02/5.23 tff(304,plain,
% 5.02/5.23 (member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[303, 302])).
% 5.02/5.23 tff(305,plain,
% 5.02/5.23 ((~(member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5))))) | (~member(singleton(A!6), unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))) | ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5)))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(306,plain,
% 5.02/5.23 ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[305, 304, 299])).
% 5.02/5.23 tff(307,assumption,(~(singleton(A!6) = unordered_pair(U!4, V!3))), introduced(assumption)).
% 5.02/5.23 tff(308,plain,
% 5.02/5.23 ((~((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5)))) | (singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(309,plain,
% 5.02/5.23 ((~((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(A!6) = unordered_pair(A!6, B!5)))) | (singleton(A!6) = unordered_pair(A!6, B!5))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[308, 307])).
% 5.02/5.23 tff(310,plain,
% 5.02/5.23 ($false),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[309, 306, 297])).
% 5.02/5.23 tff(311,plain,((~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(U!4) = singleton(A!6))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.23 tff(312,plain,
% 5.02/5.23 ((singleton(A!6) = unordered_pair(U!4, V!3)) | (singleton(U!4) = singleton(A!6))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[311, 288])).
% 5.02/5.23 tff(313,plain,
% 5.02/5.23 (singleton(A!6) = unordered_pair(U!4, V!3)),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[312, 58])).
% 5.02/5.23 tff(314,plain,
% 5.02/5.23 (U!4 = unordered_pair(U!4, V!3)),
% 5.02/5.23 inference(transitivity,[status(thm)],[140, 142])).
% 5.02/5.23 tff(315,plain,
% 5.02/5.23 (member(U!4, singleton(A!6)) <=> member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[314, 313])).
% 5.02/5.23 tff(316,plain,
% 5.02/5.23 ((~member(U!4, singleton(A!6))) <=> (~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[315])).
% 5.02/5.23 tff(317,plain,
% 5.02/5.23 (~member(unordered_pair(U!4, V!3), unordered_pair(U!4, V!3))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[39, 316])).
% 5.02/5.23 tff(318,plain,
% 5.02/5.23 (~member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[317, 148])).
% 5.02/5.23 tff(319,plain,
% 5.02/5.23 (((~![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(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(unordered_pair(U!4, V!3), V!3)))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(320,plain,
% 5.02/5.23 ((member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)) <=> $true) <=> member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(321,plain,
% 5.02/5.23 (((unordered_pair(U!4, V!3) = V!3) | $true) <=> $true),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(322,plain,
% 5.02/5.23 ((unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)) <=> $true),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(323,plain,
% 5.02/5.23 (((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3))) <=> ((unordered_pair(U!4, V!3) = V!3) | $true)),
% 5.02/5.23 inference(monotonicity,[status(thm)],[322])).
% 5.02/5.23 tff(324,plain,
% 5.02/5.23 (((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3))) <=> $true),
% 5.02/5.23 inference(transitivity,[status(thm)],[323, 321])).
% 5.02/5.23 tff(325,plain,
% 5.02/5.23 ((member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)))) <=> (member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)) <=> $true)),
% 5.02/5.23 inference(monotonicity,[status(thm)],[324])).
% 5.02/5.23 tff(326,plain,
% 5.02/5.23 ((member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3)))) <=> member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 5.02/5.23 inference(transitivity,[status(thm)],[325, 320])).
% 5.02/5.23 tff(327,plain,
% 5.02/5.23 (((~![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(unordered_pair(U!4, V!3), V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = 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(unordered_pair(U!4, V!3), V!3)))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[326])).
% 5.02/5.23 tff(328,plain,
% 5.02/5.23 (((~![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(unordered_pair(U!4, V!3), V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = 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(unordered_pair(U!4, V!3), V!3)))),
% 5.02/5.23 inference(transitivity,[status(thm)],[327, 319])).
% 5.02/5.23 tff(329,plain,
% 5.02/5.23 ((~![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(unordered_pair(U!4, V!3), V!3)) <=> ((unordered_pair(U!4, V!3) = V!3) | (unordered_pair(U!4, V!3) = unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(330,plain,
% 5.02/5.23 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 5.02/5.23 inference(modus_ponens,[status(thm)],[329, 328])).
% 5.02/5.23 tff(331,plain,
% 5.02/5.23 (member(unordered_pair(U!4, V!3), unordered_pair(unordered_pair(U!4, V!3), V!3))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[330, 10])).
% 5.02/5.23 tff(332,plain,
% 5.02/5.23 ($false),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[331, 318])).
% 5.02/5.23 tff(333,plain,(~(B!5 = unordered_pair(U!4, V!3))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.23 tff(334,assumption,(~(member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))))), introduced(assumption)).
% 5.02/5.23 tff(335,plain,
% 5.02/5.23 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | (member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(336,plain,
% 5.02/5.23 ($false),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[335, 10, 334])).
% 5.02/5.23 tff(337,plain,(member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.23 tff(338,plain,
% 5.02/5.23 (unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)) = unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[132])).
% 5.02/5.23 tff(339,plain,
% 5.02/5.23 (member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(monotonicity,[status(thm)],[141, 338])).
% 5.02/5.23 tff(340,plain,
% 5.02/5.23 (member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(symmetry,[status(thm)],[339])).
% 5.02/5.23 tff(341,plain,
% 5.02/5.23 ((~![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(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(342,plain,
% 5.02/5.23 (~((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[341, 96])).
% 5.02/5.23 tff(343,plain,
% 5.02/5.23 (((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(A!6, B!5)), unordered_pair(A!6, B!5))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(A!6, B!5)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | ((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.23 inference(tautology,[status(thm)],[])).
% 5.02/5.23 tff(344,plain,
% 5.02/5.23 ((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[343, 342])).
% 5.02/5.23 tff(345,plain,
% 5.02/5.23 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.23 inference(quant_inst,[status(thm)],[])).
% 5.02/5.23 tff(346,plain,
% 5.02/5.23 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.23 inference(unit_resolution,[status(thm)],[345, 196])).
% 5.02/5.23 tff(347,plain,
% 5.02/5.23 (((~![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)))))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(348,plain,
% 5.02/5.23 ((~(~(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))))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(349,plain,
% 5.02/5.23 ((~(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)))))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(350,plain,
% 5.02/5.23 (((~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)))))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.23 tff(351,plain,
% 5.02/5.23 (((~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)))))),
% 5.02/5.23 inference(rewrite,[status(thm)],[])).
% 5.02/5.24 tff(352,plain,
% 5.02/5.24 ((((~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))))))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[351])).
% 5.02/5.24 tff(353,plain,
% 5.02/5.24 ((((~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)))))))),
% 5.02/5.24 inference(transitivity,[status(thm)],[352, 350])).
% 5.02/5.24 tff(354,plain,
% 5.02/5.24 ((((~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)))))))),
% 5.02/5.24 inference(transitivity,[status(thm)],[353, 349])).
% 5.02/5.24 tff(355,plain,
% 5.02/5.24 ((~(((~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))))))))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[354])).
% 5.02/5.24 tff(356,plain,
% 5.02/5.24 ((~(((~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))))))),
% 5.02/5.24 inference(transitivity,[status(thm)],[355, 348])).
% 5.02/5.24 tff(357,plain,
% 5.02/5.24 (((~![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)))))))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[356])).
% 5.02/5.24 tff(358,plain,
% 5.02/5.24 (((~![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)))))))),
% 5.02/5.24 inference(transitivity,[status(thm)],[357, 347])).
% 5.02/5.24 tff(359,plain,
% 5.02/5.24 ((~![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)))))))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(360,plain,
% 5.02/5.24 ((~![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))))))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[359, 358])).
% 5.02/5.24 tff(361,plain,
% 5.02/5.24 (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)))))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[360, 174])).
% 5.02/5.24 tff(362,plain,
% 5.02/5.24 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[132])).
% 5.02/5.24 tff(363,plain,
% 5.02/5.24 (member(singleton(U!4), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) <=> member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(symmetry,[status(thm)],[362])).
% 5.02/5.24 tff(364,plain,
% 5.02/5.24 (member(unordered_pair(A!6, B!5), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[125, 363])).
% 5.02/5.24 tff(365,plain,
% 5.02/5.24 ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3))))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(366,plain,
% 5.02/5.24 (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(A!6), unordered_pair(A!6, B!5))), unordered_pair(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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3)))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[365, 10])).
% 5.02/5.24 tff(367,plain,
% 5.02/5.24 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 5.02/5.24 inference(symmetry,[status(thm)],[313])).
% 5.02/5.24 tff(368,plain,
% 5.02/5.24 (unordered_pair(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)) = unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[367])).
% 5.02/5.24 tff(369,plain,
% 5.02/5.24 (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(A!6), unordered_pair(A!6, B!5))), unordered_pair(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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[368])).
% 5.02/5.24 tff(370,plain,
% 5.02/5.24 (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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(symmetry,[status(thm)],[369])).
% 5.02/5.24 tff(371,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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))), introduced(assumption)).
% 5.02/5.24 tff(372,plain,
% 5.02/5.24 (((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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)))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(373,plain,
% 5.02/5.24 (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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[372, 371])).
% 5.02/5.24 tff(374,plain,
% 5.02/5.24 (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(A!6), unordered_pair(A!6, B!5))), unordered_pair(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[373, 370])).
% 5.02/5.24 tff(375,plain,
% 5.02/5.24 ((~(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(A!6), unordered_pair(A!6, B!5))), unordered_pair(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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3)))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(376,plain,
% 5.02/5.24 ((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[375, 374, 366])).
% 5.02/5.24 tff(377,plain,
% 5.02/5.24 (((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(378,plain,
% 5.02/5.24 (~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(A!6), 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)))))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[377, 371])).
% 5.02/5.24 tff(379,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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3)), introduced(assumption)).
% 5.02/5.24 tff(380,plain,
% 5.02/5.24 (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) = singleton(A!6)),
% 5.02/5.24 inference(transitivity,[status(thm)],[379, 367])).
% 5.02/5.24 tff(381,plain,
% 5.02/5.24 (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(A!6), 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(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)))))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[380])).
% 5.02/5.24 tff(382,plain,
% 5.02/5.24 (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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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)))))),
% 5.02/5.24 inference(symmetry,[status(thm)],[381])).
% 5.02/5.24 tff(383,assumption,(~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))), introduced(assumption)).
% 5.02/5.24 tff(384,plain,
% 5.02/5.24 ((~![X: $i, A: $i] : (member(X, power_set(A)) <=> subset(X, A))) | (member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(385,plain,
% 5.02/5.24 ($false),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[384, 196, 383])).
% 5.02/5.24 tff(386,plain,(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.24 tff(387,assumption,(~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))), introduced(assumption)).
% 5.02/5.24 tff(388,plain,
% 5.02/5.24 (((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), singleton(A!6))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(389,plain,
% 5.02/5.24 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[388, 387])).
% 5.02/5.24 tff(390,plain,
% 5.02/5.24 (((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(391,plain,
% 5.02/5.24 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[390, 387])).
% 5.02/5.24 tff(392,assumption,(~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))), introduced(assumption)).
% 5.02/5.24 tff(393,plain,
% 5.02/5.24 ((~![X: $i, A: $i] : (member(X, singleton(A)) <=> (X = A))) | (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(394,plain,
% 5.02/5.24 ($false),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[393, 20, 392])).
% 5.02/5.24 tff(395,plain,(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)), inference(lemma,lemma(discharge,[]))).
% 5.02/5.24 tff(396,assumption,(singleton(U!4) = unordered_pair(A!6, B!5)), introduced(assumption)).
% 5.02/5.24 tff(397,plain,
% 5.02/5.24 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(A!6, B!5))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[396])).
% 5.02/5.24 tff(398,plain,
% 5.02/5.24 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), singleton(U!4))),
% 5.02/5.24 inference(symmetry,[status(thm)],[397])).
% 5.02/5.24 tff(399,plain,
% 5.02/5.24 (^[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)))))),
% 5.02/5.24 inference(bind,[status(th)],[])).
% 5.02/5.24 tff(400,plain,
% 5.02/5.24 (![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))))),
% 5.02/5.24 inference(quant_intro,[status(thm)],[399])).
% 5.02/5.24 tff(401,plain,
% 5.02/5.24 (^[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))))))),
% 5.02/5.24 inference(bind,[status(th)],[])).
% 5.02/5.24 tff(402,plain,
% 5.02/5.24 (![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))))),
% 5.02/5.24 inference(quant_intro,[status(thm)],[401])).
% 5.02/5.24 tff(403,plain,
% 5.02/5.24 (![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))))),
% 5.02/5.24 inference(rewrite,[status(thm)],[])).
% 5.02/5.24 tff(404,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','difference')).
% 5.02/5.24 tff(405,plain,
% 5.02/5.24 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[404, 403])).
% 5.02/5.24 tff(406,plain,(
% 5.02/5.24 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 5.02/5.24 inference(skolemize,[status(sab)],[405])).
% 5.02/5.24 tff(407,plain,
% 5.02/5.24 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[406, 402])).
% 5.02/5.24 tff(408,plain,
% 5.02/5.24 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[407, 400])).
% 5.02/5.24 tff(409,plain,
% 5.02/5.24 ((~![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)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(410,plain,
% 5.02/5.24 (~(((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5))))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[409, 408])).
% 5.02/5.24 tff(411,plain,
% 5.02/5.24 (unordered_pair(A!6, B!5) = singleton(U!4)),
% 5.02/5.24 inference(symmetry,[status(thm)],[396])).
% 5.02/5.24 tff(412,plain,
% 5.02/5.24 (difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)) = difference(unordered_pair(U!4, V!3), singleton(U!4))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[411])).
% 5.02/5.24 tff(413,plain,
% 5.02/5.24 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5))) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[412])).
% 5.02/5.24 tff(414,plain,
% 5.02/5.24 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))),
% 5.02/5.24 inference(symmetry,[status(thm)],[413])).
% 5.02/5.24 tff(415,plain,
% 5.02/5.24 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5))))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[414])).
% 5.02/5.24 tff(416,assumption,(~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 5.02/5.24 tff(417,assumption,(singleton(A!6) = unordered_pair(U!4, V!3)), introduced(assumption)).
% 5.02/5.24 tff(418,plain,
% 5.02/5.24 (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))),
% 5.02/5.24 inference(monotonicity,[status(thm)],[417])).
% 5.02/5.24 tff(419,plain,
% 5.02/5.24 (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))),
% 5.02/5.24 inference(symmetry,[status(thm)],[418])).
% 5.02/5.24 tff(420,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))) | 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)))), introduced(assumption)).
% 5.02/5.24 tff(421,plain,
% 5.02/5.24 (((~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))) | 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))),
% 5.02/5.24 inference(tautology,[status(thm)],[])).
% 5.02/5.24 tff(422,plain,
% 5.02/5.24 (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))),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[421, 420])).
% 5.02/5.24 tff(423,plain,
% 5.02/5.24 (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))),
% 5.02/5.24 inference(modus_ponens,[status(thm)],[422, 419])).
% 5.02/5.24 tff(424,plain,
% 5.02/5.24 ((~![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))),
% 5.02/5.24 inference(quant_inst,[status(thm)],[])).
% 5.02/5.24 tff(425,plain,
% 5.02/5.24 (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)),
% 5.02/5.24 inference(unit_resolution,[status(thm)],[424, 20])).
% 5.02/5.24 tff(426,plain,
% 5.02/5.24 ((~![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)))),
% 5.02/5.25 inference(quant_inst,[status(thm)],[])).
% 5.02/5.25 tff(427,plain,
% 5.02/5.25 (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))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[426, 10])).
% 5.02/5.25 tff(428,plain,
% 5.02/5.25 (((~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))) | (~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)))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(429,plain,
% 5.02/5.25 (~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))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[428, 420])).
% 5.02/5.25 tff(430,plain,
% 5.02/5.25 ((~(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))) = 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)))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(431,plain,
% 5.02/5.25 ((~(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)))) | (~((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)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[430, 429])).
% 5.02/5.25 tff(432,plain,
% 5.02/5.25 (~((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))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[431, 427])).
% 5.02/5.25 tff(433,plain,
% 5.02/5.25 (((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))) = A!6))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(434,plain,
% 5.02/5.25 (~(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)),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[433, 432])).
% 5.02/5.25 tff(435,plain,
% 5.02/5.25 ((~(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)),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(436,plain,
% 5.02/5.25 (~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))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[435, 434, 425])).
% 5.02/5.25 tff(437,plain,
% 5.02/5.25 ($false),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[436, 423])).
% 5.02/5.25 tff(438,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))), 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))) | (~(singleton(A!6) = unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.25 tff(439,plain,
% 5.02/5.25 ((~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))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[438, 417])).
% 5.02/5.25 tff(440,plain,
% 5.02/5.25 (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), 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))), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 5.02/5.25 inference(monotonicity,[status(thm)],[412])).
% 5.02/5.25 tff(441,plain,
% 5.02/5.25 (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), unordered_pair(A!6, B!5)))),
% 5.02/5.25 inference(symmetry,[status(thm)],[440])).
% 5.02/5.25 tff(442,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)).
% 5.02/5.25 tff(443,plain,
% 5.02/5.25 (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), unordered_pair(A!6, B!5)))),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[442, 441])).
% 5.02/5.25 tff(444,plain,
% 5.02/5.25 ((~![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))), 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))), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))))),
% 5.02/5.25 inference(quant_inst,[status(thm)],[])).
% 5.02/5.25 tff(445,plain,
% 5.02/5.25 (~(((~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))) <=> 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), unordered_pair(A!6, B!5))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[444, 408])).
% 5.02/5.25 tff(446,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))) | 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))), introduced(assumption)).
% 5.02/5.25 tff(447,plain,
% 5.02/5.25 ((((~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))) <=> 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), 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))) | 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))), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5))))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(448,plain,
% 5.02/5.25 ((((~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))) <=> 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), 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))), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[447, 446])).
% 5.02/5.25 tff(449,plain,
% 5.02/5.25 (~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), unordered_pair(A!6, B!5)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[448, 445])).
% 5.02/5.25 tff(450,plain,
% 5.02/5.25 ($false),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[449, 443])).
% 5.02/5.25 tff(451,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) = 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))) | 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))))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.25 tff(452,plain,
% 5.02/5.25 (~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)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[451, 396, 439])).
% 5.02/5.25 tff(453,plain,
% 5.02/5.25 (((~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)))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(454,plain,
% 5.02/5.25 ((~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)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[453, 452])).
% 5.02/5.25 tff(455,plain,
% 5.02/5.25 ((~![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)))))))))),
% 5.02/5.25 inference(quant_inst,[status(thm)],[])).
% 5.02/5.25 tff(456,plain,
% 5.02/5.25 (~((~((~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))))))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[455, 96])).
% 5.02/5.25 tff(457,plain,
% 5.02/5.25 (((~((~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))))))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(458,plain,
% 5.02/5.25 (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)))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[457, 456])).
% 5.02/5.25 tff(459,plain,
% 5.02/5.25 ((~(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)))))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(460,plain,
% 5.02/5.25 (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)))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[459, 458])).
% 5.02/5.25 tff(461,plain,
% 5.02/5.25 (subset(difference(unordered_pair(U!4, V!3), singleton(U!4)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[460, 454])).
% 5.02/5.25 tff(462,plain,
% 5.02/5.25 (((~((~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)))))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(463,plain,
% 5.02/5.25 ((~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))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[462, 456])).
% 5.02/5.25 tff(464,plain,
% 5.02/5.25 ((~((~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))))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(465,plain,
% 5.02/5.25 ((~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))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[464, 463])).
% 5.02/5.25 tff(466,plain,
% 5.02/5.25 (![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))))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[465, 461])).
% 5.02/5.25 tff(467,plain,
% 5.02/5.25 (((~![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(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), 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(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.25 inference(rewrite,[status(thm)],[])).
% 5.02/5.25 tff(468,plain,
% 5.02/5.25 ((~![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(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.25 inference(quant_inst,[status(thm)],[])).
% 5.02/5.25 tff(469,plain,
% 5.02/5.25 ((~![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(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), 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)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[468, 467])).
% 5.02/5.25 tff(470,plain,
% 5.02/5.25 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), difference(unordered_pair(U!4, V!3), singleton(U!4)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[469, 466, 416])).
% 5.02/5.25 tff(471,plain,
% 5.02/5.25 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[470, 415])).
% 5.02/5.25 tff(472,plain,
% 5.02/5.25 ((((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))) | ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), difference(unordered_pair(U!4, V!3), unordered_pair(A!6, B!5)))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(473,plain,
% 5.02/5.25 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(A!6, B!5))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[472, 471, 410])).
% 5.02/5.25 tff(474,plain,
% 5.02/5.25 (unordered_pair(U!4, V!3) = singleton(A!6)),
% 5.02/5.25 inference(symmetry,[status(thm)],[417])).
% 5.02/5.25 tff(475,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))),
% 5.02/5.25 inference(monotonicity,[status(thm)],[474])).
% 5.02/5.25 tff(476,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))),
% 5.02/5.25 inference(symmetry,[status(thm)],[475])).
% 5.02/5.25 tff(477,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))), introduced(assumption)).
% 5.02/5.25 tff(478,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[477, 476])).
% 5.02/5.25 tff(479,plain,
% 5.02/5.25 ((~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(A!6, B!5))),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(480,plain,
% 5.02/5.25 ((~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), 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)), singleton(A!6)), unordered_pair(A!6, B!5))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[479, 478])).
% 5.02/5.25 tff(481,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(A!6, B!5))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[480, 473])).
% 5.02/5.25 tff(482,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[481, 398])).
% 5.02/5.25 tff(483,plain,
% 5.02/5.25 ((~![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)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))),
% 5.02/5.25 inference(quant_inst,[status(thm)],[])).
% 5.02/5.25 tff(484,plain,
% 5.02/5.25 (member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[483, 20])).
% 5.02/5.25 tff(485,assumption,(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)), introduced(assumption)).
% 5.02/5.25 tff(486,plain,
% 5.02/5.25 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(487,plain,
% 5.02/5.25 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6)),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[486, 477])).
% 5.02/5.25 tff(488,plain,
% 5.02/5.25 (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[487, 485])).
% 5.02/5.25 tff(489,plain,
% 5.02/5.25 (A!6 = tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6))),
% 5.02/5.25 inference(symmetry,[status(thm)],[488])).
% 5.02/5.25 tff(490,plain,
% 5.02/5.25 ((A!6 = U!4) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 5.02/5.25 inference(monotonicity,[status(thm)],[489])).
% 5.02/5.25 tff(491,plain,
% 5.02/5.25 ((~(A!6 = U!4)) <=> (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))),
% 5.02/5.25 inference(monotonicity,[status(thm)],[490])).
% 5.02/5.25 tff(492,plain,
% 5.02/5.25 (~(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 5.02/5.25 inference(modus_ponens,[status(thm)],[34, 491])).
% 5.02/5.25 tff(493,plain,
% 5.02/5.25 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))) | (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4)),
% 5.02/5.25 inference(tautology,[status(thm)],[])).
% 5.02/5.25 tff(494,plain,
% 5.02/5.25 ((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = U!4))) | (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4)))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[493, 492])).
% 5.02/5.25 tff(495,plain,
% 5.02/5.25 (~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(U!4))),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[494, 484])).
% 5.02/5.25 tff(496,plain,
% 5.02/5.25 ($false),
% 5.02/5.25 inference(unit_resolution,[status(thm)],[495, 482])).
% 5.02/5.25 tff(497,plain,((~(member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6)) <=> (tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)) = A!6))) | (~(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)), singleton(A!6)), singleton(A!6))) | (~(singleton(A!6) = unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(498,plain,
% 5.02/5.26 ((~(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)), singleton(A!6)), singleton(A!6))) | (~(singleton(A!6) = unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[497, 395])).
% 5.02/5.26 tff(499,plain,
% 5.02/5.26 ((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[498, 313, 131])).
% 5.02/5.26 tff(500,plain,
% 5.02/5.26 ($false),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[499, 391, 389])).
% 5.02/5.26 tff(501,plain,((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(502,assumption,((~((~subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))), introduced(assumption)).
% 5.02/5.26 tff(503,plain,
% 5.02/5.26 ((~![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(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~((~member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 5.02/5.26 inference(quant_inst,[status(thm)],[])).
% 5.02/5.26 tff(504,plain,
% 5.02/5.26 ($false),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[503, 96, 502])).
% 5.02/5.26 tff(505,plain,(~((~((~subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(506,plain,
% 5.02/5.26 (((~((~subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, singleton(A!6))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) | (subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 5.02/5.26 inference(tautology,[status(thm)],[])).
% 5.02/5.26 tff(507,plain,
% 5.02/5.26 (subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[506, 505])).
% 5.02/5.26 tff(508,plain,
% 5.02/5.26 ((~(subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))) | subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.26 inference(tautology,[status(thm)],[])).
% 5.02/5.26 tff(509,plain,
% 5.02/5.26 (subset(singleton(A!6), 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)), singleton(A!6)), singleton(A!6))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), singleton(A!6)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[508, 507])).
% 5.02/5.26 tff(510,plain,
% 5.02/5.26 (subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[509, 501])).
% 5.02/5.26 tff(511,plain,
% 5.02/5.26 (subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[367])).
% 5.02/5.26 tff(512,plain,
% 5.02/5.26 (subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(symmetry,[status(thm)],[511])).
% 5.02/5.26 tff(513,assumption,(subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 5.02/5.26 tff(514,plain,
% 5.02/5.26 (subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(modus_ponens,[status(thm)],[513, 512])).
% 5.02/5.26 tff(515,assumption,(~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), introduced(assumption)).
% 5.02/5.26 tff(516,plain,
% 5.02/5.26 ($false),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[515, 514])).
% 5.02/5.26 tff(517,plain,(subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))) | (~subset(singleton(A!6), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(518,plain,
% 5.02/5.26 (subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[517, 510])).
% 5.02/5.26 tff(519,plain,
% 5.02/5.26 ((~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | (~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.26 inference(tautology,[status(thm)],[])).
% 5.02/5.26 tff(520,plain,
% 5.02/5.26 ((~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[519, 518])).
% 5.02/5.26 tff(521,plain,
% 5.02/5.26 (member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[520, 386])).
% 5.02/5.26 tff(522,plain,
% 5.02/5.26 (member(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(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)))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[367])).
% 5.02/5.26 tff(523,plain,
% 5.02/5.26 (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(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)))))),
% 5.02/5.26 inference(symmetry,[status(thm)],[522])).
% 5.02/5.26 tff(524,plain,
% 5.02/5.26 ((~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(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))))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[523])).
% 5.02/5.26 tff(525,assumption,(~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)))))), introduced(assumption)).
% 5.02/5.26 tff(526,plain,
% 5.02/5.26 (~member(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)))))),
% 5.02/5.26 inference(modus_ponens,[status(thm)],[525, 524])).
% 5.02/5.26 tff(527,plain,
% 5.02/5.26 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(rewrite,[status(thm)],[])).
% 5.02/5.26 tff(528,plain,
% 5.02/5.26 ((~(~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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))))))),
% 5.02/5.26 inference(rewrite,[status(thm)],[])).
% 5.02/5.26 tff(529,plain,
% 5.02/5.26 ((~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(rewrite,[status(thm)],[])).
% 5.02/5.26 tff(530,plain,
% 5.02/5.26 (((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(rewrite,[status(thm)],[])).
% 5.02/5.26 tff(531,plain,
% 5.02/5.26 (((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.26 inference(rewrite,[status(thm)],[])).
% 5.02/5.26 tff(532,plain,
% 5.02/5.26 ((((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> member(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))))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[531])).
% 5.02/5.26 tff(533,plain,
% 5.02/5.26 ((((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(transitivity,[status(thm)],[532, 530])).
% 5.02/5.26 tff(534,plain,
% 5.02/5.26 ((((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(transitivity,[status(thm)],[533, 529])).
% 5.02/5.26 tff(535,plain,
% 5.02/5.26 ((~(((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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))))))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[534])).
% 5.02/5.26 tff(536,plain,
% 5.02/5.26 ((~(((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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))))))),
% 5.02/5.26 inference(transitivity,[status(thm)],[535, 528])).
% 5.02/5.26 tff(537,plain,
% 5.02/5.26 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[536])).
% 5.02/5.26 tff(538,plain,
% 5.02/5.26 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))))),
% 5.02/5.26 inference(transitivity,[status(thm)],[537, 527])).
% 5.02/5.26 tff(539,plain,
% 5.02/5.26 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) <=> member(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)))))))),
% 5.02/5.26 inference(quant_inst,[status(thm)],[])).
% 5.02/5.26 tff(540,plain,
% 5.02/5.26 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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))))))),
% 5.02/5.26 inference(modus_ponens,[status(thm)],[539, 538])).
% 5.02/5.26 tff(541,plain,
% 5.02/5.26 (member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[540, 174])).
% 5.02/5.26 tff(542,assumption,(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))), introduced(assumption)).
% 5.02/5.26 tff(543,plain,
% 5.02/5.26 ((~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | member(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)))))),
% 5.02/5.26 inference(tautology,[status(thm)],[])).
% 5.02/5.26 tff(544,plain,
% 5.02/5.26 ((~(member(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> member(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(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)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[543, 542])).
% 5.02/5.26 tff(545,plain,
% 5.02/5.26 (member(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)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[544, 541])).
% 5.02/5.26 tff(546,plain,
% 5.02/5.26 ($false),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[545, 526])).
% 5.02/5.26 tff(547,plain,(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(unordered_pair(U!4, V!3), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(548,plain,
% 5.02/5.26 (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)))))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[547, 521])).
% 5.02/5.26 tff(549,plain,
% 5.02/5.26 (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(A!6), 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)))))),
% 5.02/5.26 inference(modus_ponens,[status(thm)],[548, 382])).
% 5.02/5.26 tff(550,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(A!6), 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)))))), introduced(assumption)).
% 5.02/5.26 tff(551,plain,
% 5.02/5.26 ($false),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[550, 549])).
% 5.02/5.26 tff(552,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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), 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)))))), inference(lemma,lemma(discharge,[]))).
% 5.02/5.26 tff(553,plain,
% 5.02/5.26 (~(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3))),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[552, 378])).
% 5.02/5.26 tff(554,plain,
% 5.02/5.26 ((~((tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = 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(A!6), unordered_pair(A!6, B!5))) = unordered_pair(U!4, V!3))),
% 5.02/5.26 inference(tautology,[status(thm)],[])).
% 5.02/5.26 tff(555,plain,
% 5.02/5.26 (tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))) = unordered_pair(A!6, B!5)),
% 5.02/5.26 inference(unit_resolution,[status(thm)],[554, 553, 376])).
% 5.02/5.26 tff(556,plain,
% 5.02/5.26 (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(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.26 inference(symmetry,[status(thm)],[555])).
% 5.02/5.26 tff(557,plain,
% 5.02/5.26 (singleton(U!4) = tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))),
% 5.02/5.26 inference(transitivity,[status(thm)],[131, 556])).
% 5.02/5.26 tff(558,plain,
% 5.02/5.26 (member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)) <=> member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))),
% 5.02/5.26 inference(monotonicity,[status(thm)],[557])).
% 5.02/5.26 tff(559,plain,
% 5.02/5.26 (member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5)))) <=> member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4))),
% 5.02/5.26 inference(symmetry,[status(thm)],[558])).
% 5.02/5.26 tff(560,plain,
% 5.02/5.26 (((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(561,plain,
% 5.02/5.27 ((~((~((~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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(562,plain,
% 5.02/5.27 (((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.27 inference(monotonicity,[status(thm)],[561])).
% 5.02/5.27 tff(563,plain,
% 5.02/5.27 (((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.02/5.27 inference(transitivity,[status(thm)],[562, 560])).
% 5.02/5.27 tff(564,plain,
% 5.02/5.27 ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 5.02/5.27 inference(quant_inst,[status(thm)],[])).
% 5.02/5.27 tff(565,plain,
% 5.02/5.27 ((~![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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.02/5.27 inference(modus_ponens,[status(thm)],[564, 563])).
% 5.02/5.27 tff(566,plain,
% 5.02/5.27 (~((~((~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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 5.02/5.27 inference(unit_resolution,[status(thm)],[565, 96])).
% 5.02/5.27 tff(567,plain,
% 5.02/5.27 (((~((~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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.27 inference(tautology,[status(thm)],[])).
% 5.02/5.27 tff(568,plain,
% 5.02/5.27 ((~((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.27 inference(unit_resolution,[status(thm)],[567, 566])).
% 5.02/5.27 tff(569,plain,
% 5.02/5.27 ((~![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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.27 inference(quant_inst,[status(thm)],[])).
% 5.02/5.27 tff(570,plain,
% 5.02/5.27 (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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.27 inference(unit_resolution,[status(thm)],[569, 196])).
% 5.02/5.27 tff(571,plain,
% 5.02/5.27 (((~![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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(572,plain,
% 5.02/5.27 ((~(~(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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(573,plain,
% 5.02/5.27 ((~(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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(574,plain,
% 5.02/5.27 (((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(575,plain,
% 5.02/5.27 (((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.27 inference(rewrite,[status(thm)],[])).
% 5.02/5.27 tff(576,plain,
% 5.02/5.27 ((((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))),
% 5.02/5.27 inference(monotonicity,[status(thm)],[575])).
% 5.02/5.27 tff(577,plain,
% 5.02/5.27 ((((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.27 inference(transitivity,[status(thm)],[576, 574])).
% 5.02/5.27 tff(578,plain,
% 5.02/5.27 ((((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.27 inference(transitivity,[status(thm)],[577, 573])).
% 5.02/5.27 tff(579,plain,
% 5.02/5.27 ((~(((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))))),
% 5.02/5.28 inference(monotonicity,[status(thm)],[578])).
% 5.02/5.28 tff(580,plain,
% 5.02/5.28 ((~(((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))),
% 5.02/5.28 inference(transitivity,[status(thm)],[579, 572])).
% 5.02/5.28 tff(581,plain,
% 5.02/5.28 (((~![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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.28 inference(monotonicity,[status(thm)],[580])).
% 5.02/5.28 tff(582,plain,
% 5.02/5.28 (((~![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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.28 inference(transitivity,[status(thm)],[581, 571])).
% 5.02/5.28 tff(583,plain,
% 5.02/5.28 ((~![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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))))),
% 5.02/5.28 inference(quant_inst,[status(thm)],[])).
% 5.02/5.28 tff(584,plain,
% 5.02/5.28 ((~![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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))),
% 5.02/5.28 inference(modus_ponens,[status(thm)],[583, 582])).
% 5.02/5.28 tff(585,plain,
% 5.02/5.28 (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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))),
% 5.02/5.28 inference(unit_resolution,[status(thm)],[584, 174])).
% 5.02/5.28 tff(586,plain,
% 5.02/5.28 ((~(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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))),
% 5.02/5.28 inference(tautology,[status(thm)],[])).
% 5.02/5.28 tff(587,plain,
% 5.02/5.28 ((~(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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.02/5.28 inference(unit_resolution,[status(thm)],[586, 378])).
% 5.02/5.28 tff(588,plain,
% 5.02/5.28 (~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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.28 inference(unit_resolution,[status(thm)],[587, 585])).
% 5.02/5.28 tff(589,plain,
% 5.02/5.28 ((~(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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), 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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.28 inference(tautology,[status(thm)],[])).
% 5.02/5.28 tff(590,plain,
% 5.02/5.28 ((~(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(A!6), unordered_pair(A!6, B!5))), power_set(unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.02/5.28 inference(unit_resolution,[status(thm)],[589, 588])).
% 5.02/5.28 tff(591,plain,
% 5.02/5.28 (~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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.02/5.28 inference(unit_resolution,[status(thm)],[590, 570])).
% 5.02/5.28 tff(592,plain,
% 5.02/5.28 ((~((~((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(A!6), unordered_pair(A!6, B!5))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.28 inference(tautology,[status(thm)],[])).
% 5.11/5.28 tff(593,plain,
% 5.11/5.28 ((~((~((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), 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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.11/5.28 inference(unit_resolution,[status(thm)],[592, 591])).
% 5.11/5.28 tff(594,plain,
% 5.11/5.28 (~((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.28 inference(unit_resolution,[status(thm)],[593, 568])).
% 5.11/5.28 tff(595,plain,
% 5.11/5.28 (((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(A!6), unordered_pair(A!6, B!5))))),
% 5.11/5.28 inference(tautology,[status(thm)],[])).
% 5.11/5.28 tff(596,plain,
% 5.11/5.28 (member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))),
% 5.11/5.28 inference(unit_resolution,[status(thm)],[595, 594])).
% 5.11/5.28 tff(597,plain,
% 5.11/5.28 (member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4))),
% 5.11/5.28 inference(modus_ponens,[status(thm)],[596, 559])).
% 5.11/5.28 tff(598,plain,
% 5.11/5.28 ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)) <=> (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4))),
% 5.11/5.28 inference(quant_inst,[status(thm)],[])).
% 5.11/5.28 tff(599,plain,
% 5.11/5.28 (member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)) <=> (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)),
% 5.11/5.28 inference(unit_resolution,[status(thm)],[598, 20])).
% 5.11/5.28 tff(600,plain,
% 5.11/5.28 (((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))) <=> ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3))))),
% 5.11/5.28 inference(rewrite,[status(thm)],[])).
% 5.11/5.28 tff(601,plain,
% 5.11/5.28 ((member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4))) <=> (member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))),
% 5.11/5.28 inference(rewrite,[status(thm)],[])).
% 5.11/5.28 tff(602,plain,
% 5.11/5.28 (((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)))) <=> ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3))))),
% 5.11/5.28 inference(monotonicity,[status(thm)],[601])).
% 5.11/5.28 tff(603,plain,
% 5.11/5.28 (((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)))) <=> ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3))))),
% 5.11/5.29 inference(transitivity,[status(thm)],[602, 600])).
% 5.11/5.29 tff(604,plain,
% 5.11/5.29 ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)))),
% 5.11/5.29 inference(quant_inst,[status(thm)],[])).
% 5.11/5.29 tff(605,plain,
% 5.11/5.29 ((~![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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))),
% 5.11/5.29 inference(modus_ponens,[status(thm)],[604, 603])).
% 5.11/5.29 tff(606,plain,
% 5.11/5.29 (member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[605, 10])).
% 5.11/5.29 tff(607,plain,
% 5.11/5.29 (((~member(tptp_fun_X_0(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(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(A!6), unordered_pair(A!6, B!5))))) | member(tptp_fun_X_0(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(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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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))))),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(608,plain,
% 5.11/5.29 (~member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[607, 594])).
% 5.11/5.29 tff(609,plain,
% 5.11/5.29 (((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))) <=> ((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.11/5.29 inference(rewrite,[status(thm)],[])).
% 5.11/5.29 tff(610,plain,
% 5.11/5.29 ((~((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))) <=> (~((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.11/5.29 inference(rewrite,[status(thm)],[])).
% 5.11/5.29 tff(611,plain,
% 5.11/5.29 (((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.11/5.29 inference(monotonicity,[status(thm)],[610])).
% 5.11/5.29 tff(612,plain,
% 5.11/5.29 (((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))) <=> ((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))))),
% 5.11/5.29 inference(transitivity,[status(thm)],[611, 609])).
% 5.11/5.29 tff(613,plain,
% 5.11/5.29 ((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~(subset(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(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))))),
% 5.11/5.29 inference(quant_inst,[status(thm)],[])).
% 5.11/5.29 tff(614,plain,
% 5.11/5.29 ((~![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(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))))),
% 5.11/5.29 inference(modus_ponens,[status(thm)],[613, 612])).
% 5.11/5.29 tff(615,plain,
% 5.11/5.29 (~((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[614, 96])).
% 5.11/5.29 tff(616,plain,
% 5.11/5.29 (((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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(U!4, V!3)), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)), unordered_pair(U!4, V!3)), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(617,plain,
% 5.11/5.29 ((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[616, 615])).
% 5.11/5.29 tff(618,plain,
% 5.11/5.29 ((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(619,plain,
% 5.11/5.29 ((~((~subset(unordered_pair(U!4, V!3), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | ![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[618, 518])).
% 5.11/5.29 tff(620,plain,
% 5.11/5.29 (![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[619, 617])).
% 5.11/5.29 tff(621,plain,
% 5.11/5.29 (((~![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(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(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(U!4, V!3))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(rewrite,[status(thm)],[])).
% 5.11/5.29 tff(622,plain,
% 5.11/5.29 ((~![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.29 inference(quant_inst,[status(thm)],[])).
% 5.11/5.29 tff(623,plain,
% 5.11/5.29 ((~![X: $i] : ((~member(X, unordered_pair(U!4, V!3))) | member(X, 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)), tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.29 inference(modus_ponens,[status(thm)],[622, 621])).
% 5.11/5.29 tff(624,plain,
% 5.11/5.29 (~member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[623, 620, 608])).
% 5.11/5.29 tff(625,plain,
% 5.11/5.29 ((~(member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))) | member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) | (~((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(626,plain,
% 5.11/5.29 ((~(member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), unordered_pair(U!4, V!3)) <=> ((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))) | (~((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[625, 624])).
% 5.11/5.29 tff(627,plain,
% 5.11/5.29 (~((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3))),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[626, 606])).
% 5.11/5.29 tff(628,plain,
% 5.11/5.29 (((tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = V!3)) | (~(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4))),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(629,plain,
% 5.11/5.29 (~(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)),
% 5.11/5.29 inference(unit_resolution,[status(thm)],[628, 627])).
% 5.11/5.29 tff(630,plain,
% 5.11/5.29 ((~(member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)) <=> (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4))) | (~member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4))) | (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4)),
% 5.11/5.29 inference(tautology,[status(thm)],[])).
% 5.11/5.29 tff(631,plain,
% 5.11/5.29 ((~(member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)) <=> (tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))) = U!4))) | (~member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4)))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[630, 629])).
% 5.11/5.30 tff(632,plain,
% 5.11/5.30 (~member(tptp_fun_X_0(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(A!6), unordered_pair(A!6, B!5)))), singleton(U!4))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[631, 599])).
% 5.11/5.30 tff(633,plain,
% 5.11/5.30 ($false),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[632, 597])).
% 5.11/5.30 tff(634,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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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)))))), inference(lemma,lemma(discharge,[]))).
% 5.11/5.30 tff(635,plain,
% 5.11/5.30 (((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))))))) <=> ((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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))))))))))),
% 5.11/5.30 inference(rewrite,[status(thm)],[])).
% 5.11/5.30 tff(636,plain,
% 5.11/5.30 ((~((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))))))) <=> (~((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))))))),
% 5.11/5.30 inference(rewrite,[status(thm)],[])).
% 5.11/5.30 tff(637,plain,
% 5.11/5.30 (((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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)))))))))))) <=> ((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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))))))))))),
% 5.11/5.30 inference(monotonicity,[status(thm)],[636])).
% 5.11/5.30 tff(638,plain,
% 5.11/5.30 (((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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)))))))))))) <=> ((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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))))))))))),
% 5.11/5.30 inference(transitivity,[status(thm)],[637, 635])).
% 5.11/5.30 tff(639,plain,
% 5.11/5.30 ((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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)))))))))))),
% 5.11/5.30 inference(quant_inst,[status(thm)],[])).
% 5.11/5.30 tff(640,plain,
% 5.11/5.30 ((~![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)), intersection(power_set(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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))))))),
% 5.11/5.30 inference(modus_ponens,[status(thm)],[639, 638])).
% 5.11/5.30 tff(641,plain,
% 5.11/5.30 (~((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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))))))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[640, 96])).
% 5.11/5.30 tff(642,plain,
% 5.11/5.30 (((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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))))))),
% 5.11/5.30 inference(tautology,[status(thm)],[])).
% 5.11/5.30 tff(643,plain,
% 5.11/5.30 ((~((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[642, 641])).
% 5.11/5.30 tff(644,plain,
% 5.11/5.30 ((~((~((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))),
% 5.11/5.30 inference(tautology,[status(thm)],[])).
% 5.11/5.30 tff(645,plain,
% 5.11/5.30 ((~((~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(A!6), unordered_pair(A!6, B!5))), 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(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[644, 643])).
% 5.11/5.30 tff(646,plain,
% 5.11/5.30 (subset(unordered_pair(singleton(A!6), 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)))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[645, 634])).
% 5.11/5.30 tff(647,plain,
% 5.11/5.30 (((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(tptp_fun_X_0(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(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(intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))), unordered_pair(singleton(A!6), 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))))))) | subset(unordered_pair(singleton(A!6), 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)))))))) | ((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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)))))))),
% 5.11/5.30 inference(tautology,[status(thm)],[])).
% 5.11/5.30 tff(648,plain,
% 5.11/5.30 ((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[647, 641])).
% 5.11/5.30 tff(649,plain,
% 5.11/5.30 ((~((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(tautology,[status(thm)],[])).
% 5.11/5.30 tff(650,plain,
% 5.11/5.30 ((~subset(unordered_pair(singleton(A!6), 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(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[649, 648])).
% 5.11/5.30 tff(651,plain,
% 5.11/5.30 (![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[650, 646])).
% 5.11/5.30 tff(652,plain,
% 5.11/5.30 (((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(rewrite,[status(thm)],[])).
% 5.11/5.30 tff(653,plain,
% 5.11/5.30 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), unordered_pair(A!6, B!5)))) | 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))))))),
% 5.11/5.30 inference(quant_inst,[status(thm)],[])).
% 5.11/5.30 tff(654,plain,
% 5.11/5.30 ((~![X: $i] : ((~member(X, unordered_pair(singleton(A!6), unordered_pair(A!6, B!5)))) | 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(A!6), unordered_pair(A!6, B!5)))) | 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)))))),
% 5.11/5.30 inference(modus_ponens,[status(thm)],[653, 652])).
% 5.11/5.30 tff(655,plain,
% 5.11/5.30 ((~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), intersection(power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[654, 651])).
% 5.11/5.30 tff(656,plain,
% 5.11/5.30 (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)))))),
% 5.11/5.30 inference(unit_resolution,[status(thm)],[655, 364])).
% 5.11/5.31 tff(657,plain,
% 5.11/5.31 ((~(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))))))),
% 5.11/5.31 inference(tautology,[status(thm)],[])).
% 5.11/5.31 tff(658,plain,
% 5.11/5.31 ((~(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))))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[657, 656])).
% 5.11/5.31 tff(659,plain,
% 5.11/5.31 (member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[658, 361])).
% 5.11/5.31 tff(660,plain,
% 5.11/5.31 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), 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))))) | subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(tautology,[status(thm)],[])).
% 5.11/5.31 tff(661,plain,
% 5.11/5.31 ((~(member(unordered_pair(A!6, B!5), power_set(unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) <=> subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[660, 659])).
% 5.11/5.31 tff(662,plain,
% 5.11/5.31 (subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[661, 346])).
% 5.11/5.31 tff(663,plain,
% 5.11/5.31 ((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))))) | (~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(tautology,[status(thm)],[])).
% 5.11/5.31 tff(664,plain,
% 5.11/5.31 ((~((~subset(unordered_pair(A!6, B!5), unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))) | ![X: $i] : ((~member(X, 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(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[663, 662])).
% 5.11/5.31 tff(665,plain,
% 5.11/5.31 (![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[664, 344])).
% 5.11/5.31 tff(666,plain,
% 5.11/5.31 (((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(U!4, unordered_pair(A!6, B!5))) | member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) <=> ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(U!4, unordered_pair(A!6, B!5))) | member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(rewrite,[status(thm)],[])).
% 5.11/5.31 tff(667,plain,
% 5.11/5.31 ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | ((~member(U!4, unordered_pair(A!6, B!5))) | member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))),
% 5.11/5.31 inference(quant_inst,[status(thm)],[])).
% 5.11/5.31 tff(668,plain,
% 5.11/5.31 ((~![X: $i] : ((~member(X, unordered_pair(A!6, B!5))) | member(X, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3))))) | (~member(U!4, unordered_pair(A!6, B!5))) | member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(modus_ponens,[status(thm)],[667, 666])).
% 5.11/5.31 tff(669,plain,
% 5.11/5.31 ((~member(U!4, unordered_pair(A!6, B!5))) | member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[668, 665])).
% 5.11/5.31 tff(670,plain,
% 5.11/5.31 (member(U!4, unordered_pair(singleton(U!4), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[669, 135])).
% 5.11/5.31 tff(671,plain,
% 5.11/5.31 (member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(modus_ponens,[status(thm)],[670, 340])).
% 5.11/5.31 tff(672,plain,
% 5.11/5.31 ((~(member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))))) | (~member(B!5, unordered_pair(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))) | ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5)))),
% 5.11/5.31 inference(tautology,[status(thm)],[])).
% 5.11/5.31 tff(673,plain,
% 5.11/5.31 ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[672, 671, 337])).
% 5.11/5.31 tff(674,plain,
% 5.11/5.31 ((~((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5)))) | (B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))),
% 5.11/5.31 inference(tautology,[status(thm)],[])).
% 5.11/5.31 tff(675,plain,
% 5.11/5.31 ((B!5 = unordered_pair(U!4, V!3)) | (B!5 = unordered_pair(A!6, B!5))),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[674, 673])).
% 5.11/5.31 tff(676,plain,
% 5.11/5.31 (B!5 = unordered_pair(A!6, B!5)),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[675, 333])).
% 5.11/5.31 tff(677,plain,
% 5.11/5.31 (unordered_pair(A!6, B!5) = B!5),
% 5.11/5.31 inference(symmetry,[status(thm)],[676])).
% 5.11/5.31 tff(678,plain,
% 5.11/5.31 (unordered_pair(A!6, B!5) = U!4),
% 5.11/5.31 inference(transitivity,[status(thm)],[677, 141])).
% 5.11/5.31 tff(679,plain,
% 5.11/5.31 (unordered_pair(unordered_pair(A!6, B!5), V!3) = unordered_pair(U!4, V!3)),
% 5.11/5.31 inference(monotonicity,[status(thm)],[678])).
% 5.11/5.31 tff(680,plain,
% 5.11/5.31 (member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)) <=> member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))),
% 5.11/5.31 inference(monotonicity,[status(thm)],[679])).
% 5.11/5.31 tff(681,plain,
% 5.11/5.31 (member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)) <=> member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))),
% 5.11/5.31 inference(symmetry,[status(thm)],[680])).
% 5.11/5.31 tff(682,plain,
% 5.11/5.31 ((~member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))) <=> (~member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)))),
% 5.11/5.31 inference(monotonicity,[status(thm)],[681])).
% 5.11/5.31 tff(683,plain,
% 5.11/5.31 (U!4 = unordered_pair(A!6, B!5)),
% 5.11/5.31 inference(transitivity,[status(thm)],[140, 676])).
% 5.11/5.31 tff(684,plain,
% 5.11/5.31 (member(U!4, singleton(A!6)) <=> member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))),
% 5.11/5.31 inference(monotonicity,[status(thm)],[683, 313])).
% 5.11/5.31 tff(685,plain,
% 5.11/5.31 ((~member(U!4, singleton(A!6))) <=> (~member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3)))),
% 5.11/5.31 inference(monotonicity,[status(thm)],[684])).
% 5.11/5.31 tff(686,plain,
% 5.11/5.31 (~member(unordered_pair(A!6, B!5), unordered_pair(U!4, V!3))),
% 5.11/5.31 inference(modus_ponens,[status(thm)],[39, 685])).
% 5.11/5.31 tff(687,plain,
% 5.11/5.31 (~member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))),
% 5.11/5.31 inference(modus_ponens,[status(thm)],[686, 682])).
% 5.11/5.31 tff(688,assumption,(member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))), introduced(assumption)).
% 5.11/5.31 tff(689,plain,
% 5.11/5.31 ($false),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[688, 687])).
% 5.11/5.31 tff(690,plain,(~member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))), inference(lemma,lemma(discharge,[]))).
% 5.11/5.31 tff(691,plain,
% 5.11/5.31 (((~![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(unordered_pair(A!6, B!5), V!3))) <=> ((~![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(unordered_pair(A!6, B!5), V!3)))),
% 5.11/5.31 inference(rewrite,[status(thm)],[])).
% 5.11/5.31 tff(692,plain,
% 5.11/5.31 ((member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)) <=> $true) <=> member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))),
% 5.11/5.31 inference(rewrite,[status(thm)],[])).
% 5.11/5.31 tff(693,plain,
% 5.11/5.31 (((unordered_pair(A!6, B!5) = V!3) | $true) <=> $true),
% 5.11/5.31 inference(rewrite,[status(thm)],[])).
% 5.11/5.31 tff(694,plain,
% 5.11/5.31 ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) <=> $true),
% 5.11/5.31 inference(rewrite,[status(thm)],[])).
% 5.11/5.31 tff(695,plain,
% 5.11/5.31 (((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) <=> ((unordered_pair(A!6, B!5) = V!3) | $true)),
% 5.11/5.31 inference(monotonicity,[status(thm)],[694])).
% 5.11/5.31 tff(696,plain,
% 5.11/5.31 (((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) <=> $true),
% 5.11/5.31 inference(transitivity,[status(thm)],[695, 693])).
% 5.11/5.31 tff(697,plain,
% 5.11/5.31 ((member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)) <=> ((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)))) <=> (member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)) <=> $true)),
% 5.11/5.31 inference(monotonicity,[status(thm)],[696])).
% 5.11/5.31 tff(698,plain,
% 5.11/5.31 ((member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)) <=> ((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)))) <=> member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))),
% 5.11/5.31 inference(transitivity,[status(thm)],[697, 692])).
% 5.11/5.31 tff(699,plain,
% 5.11/5.31 (((~![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(unordered_pair(A!6, B!5), V!3)) <=> ((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, 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(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)))),
% 5.11/5.31 inference(monotonicity,[status(thm)],[698])).
% 5.11/5.31 tff(700,plain,
% 5.11/5.31 (((~![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(unordered_pair(A!6, B!5), V!3)) <=> ((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, 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(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3)))),
% 5.11/5.31 inference(transitivity,[status(thm)],[699, 691])).
% 5.11/5.31 tff(701,plain,
% 5.11/5.31 ((~![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(unordered_pair(A!6, B!5), V!3)) <=> ((unordered_pair(A!6, B!5) = V!3) | (unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))))),
% 5.11/5.31 inference(quant_inst,[status(thm)],[])).
% 5.11/5.31 tff(702,plain,
% 5.11/5.31 ((~![X: $i, A: $i, B: $i] : (member(X, unordered_pair(A, B)) <=> ((X = B) | (X = A)))) | member(unordered_pair(A!6, B!5), unordered_pair(unordered_pair(A!6, B!5), V!3))),
% 5.11/5.31 inference(modus_ponens,[status(thm)],[701, 700])).
% 5.11/5.31 tff(703,plain,
% 5.11/5.31 ($false),
% 5.11/5.31 inference(unit_resolution,[status(thm)],[702, 10, 690])).
% 5.11/5.31 % SZS output end Proof
% 5.11/5.31 % E exiting
%------------------------------------------------------------------------------