%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET018-4 : TPTP v9.0.0. Released v1.0.0.
% 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 05:24:50 AM UTC 2025
% Result : Unsatisfiable 5.81s 5.97s
% Output : Proof 5.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET018-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 04:03:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.81/5.97 % SZS status Unsatisfiable
% 5.81/5.97 % SZS output start Proof
% 5.81/5.97 tff(f2_type, type, (
% 5.81/5.97 f2: $i > $i)).
% 5.81/5.97 tff(ordered_pair_type, type, (
% 5.81/5.97 ordered_pair: ( $i * $i ) > $i)).
% 5.81/5.97 tff(d_type, type, (
% 5.81/5.97 d: $i)).
% 5.81/5.97 tff(c_type, type, (
% 5.81/5.97 c: $i)).
% 5.81/5.97 tff(b_type, type, (
% 5.81/5.97 b: $i)).
% 5.81/5.97 tff(member_type, type, (
% 5.81/5.97 member: ( $i * $i ) > $o)).
% 5.81/5.97 tff(non_ordered_pair_type, type, (
% 5.81/5.97 non_ordered_pair: ( $i * $i ) > $i)).
% 5.81/5.97 tff(a_type, type, (
% 5.81/5.97 a: $i)).
% 5.81/5.97 tff(singleton_set_type, type, (
% 5.81/5.97 singleton_set: $i > $i)).
% 5.81/5.97 tff(f3_type, type, (
% 5.81/5.97 f3: $i > $i)).
% 5.81/5.97 tff(f23_type, type, (
% 5.81/5.97 f23: ( $i * $i ) > $i)).
% 5.81/5.97 tff(disjoint_type, type, (
% 5.81/5.97 disjoint: ( $i * $i ) > $o)).
% 5.81/5.97 tff(little_set_type, type, (
% 5.81/5.97 little_set: $i > $o)).
% 5.81/5.97 tff(f16_type, type, (
% 5.81/5.97 f16: ( $i * $i ) > $i)).
% 5.81/5.97 tff(ordered_pair_predicate_type, type, (
% 5.81/5.97 ordered_pair_predicate: $i > $o)).
% 5.81/5.97 tff(universal_set_type, type, (
% 5.81/5.97 universal_set: $i)).
% 5.81/5.97 tff(sigma_type, type, (
% 5.81/5.97 sigma: $i > $i)).
% 5.81/5.97 tff(1,plain,
% 5.81/5.97 ((d = b) <=> (b = d)),
% 5.81/5.97 inference(commutativity,[status(thm)],[])).
% 5.81/5.97 tff(2,plain,
% 5.81/5.97 ((singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) <=> (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))),
% 5.81/5.97 inference(commutativity,[status(thm)],[])).
% 5.81/5.97 tff(3,plain,
% 5.81/5.97 (^[X: $i] : refl((singleton_set(X) = non_ordered_pair(X, X)) <=> (singleton_set(X) = non_ordered_pair(X, X)))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(4,plain,
% 5.81/5.97 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[3])).
% 5.81/5.97 tff(5,plain,
% 5.81/5.97 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(6,axiom,(![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','singleton_set')).
% 5.81/5.97 tff(7,plain,
% 5.81/5.97 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[6, 5])).
% 5.81/5.97 tff(8,plain,(
% 5.81/5.97 ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 5.81/5.97 inference(skolemize,[status(sab)],[7])).
% 5.81/5.97 tff(9,plain,
% 5.81/5.97 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[8, 4])).
% 5.81/5.97 tff(10,plain,
% 5.81/5.97 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(11,plain,
% 5.81/5.97 (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.81/5.97 inference(unit_resolution,[status(thm)],[10, 9])).
% 5.81/5.97 tff(12,plain,
% 5.81/5.97 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = singleton_set(f2(ordered_pair(c, d)))),
% 5.81/5.97 inference(symmetry,[status(thm)],[11])).
% 5.81/5.97 tff(13,plain,
% 5.81/5.97 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) <=> (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, b))),
% 5.81/5.97 inference(monotonicity,[status(thm)],[12])).
% 5.81/5.97 tff(14,plain,
% 5.81/5.97 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) <=> (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))),
% 5.81/5.97 inference(transitivity,[status(thm)],[13, 2])).
% 5.81/5.97 tff(15,plain,
% 5.81/5.97 ((non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b))),
% 5.81/5.97 inference(symmetry,[status(thm)],[14])).
% 5.81/5.97 tff(16,plain,
% 5.81/5.97 ((~(non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))) <=> (~(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)))),
% 5.81/5.97 inference(monotonicity,[status(thm)],[15])).
% 5.81/5.97 tff(17,assumption,(~(non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))), introduced(assumption)).
% 5.81/5.97 tff(18,plain,
% 5.81/5.97 (~(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[17, 16])).
% 5.81/5.97 tff(19,plain,
% 5.81/5.97 ((singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) <=> (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))),
% 5.81/5.97 inference(commutativity,[status(thm)],[])).
% 5.81/5.97 tff(20,plain,
% 5.81/5.97 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) <=> (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.81/5.97 inference(monotonicity,[status(thm)],[12])).
% 5.81/5.97 tff(21,plain,
% 5.81/5.97 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) <=> (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))),
% 5.81/5.97 inference(transitivity,[status(thm)],[20, 19])).
% 5.81/5.97 tff(22,plain,
% 5.81/5.97 ((non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.81/5.97 inference(symmetry,[status(thm)],[21])).
% 5.81/5.97 tff(23,plain,
% 5.81/5.97 ((b = f23(non_ordered_pair(a, b), non_ordered_pair(a, a))) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.81/5.97 inference(commutativity,[status(thm)],[])).
% 5.81/5.97 tff(24,plain,
% 5.81/5.97 (little_set(a) <=> little_set(a)),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(25,axiom,(little_set(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_little_set')).
% 5.81/5.97 tff(26,plain,
% 5.81/5.97 (little_set(a)),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[25, 24])).
% 5.81/5.97 tff(27,plain,
% 5.81/5.97 (^[Y: $i, X: $i] : refl(((~little_set(X)) | member(X, non_ordered_pair(X, Y))) <=> ((~little_set(X)) | member(X, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(28,plain,
% 5.81/5.97 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[27])).
% 5.81/5.97 tff(29,plain,
% 5.81/5.97 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(30,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(elim_unused_vars,[status(thm)],[])).
% 5.81/5.97 tff(31,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~(U = X)) | (~little_set(U))) <=> ![Y: $i, U: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(destructive_equality_resolution,[status(thm)],[])).
% 5.81/5.97 tff(32,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~(U = X)) | (~little_set(U))) <=> ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(transitivity,[status(thm)],[31, 30])).
% 5.81/5.97 tff(33,plain,
% 5.81/5.97 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) <=> (member(U, non_ordered_pair(X, Y)) | (~little_set(U)))), (((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))) <=> ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))))), rewrite(((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))) <=> (member(U, non_ordered_pair(X, Y)) | (~(U = X)) | (~little_set(U)))), (((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))) <=> (member(U, non_ordered_pair(X, Y)) | (~(U = X)) | (~little_set(U)))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(34,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))) <=> ![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~(U = X)) | (~little_set(U)))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[33])).
% 5.81/5.97 tff(35,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X))) <=> ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(transitivity,[status(thm)],[34, 32])).
% 5.81/5.97 tff(36,axiom,(![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','non_ordered_pair2')).
% 5.81/5.97 tff(37,plain,
% 5.81/5.97 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[36, 35])).
% 5.81/5.97 tff(38,plain,
% 5.81/5.97 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[37, 29])).
% 5.81/5.97 tff(39,plain,(
% 5.81/5.97 ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(skolemize,[status(sab)],[38])).
% 5.81/5.97 tff(40,plain,
% 5.81/5.97 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[39, 28])).
% 5.81/5.97 tff(41,plain,
% 5.81/5.97 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, a)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, a)))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(42,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, a)))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(43,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, a))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[42, 41])).
% 5.81/5.97 tff(44,plain,
% 5.81/5.97 (member(a, non_ordered_pair(a, a))),
% 5.81/5.97 inference(unit_resolution,[status(thm)],[43, 40, 26])).
% 5.81/5.97 tff(45,plain,
% 5.81/5.97 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, b)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, b)))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(46,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, b)))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(47,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, b))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[46, 45])).
% 5.81/5.97 tff(48,plain,
% 5.81/5.97 (member(a, non_ordered_pair(a, b))),
% 5.81/5.97 inference(unit_resolution,[status(thm)],[47, 40, 26])).
% 5.81/5.97 tff(49,plain,
% 5.81/5.97 (^[Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y))) <=> ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(50,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[49])).
% 5.81/5.97 tff(51,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(52,plain,
% 5.81/5.97 (^[Y: $i, U: $i, X: $i] : rewrite((((~disjoint(X, Y)) | (~member(U, X))) | (~member(U, Y))) <=> ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(53,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : (((~disjoint(X, Y)) | (~member(U, X))) | (~member(U, Y))) <=> ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[52])).
% 5.81/5.97 tff(54,axiom,(![Y: $i, U: $i, X: $i] : (((~disjoint(X, Y)) | (~member(U, X))) | (~member(U, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','disjoint1')).
% 5.81/5.97 tff(55,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[54, 53])).
% 5.81/5.97 tff(56,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[55, 51])).
% 5.81/5.97 tff(57,plain,(
% 5.81/5.97 ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(skolemize,[status(sab)],[56])).
% 5.81/5.97 tff(58,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[57, 50])).
% 5.81/5.97 tff(59,plain,
% 5.81/5.97 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, non_ordered_pair(a, b))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(60,plain,
% 5.81/5.97 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(61,plain,
% 5.81/5.97 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, non_ordered_pair(a, b))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a)))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[60, 59])).
% 5.81/5.97 tff(62,plain,
% 5.81/5.97 (~disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a))),
% 5.81/5.97 inference(unit_resolution,[status(thm)],[61, 58, 48, 44])).
% 5.81/5.97 tff(63,plain,
% 5.81/5.97 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), Y)) <=> (disjoint(X, Y) | member(f23(X, Y), Y)))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(64,plain,
% 5.81/5.97 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[63])).
% 5.81/5.97 tff(65,plain,
% 5.81/5.97 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(66,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','disjoint3')).
% 5.81/5.97 tff(67,plain,
% 5.81/5.97 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[66, 65])).
% 5.81/5.97 tff(68,plain,(
% 5.81/5.97 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 5.81/5.97 inference(skolemize,[status(sab)],[67])).
% 5.81/5.97 tff(69,plain,
% 5.81/5.97 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[68, 64])).
% 5.81/5.97 tff(70,plain,
% 5.81/5.97 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(71,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(72,plain,
% 5.81/5.97 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(a, b), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[71, 70])).
% 5.81/5.97 tff(73,plain,
% 5.81/5.97 (member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 5.81/5.97 inference(unit_resolution,[status(thm)],[72, 69, 62])).
% 5.81/5.97 tff(74,plain,
% 5.81/5.97 (^[Y: $i, U: $i, X: $i] : refl(((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y)))) <=> ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y)))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(75,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[74])).
% 5.81/5.97 tff(76,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(77,plain,
% 5.81/5.97 (^[Y: $i, U: $i, X: $i] : rewrite((((~member(U, non_ordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y)))))),
% 5.81/5.97 inference(bind,[status(th)],[])).
% 5.81/5.97 tff(78,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : (((~member(U, non_ordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(quant_intro,[status(thm)],[77])).
% 5.81/5.97 tff(79,axiom,(![Y: $i, U: $i, X: $i] : (((~member(U, non_ordered_pair(X, Y))) | (U = X)) | (U = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','non_ordered_pair1')).
% 5.81/5.97 tff(80,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[79, 78])).
% 5.81/5.97 tff(81,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[80, 76])).
% 5.81/5.97 tff(82,plain,(
% 5.81/5.97 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(skolemize,[status(sab)],[81])).
% 5.81/5.97 tff(83,plain,
% 5.81/5.97 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 5.81/5.97 inference(modus_ponens,[status(thm)],[82, 75])).
% 5.81/5.97 tff(84,plain,
% 5.81/5.97 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(85,plain,
% 5.81/5.97 (((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))) <=> ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(rewrite,[status(thm)],[])).
% 5.81/5.97 tff(86,plain,
% 5.81/5.97 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))))),
% 5.81/5.97 inference(monotonicity,[status(thm)],[85])).
% 5.81/5.97 tff(87,plain,
% 5.81/5.97 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(transitivity,[status(thm)],[86, 84])).
% 5.81/5.97 tff(88,plain,
% 5.81/5.97 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 5.81/5.97 inference(quant_inst,[status(thm)],[])).
% 5.81/5.97 tff(89,plain,
% 5.81/5.97 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, b), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[88, 87])).
% 5.81/5.98 tff(90,plain,
% 5.81/5.98 (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = a),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[89, 83, 73])).
% 5.81/5.98 tff(91,plain,
% 5.81/5.98 (a = f23(non_ordered_pair(a, b), non_ordered_pair(a, a))),
% 5.81/5.98 inference(symmetry,[status(thm)],[90])).
% 5.81/5.98 tff(92,assumption,(~(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))), introduced(assumption)).
% 5.81/5.98 tff(93,plain,
% 5.81/5.98 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) <=> (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(commutativity,[status(thm)],[])).
% 5.81/5.98 tff(94,plain,
% 5.81/5.98 ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(symmetry,[status(thm)],[93])).
% 5.81/5.98 tff(95,assumption,(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)), introduced(assumption)).
% 5.81/5.98 tff(96,plain,
% 5.81/5.98 (non_ordered_pair(a, a) = f16(a, ordered_pair(c, d))),
% 5.81/5.98 inference(symmetry,[status(thm)],[95])).
% 5.81/5.98 tff(97,plain,
% 5.81/5.98 ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[96])).
% 5.81/5.98 tff(98,plain,
% 5.81/5.98 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(symmetry,[status(thm)],[97])).
% 5.81/5.98 tff(99,plain,
% 5.81/5.98 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(commutativity,[status(thm)],[])).
% 5.81/5.98 tff(100,plain,
% 5.81/5.98 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(transitivity,[status(thm)],[99, 98, 94])).
% 5.81/5.98 tff(101,plain,
% 5.81/5.98 (^[Y: $i, X: $i] : refl((ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y))) <=> (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(102,plain,
% 5.81/5.98 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[101])).
% 5.81/5.98 tff(103,plain,
% 5.81/5.98 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(104,axiom,(![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','ordered_pair')).
% 5.81/5.98 tff(105,plain,
% 5.81/5.98 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[104, 103])).
% 5.81/5.98 tff(106,plain,(
% 5.81/5.98 ![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(skolemize,[status(sab)],[105])).
% 5.81/5.98 tff(107,plain,
% 5.81/5.98 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[106, 102])).
% 5.81/5.98 tff(108,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(109,plain,
% 5.81/5.98 (ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[108, 107])).
% 5.81/5.98 tff(110,plain,
% 5.81/5.98 ((ordered_pair(a, b) = ordered_pair(c, d)) <=> (ordered_pair(a, b) = ordered_pair(c, d))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(111,axiom,(ordered_pair(a, b) = ordered_pair(c, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_ordered_pair')).
% 5.81/5.98 tff(112,plain,
% 5.81/5.98 (ordered_pair(a, b) = ordered_pair(c, d)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[111, 110])).
% 5.81/5.98 tff(113,plain,
% 5.81/5.98 (ordered_pair(c, d) = ordered_pair(a, b)),
% 5.81/5.98 inference(symmetry,[status(thm)],[112])).
% 5.81/5.98 tff(114,plain,
% 5.81/5.98 (ordered_pair_predicate(ordered_pair(c, d)) <=> ordered_pair_predicate(ordered_pair(a, b))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[113])).
% 5.81/5.98 tff(115,plain,
% 5.81/5.98 (ordered_pair_predicate(ordered_pair(a, b)) <=> ordered_pair_predicate(ordered_pair(c, d))),
% 5.81/5.98 inference(symmetry,[status(thm)],[114])).
% 5.81/5.98 tff(116,plain,
% 5.81/5.98 (little_set(b) <=> little_set(b)),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(117,axiom,(little_set(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_little_set')).
% 5.81/5.98 tff(118,plain,
% 5.81/5.98 (little_set(b)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[117, 116])).
% 5.81/5.98 tff(119,plain,
% 5.81/5.98 (^[Z: $i, Y: $i] : refl(((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(120,plain,
% 5.81/5.98 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[119])).
% 5.81/5.98 tff(121,plain,
% 5.81/5.98 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(122,plain,
% 5.81/5.98 (![Z: $i, Y: $i, X: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(elim_unused_vars,[status(thm)],[])).
% 5.81/5.98 tff(123,plain,
% 5.81/5.98 (![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(destructive_equality_resolution,[status(thm)],[])).
% 5.81/5.98 tff(124,plain,
% 5.81/5.98 (![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(transitivity,[status(thm)],[123, 122])).
% 5.81/5.98 tff(125,plain,
% 5.81/5.98 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z)))), ((((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> (((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))))), rewrite((((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))), ((((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(126,plain,
% 5.81/5.98 (![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[125])).
% 5.81/5.98 tff(127,plain,
% 5.81/5.98 (![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(transitivity,[status(thm)],[126, 124])).
% 5.81/5.98 tff(128,axiom,(![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','ordered_pair_predicate4')).
% 5.81/5.98 tff(129,plain,
% 5.81/5.98 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[128, 127])).
% 5.81/5.98 tff(130,plain,
% 5.81/5.98 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[129, 121])).
% 5.81/5.98 tff(131,plain,(
% 5.81/5.98 ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(skolemize,[status(sab)],[130])).
% 5.81/5.98 tff(132,plain,
% 5.81/5.98 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[131, 120])).
% 5.81/5.98 tff(133,plain,
% 5.81/5.98 (((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(b)) | (~little_set(a)) | ordered_pair_predicate(ordered_pair(a, b)))) <=> ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | (~little_set(b)) | (~little_set(a)) | ordered_pair_predicate(ordered_pair(a, b)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(134,plain,
% 5.81/5.98 ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(b)) | (~little_set(a)) | ordered_pair_predicate(ordered_pair(a, b)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(135,plain,
% 5.81/5.98 ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | (~little_set(b)) | (~little_set(a)) | ordered_pair_predicate(ordered_pair(a, b))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[134, 133])).
% 5.81/5.98 tff(136,plain,
% 5.81/5.98 (ordered_pair_predicate(ordered_pair(a, b))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[135, 132, 26, 118])).
% 5.81/5.98 tff(137,plain,
% 5.81/5.98 (ordered_pair_predicate(ordered_pair(c, d))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[136, 115])).
% 5.81/5.98 tff(138,plain,
% 5.81/5.98 (^[X: $i] : refl(((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X)))) <=> ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X)))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(139,plain,
% 5.81/5.98 (![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X)))) <=> ![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[138])).
% 5.81/5.98 tff(140,plain,
% 5.81/5.98 (![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X)))) <=> ![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(141,axiom,(![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','ordered_pair_predicate3')).
% 5.81/5.98 tff(142,plain,
% 5.81/5.98 (![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[141, 140])).
% 5.81/5.98 tff(143,plain,(
% 5.81/5.98 ![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))),
% 5.81/5.98 inference(skolemize,[status(sab)],[142])).
% 5.81/5.98 tff(144,plain,
% 5.81/5.98 (![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[143, 139])).
% 5.81/5.98 tff(145,plain,
% 5.81/5.98 (((~![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))) | ((~ordered_pair_predicate(ordered_pair(c, d))) | (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))) <=> ((~![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))) | (~ordered_pair_predicate(ordered_pair(c, d))) | (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(146,plain,
% 5.81/5.98 ((~![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))) | ((~ordered_pair_predicate(ordered_pair(c, d))) | (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(147,plain,
% 5.81/5.98 ((~![X: $i] : ((~ordered_pair_predicate(X)) | (X = ordered_pair(f2(X), f3(X))))) | (~ordered_pair_predicate(ordered_pair(c, d))) | (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[146, 145])).
% 5.81/5.98 tff(148,plain,
% 5.81/5.98 ((~ordered_pair_predicate(ordered_pair(c, d))) | (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[147, 144])).
% 5.81/5.98 tff(149,plain,
% 5.81/5.98 (ordered_pair(c, d) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[148, 137])).
% 5.81/5.98 tff(150,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(c, d) = non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(151,plain,
% 5.81/5.98 (ordered_pair(c, d) = non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[150, 107])).
% 5.81/5.98 tff(152,plain,
% 5.81/5.98 (non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)) = ordered_pair(c, d)),
% 5.81/5.98 inference(symmetry,[status(thm)],[151])).
% 5.81/5.98 tff(153,plain,
% 5.81/5.98 ((non_ordered_pair(c, d) = f16(a, ordered_pair(c, d))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d))),
% 5.81/5.98 inference(commutativity,[status(thm)],[])).
% 5.81/5.98 tff(154,plain,
% 5.81/5.98 ((non_ordered_pair(c, d) = non_ordered_pair(a, a)) <=> (non_ordered_pair(c, d) = f16(a, ordered_pair(c, d)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[96])).
% 5.81/5.98 tff(155,plain,
% 5.81/5.98 ((non_ordered_pair(c, d) = non_ordered_pair(a, a)) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d))),
% 5.81/5.98 inference(transitivity,[status(thm)],[154, 153])).
% 5.81/5.98 tff(156,plain,
% 5.81/5.98 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) <=> (non_ordered_pair(c, d) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(symmetry,[status(thm)],[155])).
% 5.81/5.98 tff(157,plain,
% 5.81/5.98 ((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d))) <=> (~(non_ordered_pair(c, d) = non_ordered_pair(a, a)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[156])).
% 5.81/5.98 tff(158,assumption,(~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d))), introduced(assumption)).
% 5.81/5.98 tff(159,plain,
% 5.81/5.98 (~(non_ordered_pair(c, d) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[158, 157])).
% 5.81/5.98 tff(160,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(a, b) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(161,plain,
% 5.81/5.98 (ordered_pair(a, b) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[160, 107])).
% 5.81/5.98 tff(162,plain,
% 5.81/5.98 (non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)) = ordered_pair(a, b)),
% 5.81/5.98 inference(symmetry,[status(thm)],[161])).
% 5.81/5.98 tff(163,plain,
% 5.81/5.98 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(a) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(164,plain,
% 5.81/5.98 (singleton_set(a) = non_ordered_pair(a, a)),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[163, 9])).
% 5.81/5.98 tff(165,plain,
% 5.81/5.98 (non_ordered_pair(a, a) = singleton_set(a)),
% 5.81/5.98 inference(symmetry,[status(thm)],[164])).
% 5.81/5.98 tff(166,plain,
% 5.81/5.98 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[165])).
% 5.81/5.98 tff(167,plain,
% 5.81/5.98 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)) = non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))),
% 5.81/5.98 inference(transitivity,[status(thm)],[166, 162, 112, 151])).
% 5.81/5.98 tff(168,plain,
% 5.81/5.98 (member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[167])).
% 5.81/5.98 tff(169,plain,
% 5.81/5.98 (member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))) <=> member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.81/5.98 inference(symmetry,[status(thm)],[168])).
% 5.81/5.98 tff(170,plain,
% 5.81/5.98 (^[Y: $i, X: $i] : refl(little_set(non_ordered_pair(X, Y)) <=> little_set(non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(171,plain,
% 5.81/5.98 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[170])).
% 5.81/5.98 tff(172,plain,
% 5.81/5.98 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(173,axiom,(![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','non_ordered_pair4')).
% 5.81/5.98 tff(174,plain,
% 5.81/5.98 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[173, 172])).
% 5.81/5.98 tff(175,plain,(
% 5.81/5.98 ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 5.81/5.98 inference(skolemize,[status(sab)],[174])).
% 5.81/5.98 tff(176,plain,
% 5.81/5.98 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[175, 171])).
% 5.81/5.98 tff(177,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(c, d))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(178,plain,
% 5.81/5.98 (little_set(non_ordered_pair(c, d))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[177, 176])).
% 5.81/5.98 tff(179,plain,
% 5.81/5.98 (^[Y: $i, X: $i] : refl(((~little_set(Y)) | member(Y, non_ordered_pair(X, Y))) <=> ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(180,plain,
% 5.81/5.98 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[179])).
% 5.81/5.98 tff(181,plain,
% 5.81/5.98 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(182,plain,
% 5.81/5.98 (^[Y: $i, X: $i] : rewrite((member(Y, non_ordered_pair(X, Y)) | (~little_set(Y))) <=> ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(183,plain,
% 5.81/5.98 (![Y: $i, X: $i] : (member(Y, non_ordered_pair(X, Y)) | (~little_set(Y))) <=> ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[182])).
% 5.81/5.98 tff(184,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : (member(Y, non_ordered_pair(X, Y)) | (~little_set(Y))) <=> ![Y: $i, X: $i] : (member(Y, non_ordered_pair(X, Y)) | (~little_set(Y)))),
% 5.81/5.98 inference(elim_unused_vars,[status(thm)],[])).
% 5.81/5.98 tff(185,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y))) <=> ![Y: $i, U: $i, X: $i] : (member(Y, non_ordered_pair(X, Y)) | (~little_set(Y)))),
% 5.81/5.98 inference(destructive_equality_resolution,[status(thm)],[])).
% 5.81/5.98 tff(186,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y))) <=> ![Y: $i, X: $i] : (member(Y, non_ordered_pair(X, Y)) | (~little_set(Y)))),
% 5.81/5.98 inference(transitivity,[status(thm)],[185, 184])).
% 5.81/5.98 tff(187,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y))) <=> ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(transitivity,[status(thm)],[186, 183])).
% 5.81/5.98 tff(188,plain,
% 5.81/5.98 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) <=> (member(U, non_ordered_pair(X, Y)) | (~little_set(U)))), (((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))) <=> ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))))), rewrite(((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))) <=> (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y)))), (((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))) <=> (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y)))))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(189,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, non_ordered_pair(X, Y)) | (~little_set(U)) | (~(U = Y)))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[188])).
% 5.81/5.98 tff(190,plain,
% 5.81/5.98 (![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y))) <=> ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(transitivity,[status(thm)],[189, 187])).
% 5.81/5.98 tff(191,axiom,(![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','non_ordered_pair3')).
% 5.81/5.98 tff(192,plain,
% 5.81/5.98 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[191, 190])).
% 5.81/5.98 tff(193,plain,
% 5.81/5.98 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[192, 181])).
% 5.81/5.98 tff(194,plain,(
% 5.81/5.98 ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(skolemize,[status(sab)],[193])).
% 5.81/5.98 tff(195,plain,
% 5.81/5.98 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[194, 180])).
% 5.81/5.98 tff(196,plain,
% 5.81/5.98 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(c, d))) | member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(c, d))) | member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(197,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(c, d))) | member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(198,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(c, d))) | member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[197, 196])).
% 5.81/5.98 tff(199,plain,
% 5.81/5.98 ((~little_set(non_ordered_pair(c, d))) | member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[198, 195])).
% 5.81/5.98 tff(200,plain,
% 5.81/5.98 (member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[199, 178])).
% 5.81/5.98 tff(201,plain,
% 5.81/5.98 (member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[200, 169])).
% 5.81/5.98 tff(202,plain,
% 5.81/5.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(203,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(204,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[203, 202])).
% 5.81/5.98 tff(205,plain,
% 5.81/5.98 ((non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, d), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[204, 83])).
% 5.81/5.98 tff(206,plain,
% 5.81/5.98 ((non_ordered_pair(c, d) = non_ordered_pair(a, b)) | (non_ordered_pair(c, d) = non_ordered_pair(a, a))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[205, 201])).
% 5.81/5.98 tff(207,plain,
% 5.81/5.98 (non_ordered_pair(c, d) = non_ordered_pair(a, b)),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[206, 159])).
% 5.81/5.98 tff(208,plain,
% 5.81/5.98 (non_ordered_pair(a, b) = non_ordered_pair(c, d)),
% 5.81/5.98 inference(symmetry,[status(thm)],[207])).
% 5.81/5.98 tff(209,plain,
% 5.81/5.98 (member(d, non_ordered_pair(a, b)) <=> member(d, non_ordered_pair(c, d))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[208])).
% 5.81/5.98 tff(210,plain,
% 5.81/5.98 (member(d, non_ordered_pair(c, d)) <=> member(d, non_ordered_pair(a, b))),
% 5.81/5.98 inference(symmetry,[status(thm)],[209])).
% 5.81/5.98 tff(211,plain,
% 5.81/5.98 (little_set(d) <=> little_set(d)),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(212,axiom,(little_set(d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_little_set')).
% 5.81/5.98 tff(213,plain,
% 5.81/5.98 (little_set(d)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[212, 211])).
% 5.81/5.98 tff(214,plain,
% 5.81/5.98 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(d)) | member(d, non_ordered_pair(c, d)))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(d)) | member(d, non_ordered_pair(c, d)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(215,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(d)) | member(d, non_ordered_pair(c, d)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(216,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(d)) | member(d, non_ordered_pair(c, d))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[215, 214])).
% 5.81/5.98 tff(217,plain,
% 5.81/5.98 (member(d, non_ordered_pair(c, d))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[216, 195, 213])).
% 5.81/5.98 tff(218,plain,
% 5.81/5.98 (member(d, non_ordered_pair(a, b))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[217, 210])).
% 5.81/5.98 tff(219,plain,
% 5.81/5.98 ((b = d) <=> (d = b)),
% 5.81/5.98 inference(symmetry,[status(thm)],[1])).
% 5.81/5.98 tff(220,plain,
% 5.81/5.98 ((~(b = d)) <=> (~(d = b))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[219])).
% 5.81/5.98 tff(221,plain,
% 5.81/5.98 ((~(b = d)) <=> (~(b = d))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(222,axiom,(~(b = d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_second_components_equal')).
% 5.81/5.98 tff(223,plain,
% 5.81/5.98 (~(b = d)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[222, 221])).
% 5.81/5.98 tff(224,plain,
% 5.81/5.98 (~(d = b)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[223, 220])).
% 5.81/5.98 tff(225,plain,
% 5.81/5.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(226,plain,
% 5.81/5.98 (((d = b) | (d = a) | (~member(d, non_ordered_pair(a, b)))) <=> ((~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(227,plain,
% 5.81/5.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = b) | (d = a) | (~member(d, non_ordered_pair(a, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[226])).
% 5.81/5.98 tff(228,plain,
% 5.81/5.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = b) | (d = a) | (~member(d, non_ordered_pair(a, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a))),
% 5.81/5.98 inference(transitivity,[status(thm)],[227, 225])).
% 5.81/5.98 tff(229,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = b) | (d = a) | (~member(d, non_ordered_pair(a, b))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(230,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[229, 228])).
% 5.81/5.98 tff(231,plain,
% 5.81/5.98 ((~member(d, non_ordered_pair(a, b))) | (d = a)),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[230, 83, 224])).
% 5.81/5.98 tff(232,plain,
% 5.81/5.98 (d = a),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[231, 218])).
% 5.81/5.98 tff(233,plain,
% 5.81/5.98 (d = f23(non_ordered_pair(a, b), non_ordered_pair(a, a))),
% 5.81/5.98 inference(transitivity,[status(thm)],[232, 91])).
% 5.81/5.98 tff(234,plain,
% 5.81/5.98 ((b = d) <=> (b = f23(non_ordered_pair(a, b), non_ordered_pair(a, a)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[233])).
% 5.81/5.98 tff(235,plain,
% 5.81/5.98 ((b = d) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.81/5.98 inference(transitivity,[status(thm)],[234, 23])).
% 5.81/5.98 tff(236,plain,
% 5.81/5.98 ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b) <=> (b = d)),
% 5.81/5.98 inference(symmetry,[status(thm)],[235])).
% 5.81/5.98 tff(237,plain,
% 5.81/5.98 ((b = a) <=> (b = f23(non_ordered_pair(a, b), non_ordered_pair(a, a)))),
% 5.81/5.98 inference(monotonicity,[status(thm)],[91])).
% 5.81/5.98 tff(238,plain,
% 5.81/5.98 ((b = a) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.81/5.98 inference(transitivity,[status(thm)],[237, 23])).
% 5.81/5.98 tff(239,plain,
% 5.81/5.98 (little_set(c) <=> little_set(c)),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(240,axiom,(little_set(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_little_set')).
% 5.81/5.98 tff(241,plain,
% 5.81/5.98 (little_set(c)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[240, 239])).
% 5.81/5.98 tff(242,plain,
% 5.81/5.98 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(c)) | member(c, non_ordered_pair(c, c)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(c)) | member(c, non_ordered_pair(c, c)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(243,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(c)) | member(c, non_ordered_pair(c, c)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(244,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(c)) | member(c, non_ordered_pair(c, c))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[243, 242])).
% 5.81/5.98 tff(245,plain,
% 5.81/5.98 (member(c, non_ordered_pair(c, c))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[244, 40, 241])).
% 5.81/5.98 tff(246,plain,
% 5.81/5.98 (^[Z: $i] : refl(((~little_set(Z)) | member(Z, universal_set)) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(247,plain,
% 5.81/5.98 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[246])).
% 5.81/5.98 tff(248,plain,
% 5.81/5.98 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(249,plain,
% 5.81/5.98 (^[Z: $i] : rewrite((member(Z, universal_set) | (~little_set(Z))) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 5.81/5.98 inference(bind,[status(th)],[])).
% 5.81/5.98 tff(250,plain,
% 5.81/5.98 (![Z: $i] : (member(Z, universal_set) | (~little_set(Z))) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(quant_intro,[status(thm)],[249])).
% 5.81/5.98 tff(251,axiom,(![Z: $i] : (member(Z, universal_set) | (~little_set(Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','universal_set')).
% 5.81/5.98 tff(252,plain,
% 5.81/5.98 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[251, 250])).
% 5.81/5.98 tff(253,plain,
% 5.81/5.98 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[252, 248])).
% 5.81/5.98 tff(254,plain,(
% 5.81/5.98 ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(skolemize,[status(sab)],[253])).
% 5.81/5.98 tff(255,plain,
% 5.81/5.98 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[254, 247])).
% 5.81/5.98 tff(256,plain,
% 5.81/5.98 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(c)) | member(c, universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(c)) | member(c, universal_set))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(257,plain,
% 5.81/5.98 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(c)) | member(c, universal_set))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(258,plain,
% 5.81/5.98 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(c)) | member(c, universal_set)),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[257, 256])).
% 5.81/5.98 tff(259,plain,
% 5.81/5.98 (member(c, universal_set)),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[258, 255, 241])).
% 5.81/5.98 tff(260,plain,
% 5.81/5.98 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, universal_set)) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(universal_set, non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, universal_set)) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(universal_set, non_ordered_pair(c, c))))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(261,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, universal_set)) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(universal_set, non_ordered_pair(c, c))))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(262,plain,
% 5.81/5.98 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, universal_set)) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(universal_set, non_ordered_pair(c, c)))),
% 5.81/5.98 inference(modus_ponens,[status(thm)],[261, 260])).
% 5.81/5.98 tff(263,plain,
% 5.81/5.98 (~disjoint(universal_set, non_ordered_pair(c, c))),
% 5.81/5.98 inference(unit_resolution,[status(thm)],[262, 58, 259, 245])).
% 5.81/5.98 tff(264,plain,
% 5.81/5.98 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(c, c)) | member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(c, c)) | member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c)))),
% 5.81/5.98 inference(rewrite,[status(thm)],[])).
% 5.81/5.98 tff(265,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(c, c)) | member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c)))),
% 5.81/5.98 inference(quant_inst,[status(thm)],[])).
% 5.81/5.98 tff(266,plain,
% 5.81/5.98 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(c, c)) | member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[265, 264])).
% 5.81/5.99 tff(267,plain,
% 5.81/5.99 (member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[266, 69, 263])).
% 5.81/5.99 tff(268,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(269,plain,
% 5.81/5.99 (((f23(universal_set, non_ordered_pair(c, c)) = c) | (f23(universal_set, non_ordered_pair(c, c)) = c) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c)))) <=> ((~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(270,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(c, c)) = c) | (f23(universal_set, non_ordered_pair(c, c)) = c) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c)))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[269])).
% 5.81/5.99 tff(271,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(c, c)) = c) | (f23(universal_set, non_ordered_pair(c, c)) = c) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c))),
% 5.81/5.99 inference(transitivity,[status(thm)],[270, 268])).
% 5.81/5.99 tff(272,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(c, c)) = c) | (f23(universal_set, non_ordered_pair(c, c)) = c) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(273,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(c, c)), non_ordered_pair(c, c))) | (f23(universal_set, non_ordered_pair(c, c)) = c)),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[272, 271])).
% 5.81/5.99 tff(274,plain,
% 5.81/5.99 (f23(universal_set, non_ordered_pair(c, c)) = c),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[273, 83, 267])).
% 5.81/5.99 tff(275,plain,
% 5.81/5.99 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(c) = non_ordered_pair(c, c))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(276,plain,
% 5.81/5.99 (singleton_set(c) = non_ordered_pair(c, c)),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[275, 9])).
% 5.81/5.99 tff(277,plain,
% 5.81/5.99 (non_ordered_pair(c, c) = singleton_set(c)),
% 5.81/5.99 inference(symmetry,[status(thm)],[276])).
% 5.81/5.99 tff(278,plain,
% 5.81/5.99 (non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)) = non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[277])).
% 5.81/5.99 tff(279,plain,
% 5.81/5.99 (non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)) = ordered_pair(c, d)),
% 5.81/5.99 inference(transitivity,[status(thm)],[278, 152])).
% 5.81/5.99 tff(280,plain,
% 5.81/5.99 (member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))) <=> member(f16(a, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[279])).
% 5.81/5.99 tff(281,plain,
% 5.81/5.99 (member(f16(a, ordered_pair(c, d)), ordered_pair(c, d)) <=> member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))),
% 5.81/5.99 inference(symmetry,[status(thm)],[280])).
% 5.81/5.99 tff(282,plain,
% 5.81/5.99 (ordered_pair(c, d) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))),
% 5.81/5.99 inference(transitivity,[status(thm)],[113, 161])).
% 5.81/5.99 tff(283,plain,
% 5.81/5.99 (member(non_ordered_pair(a, b), ordered_pair(c, d)) <=> member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[282])).
% 5.81/5.99 tff(284,plain,
% 5.81/5.99 (member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(a, b), ordered_pair(c, d))),
% 5.81/5.99 inference(symmetry,[status(thm)],[283])).
% 5.81/5.99 tff(285,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(a, b))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(286,plain,
% 5.81/5.99 (little_set(non_ordered_pair(a, b))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[285, 176])).
% 5.81/5.99 tff(287,plain,
% 5.81/5.99 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(a, b))) | member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(a, b))) | member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(288,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(a, b))) | member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(289,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(a, b))) | member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[288, 287])).
% 5.81/5.99 tff(290,plain,
% 5.81/5.99 ((~little_set(non_ordered_pair(a, b))) | member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[289, 195])).
% 5.81/5.99 tff(291,plain,
% 5.81/5.99 (member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[290, 286])).
% 5.81/5.99 tff(292,plain,
% 5.81/5.99 (member(non_ordered_pair(a, b), ordered_pair(c, d))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[291, 284])).
% 5.81/5.99 tff(293,plain,
% 5.81/5.99 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X))) <=> ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X))))),
% 5.81/5.99 inference(bind,[status(th)],[])).
% 5.81/5.99 tff(294,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X))) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(quant_intro,[status(thm)],[293])).
% 5.81/5.99 tff(295,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X))) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(296,plain,
% 5.81/5.99 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((member(Z, sigma(X)) | (~member(Y, X))) <=> ((~member(Y, X)) | member(Z, sigma(X)))), (((member(Z, sigma(X)) | (~member(Y, X))) | (~member(Z, Y))) <=> (((~member(Y, X)) | member(Z, sigma(X))) | (~member(Z, Y))))), rewrite((((~member(Y, X)) | member(Z, sigma(X))) | (~member(Z, Y))) <=> ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))), (((member(Z, sigma(X)) | (~member(Y, X))) | (~member(Z, Y))) <=> ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))))),
% 5.81/5.99 inference(bind,[status(th)],[])).
% 5.81/5.99 tff(297,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((member(Z, sigma(X)) | (~member(Y, X))) | (~member(Z, Y))) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(quant_intro,[status(thm)],[296])).
% 5.81/5.99 tff(298,axiom,(![Z: $i, Y: $i, X: $i] : ((member(Z, sigma(X)) | (~member(Y, X))) | (~member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','sigma3')).
% 5.81/5.99 tff(299,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[298, 297])).
% 5.81/5.99 tff(300,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[299, 295])).
% 5.81/5.99 tff(301,plain,(
% 5.81/5.99 ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(skolemize,[status(sab)],[300])).
% 5.81/5.99 tff(302,plain,
% 5.81/5.99 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[301, 294])).
% 5.81/5.99 tff(303,plain,
% 5.81/5.99 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | member(a, sigma(ordered_pair(c, d))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | member(a, sigma(ordered_pair(c, d))))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(304,plain,
% 5.81/5.99 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | member(a, sigma(ordered_pair(c, d))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(305,plain,
% 5.81/5.99 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | member(a, sigma(ordered_pair(c, d)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[304, 303])).
% 5.81/5.99 tff(306,plain,
% 5.81/5.99 ((~member(non_ordered_pair(a, b), ordered_pair(c, d))) | member(a, sigma(ordered_pair(c, d)))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[305, 302, 48])).
% 5.81/5.99 tff(307,plain,
% 5.81/5.99 (member(a, sigma(ordered_pair(c, d)))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[306, 292])).
% 5.81/5.99 tff(308,plain,
% 5.81/5.99 (^[Z: $i, X: $i] : refl(((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ((~member(Z, sigma(X))) | member(f16(Z, X), X)))),
% 5.81/5.99 inference(bind,[status(th)],[])).
% 5.81/5.99 tff(309,plain,
% 5.81/5.99 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 5.81/5.99 inference(quant_intro,[status(thm)],[308])).
% 5.81/5.99 tff(310,plain,
% 5.81/5.99 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(311,axiom,(![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','sigma1')).
% 5.81/5.99 tff(312,plain,
% 5.81/5.99 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[311, 310])).
% 5.81/5.99 tff(313,plain,(
% 5.81/5.99 ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 5.81/5.99 inference(skolemize,[status(sab)],[312])).
% 5.81/5.99 tff(314,plain,
% 5.81/5.99 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[313, 309])).
% 5.81/5.99 tff(315,plain,
% 5.81/5.99 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(a, sigma(ordered_pair(c, d)))) | member(f16(a, ordered_pair(c, d)), ordered_pair(c, d)))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(a, sigma(ordered_pair(c, d)))) | member(f16(a, ordered_pair(c, d)), ordered_pair(c, d)))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(316,plain,
% 5.81/5.99 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(a, sigma(ordered_pair(c, d)))) | member(f16(a, ordered_pair(c, d)), ordered_pair(c, d)))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(317,plain,
% 5.81/5.99 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(a, sigma(ordered_pair(c, d)))) | member(f16(a, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[316, 315])).
% 5.81/5.99 tff(318,plain,
% 5.81/5.99 (member(f16(a, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[317, 314, 307])).
% 5.81/5.99 tff(319,plain,
% 5.81/5.99 (member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[318, 281])).
% 5.81/5.99 tff(320,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(321,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(322,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[321, 320])).
% 5.81/5.99 tff(323,plain,
% 5.81/5.99 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[322, 83])).
% 5.81/5.99 tff(324,plain,
% 5.81/5.99 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[323, 319])).
% 5.81/5.99 tff(325,plain,
% 5.81/5.99 (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[324, 158])).
% 5.81/5.99 tff(326,plain,
% 5.81/5.99 (non_ordered_pair(c, c) = f16(a, ordered_pair(c, d))),
% 5.81/5.99 inference(symmetry,[status(thm)],[325])).
% 5.81/5.99 tff(327,plain,
% 5.81/5.99 (f23(universal_set, non_ordered_pair(c, c)) = f23(universal_set, f16(a, ordered_pair(c, d)))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[326])).
% 5.81/5.99 tff(328,plain,
% 5.81/5.99 (f23(universal_set, f16(a, ordered_pair(c, d))) = f23(universal_set, non_ordered_pair(c, c))),
% 5.81/5.99 inference(symmetry,[status(thm)],[327])).
% 5.81/5.99 tff(329,plain,
% 5.81/5.99 (f23(universal_set, f16(a, ordered_pair(c, d))) = f23(universal_set, non_ordered_pair(a, a))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[95])).
% 5.81/5.99 tff(330,plain,
% 5.81/5.99 (f23(universal_set, non_ordered_pair(a, a)) = f23(universal_set, f16(a, ordered_pair(c, d)))),
% 5.81/5.99 inference(symmetry,[status(thm)],[329])).
% 5.81/5.99 tff(331,plain,
% 5.81/5.99 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(a)) | member(a, universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(a)) | member(a, universal_set))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(332,plain,
% 5.81/5.99 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(a)) | member(a, universal_set))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(333,plain,
% 5.81/5.99 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(a)) | member(a, universal_set)),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[332, 331])).
% 5.81/5.99 tff(334,plain,
% 5.81/5.99 (member(a, universal_set)),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[333, 255, 26])).
% 5.81/5.99 tff(335,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, universal_set)) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(universal_set, non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, universal_set)) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(universal_set, non_ordered_pair(a, a))))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(336,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, universal_set)) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(universal_set, non_ordered_pair(a, a))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(337,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, universal_set)) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(universal_set, non_ordered_pair(a, a)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[336, 335])).
% 5.81/5.99 tff(338,plain,
% 5.81/5.99 (~disjoint(universal_set, non_ordered_pair(a, a))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[337, 58, 334, 44])).
% 5.81/5.99 tff(339,plain,
% 5.81/5.99 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(a, a)) | member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(a, a)) | member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(340,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(a, a)) | member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(341,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(a, a)) | member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[340, 339])).
% 5.81/5.99 tff(342,plain,
% 5.81/5.99 (member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[341, 69, 338])).
% 5.81/5.99 tff(343,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(344,plain,
% 5.81/5.99 (((f23(universal_set, non_ordered_pair(a, a)) = a) | (f23(universal_set, non_ordered_pair(a, a)) = a) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a)))) <=> ((~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(345,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(a, a)) = a) | (f23(universal_set, non_ordered_pair(a, a)) = a) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a)))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[344])).
% 5.81/5.99 tff(346,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(a, a)) = a) | (f23(universal_set, non_ordered_pair(a, a)) = a) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a))),
% 5.81/5.99 inference(transitivity,[status(thm)],[345, 343])).
% 5.81/5.99 tff(347,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(a, a)) = a) | (f23(universal_set, non_ordered_pair(a, a)) = a) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(348,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a)),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[347, 346])).
% 5.81/5.99 tff(349,plain,
% 5.81/5.99 (f23(universal_set, non_ordered_pair(a, a)) = a),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[348, 83, 342])).
% 5.81/5.99 tff(350,plain,
% 5.81/5.99 (a = f23(universal_set, non_ordered_pair(a, a))),
% 5.81/5.99 inference(symmetry,[status(thm)],[349])).
% 5.81/5.99 tff(351,plain,
% 5.81/5.99 (a = c),
% 5.81/5.99 inference(transitivity,[status(thm)],[350, 330, 328, 274])).
% 5.81/5.99 tff(352,plain,
% 5.81/5.99 (non_ordered_pair(a, d) = non_ordered_pair(c, d)),
% 5.81/5.99 inference(monotonicity,[status(thm)],[351])).
% 5.81/5.99 tff(353,plain,
% 5.81/5.99 (non_ordered_pair(a, d) = non_ordered_pair(a, b)),
% 5.81/5.99 inference(transitivity,[status(thm)],[352, 207])).
% 5.81/5.99 tff(354,plain,
% 5.81/5.99 (member(b, non_ordered_pair(a, d)) <=> member(b, non_ordered_pair(a, b))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[353])).
% 5.81/5.99 tff(355,plain,
% 5.81/5.99 (member(b, non_ordered_pair(a, b)) <=> member(b, non_ordered_pair(a, d))),
% 5.81/5.99 inference(symmetry,[status(thm)],[354])).
% 5.81/5.99 tff(356,plain,
% 5.81/5.99 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(a, b)))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(a, b)))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(357,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(a, b)))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(358,plain,
% 5.81/5.99 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(a, b))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[357, 356])).
% 5.81/5.99 tff(359,plain,
% 5.81/5.99 (member(b, non_ordered_pair(a, b))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[358, 195, 118])).
% 5.81/5.99 tff(360,plain,
% 5.81/5.99 (member(b, non_ordered_pair(a, d))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[359, 355])).
% 5.81/5.99 tff(361,plain,
% 5.81/5.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (b = a) | (~member(b, non_ordered_pair(a, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = d) | (b = a) | (~member(b, non_ordered_pair(a, d))))),
% 5.81/5.99 inference(rewrite,[status(thm)],[])).
% 5.81/5.99 tff(362,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (b = a) | (~member(b, non_ordered_pair(a, d))))),
% 5.81/5.99 inference(quant_inst,[status(thm)],[])).
% 5.81/5.99 tff(363,plain,
% 5.81/5.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = d) | (b = a) | (~member(b, non_ordered_pair(a, d)))),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[362, 361])).
% 5.81/5.99 tff(364,plain,
% 5.81/5.99 ((b = a) | (~member(b, non_ordered_pair(a, d)))),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[363, 83, 223])).
% 5.81/5.99 tff(365,plain,
% 5.81/5.99 (b = a),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[364, 360])).
% 5.81/5.99 tff(366,plain,
% 5.81/5.99 (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[365, 238])).
% 5.81/5.99 tff(367,plain,
% 5.81/5.99 (b = d),
% 5.81/5.99 inference(modus_ponens,[status(thm)],[366, 236])).
% 5.81/5.99 tff(368,plain,
% 5.81/5.99 ($false),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[223, 367])).
% 5.81/5.99 tff(369,plain,((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)) | (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)))), inference(lemma,lemma(discharge,[]))).
% 5.81/5.99 tff(370,plain,
% 5.81/5.99 (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)),
% 5.81/5.99 inference(unit_resolution,[status(thm)],[369, 95])).
% 5.81/5.99 tff(371,plain,
% 5.81/5.99 (non_ordered_pair(a, a) = non_ordered_pair(c, d)),
% 5.81/5.99 inference(transitivity,[status(thm)],[96, 370])).
% 5.81/5.99 tff(372,plain,
% 5.81/5.99 (member(c, non_ordered_pair(a, a)) <=> member(c, non_ordered_pair(c, d))),
% 5.81/5.99 inference(monotonicity,[status(thm)],[371])).
% 5.81/5.99 tff(373,plain,
% 5.81/5.99 (member(c, non_ordered_pair(c, d)) <=> member(c, non_ordered_pair(a, a))),
% 5.81/5.99 inference(symmetry,[status(thm)],[372])).
% 5.81/5.99 tff(374,plain,
% 5.81/5.99 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(c)) | member(c, non_ordered_pair(c, d)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(c)) | member(c, non_ordered_pair(c, d)))),
% 5.81/6.00 inference(rewrite,[status(thm)],[])).
% 5.81/6.00 tff(375,plain,
% 5.81/6.00 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(c)) | member(c, non_ordered_pair(c, d)))),
% 5.81/6.00 inference(quant_inst,[status(thm)],[])).
% 5.81/6.00 tff(376,plain,
% 5.81/6.00 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(c)) | member(c, non_ordered_pair(c, d))),
% 5.81/6.00 inference(modus_ponens,[status(thm)],[375, 374])).
% 5.81/6.00 tff(377,plain,
% 5.81/6.00 (member(c, non_ordered_pair(c, d))),
% 5.81/6.00 inference(unit_resolution,[status(thm)],[376, 40, 241])).
% 5.81/6.00 tff(378,plain,
% 5.81/6.00 (member(c, non_ordered_pair(a, a))),
% 5.81/6.00 inference(modus_ponens,[status(thm)],[377, 373])).
% 5.81/6.00 tff(379,plain,
% 5.81/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(c, non_ordered_pair(a, a))) | (c = a))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(c, non_ordered_pair(a, a))) | (c = a))),
% 5.81/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(380,plain,
% 5.84/6.00 (((c = a) | (c = a) | (~member(c, non_ordered_pair(a, a)))) <=> ((~member(c, non_ordered_pair(a, a))) | (c = a))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(381,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((c = a) | (c = a) | (~member(c, non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(c, non_ordered_pair(a, a))) | (c = a)))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[380])).
% 5.84/6.00 tff(382,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((c = a) | (c = a) | (~member(c, non_ordered_pair(a, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(c, non_ordered_pair(a, a))) | (c = a))),
% 5.84/6.00 inference(transitivity,[status(thm)],[381, 379])).
% 5.84/6.00 tff(383,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((c = a) | (c = a) | (~member(c, non_ordered_pair(a, a))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(384,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(c, non_ordered_pair(a, a))) | (c = a)),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[383, 382])).
% 5.84/6.00 tff(385,plain,
% 5.84/6.00 ((~member(c, non_ordered_pair(a, a))) | (c = a)),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[384, 83])).
% 5.84/6.00 tff(386,plain,
% 5.84/6.00 (c = a),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[385, 378])).
% 5.84/6.00 tff(387,plain,
% 5.84/6.00 (singleton_set(c) = singleton_set(a)),
% 5.84/6.00 inference(monotonicity,[status(thm)],[386])).
% 5.84/6.00 tff(388,plain,
% 5.84/6.00 (singleton_set(a) = singleton_set(c)),
% 5.84/6.00 inference(symmetry,[status(thm)],[387])).
% 5.84/6.00 tff(389,plain,
% 5.84/6.00 (f16(a, ordered_pair(c, d)) = singleton_set(c)),
% 5.84/6.00 inference(transitivity,[status(thm)],[95, 165, 388])).
% 5.84/6.00 tff(390,plain,
% 5.84/6.00 (non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))) = non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[389, 370])).
% 5.84/6.00 tff(391,plain,
% 5.84/6.00 (non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))) = non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.00 inference(transitivity,[status(thm)],[390, 152, 149, 109])).
% 5.84/6.00 tff(392,plain,
% 5.84/6.00 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d)))) <=> member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[391])).
% 5.84/6.00 tff(393,plain,
% 5.84/6.00 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))),
% 5.84/6.00 inference(symmetry,[status(thm)],[392])).
% 5.84/6.00 tff(394,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(395,plain,
% 5.84/6.00 (little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[394, 176])).
% 5.84/6.00 tff(396,plain,
% 5.84/6.00 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(397,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(398,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[397, 396])).
% 5.84/6.00 tff(399,plain,
% 5.84/6.00 ((~little_set(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[398, 195])).
% 5.84/6.00 tff(400,plain,
% 5.84/6.00 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[399, 395])).
% 5.84/6.00 tff(401,plain,
% 5.84/6.00 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[400, 393])).
% 5.84/6.00 tff(402,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(403,plain,
% 5.84/6.00 (((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d)))))) <=> ((~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(404,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d)))))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[403])).
% 5.84/6.00 tff(405,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))))),
% 5.84/6.00 inference(transitivity,[status(thm)],[404, 402])).
% 5.84/6.00 tff(406,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(407,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d)))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[406, 405])).
% 5.84/6.00 tff(408,plain,
% 5.84/6.00 ((~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(f16(a, ordered_pair(c, d)), f16(a, ordered_pair(c, d))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[407, 83])).
% 5.84/6.00 tff(409,plain,
% 5.84/6.00 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[408, 401])).
% 5.84/6.00 tff(410,plain,
% 5.84/6.00 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[409, 100])).
% 5.84/6.00 tff(411,plain,
% 5.84/6.00 ($false),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[92, 410])).
% 5.84/6.00 tff(412,plain,((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))), inference(lemma,lemma(discharge,[]))).
% 5.84/6.00 tff(413,plain,
% 5.84/6.00 (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[412, 92])).
% 5.84/6.00 tff(414,plain,
% 5.84/6.00 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)) = ordered_pair(c, d)),
% 5.84/6.00 inference(transitivity,[status(thm)],[166, 162, 112])).
% 5.84/6.00 tff(415,plain,
% 5.84/6.00 (member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))) <=> member(f16(a, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[414])).
% 5.84/6.00 tff(416,plain,
% 5.84/6.00 (member(f16(a, ordered_pair(c, d)), ordered_pair(c, d)) <=> member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(symmetry,[status(thm)],[415])).
% 5.84/6.00 tff(417,plain,
% 5.84/6.00 (member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[318, 416])).
% 5.84/6.00 tff(418,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(419,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(420,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[419, 418])).
% 5.84/6.00 tff(421,plain,
% 5.84/6.00 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a)) | (~member(f16(a, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[420, 83])).
% 5.84/6.00 tff(422,plain,
% 5.84/6.00 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, a))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[421, 417])).
% 5.84/6.00 tff(423,plain,
% 5.84/6.00 (f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[422, 413])).
% 5.84/6.00 tff(424,plain,
% 5.84/6.00 ((~(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))) <=> (~(non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[93])).
% 5.84/6.00 tff(425,plain,
% 5.84/6.00 (~(non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[92, 424])).
% 5.84/6.00 tff(426,plain,
% 5.84/6.00 (ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = ordered_pair(c, d)),
% 5.84/6.00 inference(symmetry,[status(thm)],[149])).
% 5.84/6.00 tff(427,plain,
% 5.84/6.00 (non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))),
% 5.84/6.00 inference(symmetry,[status(thm)],[109])).
% 5.84/6.00 tff(428,plain,
% 5.84/6.00 (non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))),
% 5.84/6.00 inference(transitivity,[status(thm)],[427, 426, 113, 161])).
% 5.84/6.00 tff(429,plain,
% 5.84/6.00 (member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[165, 428])).
% 5.84/6.00 tff(430,plain,
% 5.84/6.00 (member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(symmetry,[status(thm)],[429])).
% 5.84/6.00 tff(431,plain,
% 5.84/6.00 (little_set(non_ordered_pair(a, a)) <=> little_set(singleton_set(a))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[165])).
% 5.84/6.00 tff(432,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(a, a))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(433,plain,
% 5.84/6.00 (little_set(non_ordered_pair(a, a))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[432, 176])).
% 5.84/6.00 tff(434,plain,
% 5.84/6.00 (little_set(singleton_set(a))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[433, 431])).
% 5.84/6.00 tff(435,plain,
% 5.84/6.00 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(a))) | member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(a))) | member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(436,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(a))) | member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(437,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(a))) | member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[436, 435])).
% 5.84/6.00 tff(438,plain,
% 5.84/6.00 ((~little_set(singleton_set(a))) | member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[437, 40])).
% 5.84/6.00 tff(439,plain,
% 5.84/6.00 (member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[438, 434])).
% 5.84/6.00 tff(440,plain,
% 5.84/6.00 (member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[439, 430])).
% 5.84/6.00 tff(441,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(442,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(443,plain,
% 5.84/6.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[442, 441])).
% 5.84/6.00 tff(444,plain,
% 5.84/6.00 ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, a), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[443, 83])).
% 5.84/6.00 tff(445,plain,
% 5.84/6.00 ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[444, 440])).
% 5.84/6.00 tff(446,plain,
% 5.84/6.00 (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[445, 425])).
% 5.84/6.00 tff(447,plain,
% 5.84/6.00 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[423, 12])).
% 5.84/6.00 tff(448,plain,
% 5.84/6.00 ((non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.00 inference(symmetry,[status(thm)],[447])).
% 5.84/6.00 tff(449,plain,
% 5.84/6.00 ((~(non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))) <=> (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[448])).
% 5.84/6.00 tff(450,plain,
% 5.84/6.00 (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[17, 449])).
% 5.84/6.00 tff(451,assumption,(non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d)))), introduced(assumption)).
% 5.84/6.00 tff(452,plain,
% 5.84/6.00 (little_set(ordered_pair(c, d)) <=> little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[282])).
% 5.84/6.00 tff(453,plain,
% 5.84/6.00 (little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))) <=> little_set(ordered_pair(c, d))),
% 5.84/6.00 inference(symmetry,[status(thm)],[452])).
% 5.84/6.00 tff(454,plain,
% 5.84/6.00 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(455,plain,
% 5.84/6.00 (little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[454, 176])).
% 5.84/6.00 tff(456,plain,
% 5.84/6.00 (little_set(ordered_pair(c, d))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[455, 453])).
% 5.84/6.00 tff(457,plain,
% 5.84/6.00 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(c, d))) | member(ordered_pair(c, d), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(c, d))) | member(ordered_pair(c, d), universal_set))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(458,plain,
% 5.84/6.00 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(c, d))) | member(ordered_pair(c, d), universal_set))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(459,plain,
% 5.84/6.00 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(c, d))) | member(ordered_pair(c, d), universal_set)),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[458, 457])).
% 5.84/6.00 tff(460,plain,
% 5.84/6.00 (member(ordered_pair(c, d), universal_set)),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[459, 255, 456])).
% 5.84/6.00 tff(461,plain,
% 5.84/6.00 (member(non_ordered_pair(c, d), ordered_pair(c, d)) <=> member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.84/6.00 inference(monotonicity,[status(thm)],[151])).
% 5.84/6.00 tff(462,plain,
% 5.84/6.00 (member(non_ordered_pair(c, d), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))) <=> member(non_ordered_pair(c, d), ordered_pair(c, d))),
% 5.84/6.00 inference(symmetry,[status(thm)],[461])).
% 5.84/6.00 tff(463,plain,
% 5.84/6.00 (member(non_ordered_pair(c, d), ordered_pair(c, d))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[200, 462])).
% 5.84/6.00 tff(464,plain,
% 5.84/6.00 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(c, d), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(c, d), sigma(universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(c, d), sigma(universal_set)))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(465,plain,
% 5.84/6.00 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(c, d), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(c, d), sigma(universal_set)))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(466,plain,
% 5.84/6.00 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(c, d), sigma(universal_set))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[465, 464])).
% 5.84/6.00 tff(467,plain,
% 5.84/6.00 (member(non_ordered_pair(c, d), sigma(universal_set))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[466, 302, 463, 460])).
% 5.84/6.00 tff(468,plain,
% 5.84/6.00 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), sigma(universal_set))) | member(c, sigma(sigma(universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(c, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), sigma(universal_set))) | member(c, sigma(sigma(universal_set))))),
% 5.84/6.00 inference(rewrite,[status(thm)],[])).
% 5.84/6.00 tff(469,plain,
% 5.84/6.00 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), sigma(universal_set))) | member(c, sigma(sigma(universal_set))))),
% 5.84/6.00 inference(quant_inst,[status(thm)],[])).
% 5.84/6.00 tff(470,plain,
% 5.84/6.00 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(c, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), sigma(universal_set))) | member(c, sigma(sigma(universal_set)))),
% 5.84/6.00 inference(modus_ponens,[status(thm)],[469, 468])).
% 5.84/6.00 tff(471,plain,
% 5.84/6.00 (member(c, sigma(sigma(universal_set)))),
% 5.84/6.00 inference(unit_resolution,[status(thm)],[470, 302, 377, 467])).
% 5.84/6.00 tff(472,plain,
% 5.84/6.00 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, c))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, c))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set)))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(473,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, c))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set)))))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(474,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, c))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set))))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[473, 472])).
% 5.84/6.01 tff(475,plain,
% 5.84/6.01 (~disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[474, 58, 245, 471])).
% 5.84/6.01 tff(476,plain,
% 5.84/6.01 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), X)) <=> (disjoint(X, Y) | member(f23(X, Y), X)))),
% 5.84/6.01 inference(bind,[status(th)],[])).
% 5.84/6.01 tff(477,plain,
% 5.84/6.01 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 5.84/6.01 inference(quant_intro,[status(thm)],[476])).
% 5.84/6.01 tff(478,plain,
% 5.84/6.01 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(479,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','disjoint2')).
% 5.84/6.01 tff(480,plain,
% 5.84/6.01 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[479, 478])).
% 5.84/6.01 tff(481,plain,(
% 5.84/6.01 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 5.84/6.01 inference(skolemize,[status(sab)],[480])).
% 5.84/6.01 tff(482,plain,
% 5.84/6.01 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[481, 477])).
% 5.84/6.01 tff(483,plain,
% 5.84/6.01 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c)))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(484,plain,
% 5.84/6.01 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c)))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(485,plain,
% 5.84/6.01 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(c, c), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[484, 483])).
% 5.84/6.01 tff(486,plain,
% 5.84/6.01 (member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[485, 482, 475])).
% 5.84/6.01 tff(487,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(488,plain,
% 5.84/6.01 (((f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c)))) <=> ((~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(489,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[488])).
% 5.84/6.01 tff(490,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c))),
% 5.84/6.01 inference(transitivity,[status(thm)],[489, 487])).
% 5.84/6.01 tff(491,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(492,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, c), sigma(sigma(universal_set))), non_ordered_pair(c, c))) | (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c)),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[491, 490])).
% 5.84/6.01 tff(493,plain,
% 5.84/6.01 (f23(non_ordered_pair(c, c), sigma(sigma(universal_set))) = c),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[492, 83, 486])).
% 5.84/6.01 tff(494,assumption,(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)), introduced(assumption)).
% 5.84/6.01 tff(495,plain,
% 5.84/6.01 (f23(f16(a, ordered_pair(c, d)), sigma(sigma(universal_set))) = f23(non_ordered_pair(c, c), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[494])).
% 5.84/6.01 tff(496,assumption,(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)), introduced(assumption)).
% 5.84/6.01 tff(497,plain,
% 5.84/6.01 (non_ordered_pair(a, b) = f16(a, ordered_pair(c, d))),
% 5.84/6.01 inference(symmetry,[status(thm)],[496])).
% 5.84/6.01 tff(498,plain,
% 5.84/6.01 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) <=> (non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.01 inference(commutativity,[status(thm)],[])).
% 5.84/6.01 tff(499,assumption,(~(non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))), introduced(assumption)).
% 5.84/6.01 tff(500,plain,
% 5.84/6.01 (member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[428])).
% 5.84/6.01 tff(501,plain,
% 5.84/6.01 (member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.01 inference(symmetry,[status(thm)],[500])).
% 5.84/6.01 tff(502,plain,
% 5.84/6.01 (member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[291, 501])).
% 5.84/6.01 tff(503,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(504,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(505,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[504, 503])).
% 5.84/6.01 tff(506,plain,
% 5.84/6.01 ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) | (~member(non_ordered_pair(a, b), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[505, 83])).
% 5.84/6.01 tff(507,plain,
% 5.84/6.01 ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[506, 502])).
% 5.84/6.01 tff(508,plain,
% 5.84/6.01 (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[507, 499])).
% 5.84/6.01 tff(509,plain,
% 5.84/6.01 (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.84/6.01 inference(symmetry,[status(thm)],[508])).
% 5.84/6.01 tff(510,plain,
% 5.84/6.01 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.84/6.01 inference(transitivity,[status(thm)],[12, 509])).
% 5.84/6.01 tff(511,plain,
% 5.84/6.01 (member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> member(a, non_ordered_pair(a, b))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[510])).
% 5.84/6.01 tff(512,plain,
% 5.84/6.01 (member(a, non_ordered_pair(a, b)) <=> member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(symmetry,[status(thm)],[511])).
% 5.84/6.01 tff(513,plain,
% 5.84/6.01 (member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[48, 512])).
% 5.84/6.01 tff(514,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(515,plain,
% 5.84/6.01 (((a = f2(ordered_pair(c, d))) | (a = f2(ordered_pair(c, d))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(516,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = f2(ordered_pair(c, d))) | (a = f2(ordered_pair(c, d))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d)))))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[515])).
% 5.84/6.01 tff(517,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = f2(ordered_pair(c, d))) | (a = f2(ordered_pair(c, d))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(transitivity,[status(thm)],[516, 514])).
% 5.84/6.01 tff(518,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = f2(ordered_pair(c, d))) | (a = f2(ordered_pair(c, d))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(519,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[518, 517])).
% 5.84/6.01 tff(520,plain,
% 5.84/6.01 ((~member(a, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (a = f2(ordered_pair(c, d)))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[519, 83])).
% 5.84/6.01 tff(521,plain,
% 5.84/6.01 (a = f2(ordered_pair(c, d))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[520, 513])).
% 5.84/6.01 tff(522,plain,
% 5.84/6.01 (singleton_set(a) = singleton_set(f2(ordered_pair(c, d)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[521])).
% 5.84/6.01 tff(523,plain,
% 5.84/6.01 (non_ordered_pair(a, a) = non_ordered_pair(a, b)),
% 5.84/6.01 inference(transitivity,[status(thm)],[165, 522, 509])).
% 5.84/6.01 tff(524,plain,
% 5.84/6.01 ((non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[523])).
% 5.84/6.01 tff(525,plain,
% 5.84/6.01 ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.01 inference(symmetry,[status(thm)],[524])).
% 5.84/6.01 tff(526,plain,
% 5.84/6.01 ((non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.84/6.01 inference(transitivity,[status(thm)],[525, 94])).
% 5.84/6.01 tff(527,plain,
% 5.84/6.01 ((~(non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> (~(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[526])).
% 5.84/6.01 tff(528,plain,
% 5.84/6.01 (~(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[499, 527])).
% 5.84/6.01 tff(529,plain,
% 5.84/6.01 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)) = non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.01 inference(transitivity,[status(thm)],[166, 162, 112, 149, 109])).
% 5.84/6.01 tff(530,plain,
% 5.84/6.01 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[529])).
% 5.84/6.01 tff(531,plain,
% 5.84/6.01 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.84/6.01 inference(symmetry,[status(thm)],[530])).
% 5.84/6.01 tff(532,plain,
% 5.84/6.01 (member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[400, 531])).
% 5.84/6.01 tff(533,plain,
% 5.84/6.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(534,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.84/6.01 inference(quant_inst,[status(thm)],[])).
% 5.84/6.01 tff(535,plain,
% 5.84/6.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[534, 533])).
% 5.84/6.01 tff(536,plain,
% 5.84/6.01 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[535, 83])).
% 5.84/6.01 tff(537,plain,
% 5.84/6.01 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[536, 532])).
% 5.84/6.01 tff(538,plain,
% 5.84/6.01 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[537, 528])).
% 5.84/6.01 tff(539,plain,
% 5.84/6.01 (non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[538, 498])).
% 5.84/6.01 tff(540,plain,
% 5.84/6.01 ($false),
% 5.84/6.01 inference(unit_resolution,[status(thm)],[499, 539])).
% 5.84/6.01 tff(541,plain,(non_ordered_pair(a, b) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), inference(lemma,lemma(discharge,[]))).
% 5.84/6.01 tff(542,plain,
% 5.84/6.01 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.84/6.01 inference(symmetry,[status(thm)],[541])).
% 5.84/6.01 tff(543,plain,
% 5.84/6.01 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))),
% 5.84/6.01 inference(transitivity,[status(thm)],[542, 497])).
% 5.84/6.01 tff(544,plain,
% 5.84/6.01 (f23(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), sigma(sigma(universal_set))) = f23(f16(a, ordered_pair(c, d)), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[543])).
% 5.84/6.01 tff(545,plain,
% 5.84/6.01 (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = f23(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[541])).
% 5.84/6.01 tff(546,assumption,(~(f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))), introduced(assumption)).
% 5.84/6.01 tff(547,plain,
% 5.84/6.01 (f23(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), sigma(sigma(universal_set))) = f23(non_ordered_pair(a, b), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(symmetry,[status(thm)],[545])).
% 5.84/6.01 tff(548,plain,
% 5.84/6.01 (f23(f16(a, ordered_pair(c, d)), sigma(sigma(universal_set))) = f23(non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))), sigma(sigma(universal_set)))),
% 5.84/6.01 inference(symmetry,[status(thm)],[544])).
% 5.84/6.01 tff(549,assumption,(~(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)), introduced(assumption)).
% 5.84/6.01 tff(550,plain,
% 5.84/6.01 (non_ordered_pair(a, a) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.84/6.01 inference(transitivity,[status(thm)],[451, 11])).
% 5.84/6.01 tff(551,plain,
% 5.84/6.01 (f23(universal_set, non_ordered_pair(a, a)) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.01 inference(monotonicity,[status(thm)],[550])).
% 5.84/6.01 tff(552,plain,
% 5.84/6.01 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f23(universal_set, non_ordered_pair(a, a))),
% 5.84/6.01 inference(symmetry,[status(thm)],[551])).
% 5.84/6.01 tff(553,plain,
% 5.84/6.01 (^[X: $i] : refl((little_set(f2(X)) | (~ordered_pair_predicate(X))) <=> (little_set(f2(X)) | (~ordered_pair_predicate(X))))),
% 5.84/6.01 inference(bind,[status(th)],[])).
% 5.84/6.01 tff(554,plain,
% 5.84/6.01 (![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X))) <=> ![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(quant_intro,[status(thm)],[553])).
% 5.84/6.01 tff(555,plain,
% 5.84/6.01 (![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X))) <=> ![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.01 tff(556,plain,
% 5.84/6.01 (^[X: $i] : rewrite(((~ordered_pair_predicate(X)) | little_set(f2(X))) <=> (little_set(f2(X)) | (~ordered_pair_predicate(X))))),
% 5.84/6.01 inference(bind,[status(th)],[])).
% 5.84/6.01 tff(557,plain,
% 5.84/6.01 (![X: $i] : ((~ordered_pair_predicate(X)) | little_set(f2(X))) <=> ![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(quant_intro,[status(thm)],[556])).
% 5.84/6.01 tff(558,axiom,(![X: $i] : ((~ordered_pair_predicate(X)) | little_set(f2(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','ordered_pair_predicate1')).
% 5.84/6.01 tff(559,plain,
% 5.84/6.01 (![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[558, 557])).
% 5.84/6.01 tff(560,plain,
% 5.84/6.01 (![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[559, 555])).
% 5.84/6.01 tff(561,plain,(
% 5.84/6.01 ![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(skolemize,[status(sab)],[560])).
% 5.84/6.01 tff(562,plain,
% 5.84/6.01 (![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))),
% 5.84/6.01 inference(modus_ponens,[status(thm)],[561, 554])).
% 5.84/6.01 tff(563,plain,
% 5.84/6.01 (((~![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))) | (little_set(f2(ordered_pair(c, d))) | (~ordered_pair_predicate(ordered_pair(c, d))))) <=> ((~![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))) | little_set(f2(ordered_pair(c, d))) | (~ordered_pair_predicate(ordered_pair(c, d))))),
% 5.84/6.01 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(564,plain,
% 5.84/6.02 ((~![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))) | (little_set(f2(ordered_pair(c, d))) | (~ordered_pair_predicate(ordered_pair(c, d))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(565,plain,
% 5.84/6.02 ((~![X: $i] : (little_set(f2(X)) | (~ordered_pair_predicate(X)))) | little_set(f2(ordered_pair(c, d))) | (~ordered_pair_predicate(ordered_pair(c, d)))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[564, 563])).
% 5.84/6.02 tff(566,plain,
% 5.84/6.02 (little_set(f2(ordered_pair(c, d))) | (~ordered_pair_predicate(ordered_pair(c, d)))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[565, 562])).
% 5.84/6.02 tff(567,plain,
% 5.84/6.02 (little_set(f2(ordered_pair(c, d)))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[566, 137])).
% 5.84/6.02 tff(568,plain,
% 5.84/6.02 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(569,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(570,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[569, 568])).
% 5.84/6.02 tff(571,plain,
% 5.84/6.02 (member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[570, 40, 567])).
% 5.84/6.02 tff(572,plain,
% 5.84/6.02 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), universal_set))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(573,plain,
% 5.84/6.02 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), universal_set))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(574,plain,
% 5.84/6.02 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), universal_set)),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[573, 572])).
% 5.84/6.02 tff(575,plain,
% 5.84/6.02 (member(f2(ordered_pair(c, d)), universal_set)),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[574, 255, 567])).
% 5.84/6.02 tff(576,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), universal_set)) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f2(ordered_pair(c, d)), universal_set)) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(577,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), universal_set)) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(578,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f2(ordered_pair(c, d)), universal_set)) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[577, 576])).
% 5.84/6.02 tff(579,plain,
% 5.84/6.02 (~disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[578, 58, 575, 571])).
% 5.84/6.02 tff(580,plain,
% 5.84/6.02 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(581,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(582,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[581, 580])).
% 5.84/6.02 tff(583,plain,
% 5.84/6.02 (member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[582, 69, 579])).
% 5.84/6.02 tff(584,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(585,plain,
% 5.84/6.02 (((f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(586,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(monotonicity,[status(thm)],[585])).
% 5.84/6.02 tff(587,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(transitivity,[status(thm)],[586, 584])).
% 5.84/6.02 tff(588,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(589,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d)))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[588, 587])).
% 5.84/6.02 tff(590,plain,
% 5.84/6.02 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f2(ordered_pair(c, d))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[589, 83, 583])).
% 5.84/6.02 tff(591,plain,
% 5.84/6.02 (f2(ordered_pair(c, d)) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(symmetry,[status(thm)],[590])).
% 5.84/6.02 tff(592,plain,
% 5.84/6.02 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(593,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(594,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f2(ordered_pair(c, d)))) | member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[593, 592])).
% 5.84/6.02 tff(595,plain,
% 5.84/6.02 (member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[594, 40, 567])).
% 5.84/6.02 tff(596,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(597,plain,
% 5.84/6.02 (((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))) <=> ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(598,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))))),
% 5.84/6.02 inference(monotonicity,[status(thm)],[597])).
% 5.84/6.02 tff(599,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.02 inference(transitivity,[status(thm)],[598, 596])).
% 5.84/6.02 tff(600,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(601,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) | (~member(f2(ordered_pair(c, d)), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[600, 599])).
% 5.84/6.02 tff(602,plain,
% 5.84/6.02 (~disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[601, 58, 595, 571])).
% 5.84/6.02 tff(603,plain,
% 5.84/6.02 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(604,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(605,plain,
% 5.84/6.02 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) | member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(modus_ponens,[status(thm)],[604, 603])).
% 5.84/6.02 tff(606,plain,
% 5.84/6.02 (member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(unit_resolution,[status(thm)],[605, 482, 602])).
% 5.84/6.02 tff(607,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(608,plain,
% 5.84/6.02 (((f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(rewrite,[status(thm)],[])).
% 5.84/6.02 tff(609,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d)))))),
% 5.84/6.02 inference(monotonicity,[status(thm)],[608])).
% 5.84/6.02 tff(610,plain,
% 5.84/6.02 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))))),
% 5.84/6.02 inference(transitivity,[status(thm)],[609, 607])).
% 5.84/6.02 tff(611,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.84/6.02 inference(quant_inst,[status(thm)],[])).
% 5.84/6.02 tff(612,plain,
% 5.84/6.02 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d)))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[611, 610])).
% 5.84/6.03 tff(613,plain,
% 5.84/6.03 (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f2(ordered_pair(c, d))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[612, 83, 606])).
% 5.84/6.03 tff(614,plain,
% 5.84/6.03 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(c, c)),
% 5.84/6.03 inference(transitivity,[status(thm)],[542, 497, 494])).
% 5.84/6.03 tff(615,plain,
% 5.84/6.03 ((singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.03 inference(commutativity,[status(thm)],[])).
% 5.84/6.03 tff(616,plain,
% 5.84/6.03 ((non_ordered_pair(a, a) = non_ordered_pair(c, c)) <=> (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[451])).
% 5.84/6.03 tff(617,plain,
% 5.84/6.03 ((non_ordered_pair(a, a) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.03 inference(transitivity,[status(thm)],[616, 615])).
% 5.84/6.03 tff(618,plain,
% 5.84/6.03 ((non_ordered_pair(c, c) = singleton_set(f2(ordered_pair(c, d)))) <=> (non_ordered_pair(a, a) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(symmetry,[status(thm)],[617])).
% 5.84/6.03 tff(619,plain,
% 5.84/6.03 (non_ordered_pair(c, c) = f16(a, ordered_pair(c, d))),
% 5.84/6.03 inference(symmetry,[status(thm)],[494])).
% 5.84/6.03 tff(620,plain,
% 5.84/6.03 ((non_ordered_pair(c, c) = singleton_set(f2(ordered_pair(c, d)))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[619, 11])).
% 5.84/6.03 tff(621,plain,
% 5.84/6.03 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> (non_ordered_pair(c, c) = singleton_set(f2(ordered_pair(c, d))))),
% 5.84/6.03 inference(symmetry,[status(thm)],[620])).
% 5.84/6.03 tff(622,plain,
% 5.84/6.03 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> (non_ordered_pair(a, a) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(transitivity,[status(thm)],[621, 618])).
% 5.84/6.03 tff(623,plain,
% 5.84/6.03 ((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) <=> (~(non_ordered_pair(a, a) = non_ordered_pair(c, c)))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[622])).
% 5.84/6.03 tff(624,plain,
% 5.84/6.03 (~(non_ordered_pair(a, a) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[546, 623])).
% 5.84/6.03 tff(625,plain,
% 5.84/6.03 (non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))),
% 5.84/6.03 inference(transitivity,[status(thm)],[278, 152, 113, 161])).
% 5.84/6.03 tff(626,plain,
% 5.84/6.03 (member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))) <=> member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[165, 625])).
% 5.84/6.03 tff(627,plain,
% 5.84/6.03 (member(singleton_set(a), non_ordered_pair(singleton_set(a), non_ordered_pair(a, b))) <=> member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))),
% 5.84/6.03 inference(symmetry,[status(thm)],[626])).
% 5.84/6.03 tff(628,plain,
% 5.84/6.03 (member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[439, 627])).
% 5.84/6.03 tff(629,plain,
% 5.84/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c)) | (~member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c)) | (~member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(630,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c)) | (~member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d)))))),
% 5.84/6.03 inference(quant_inst,[status(thm)],[])).
% 5.84/6.03 tff(631,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c)) | (~member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[630, 629])).
% 5.84/6.03 tff(632,plain,
% 5.84/6.03 ((non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c)) | (~member(non_ordered_pair(a, a), non_ordered_pair(non_ordered_pair(c, c), non_ordered_pair(c, d))))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[631, 83])).
% 5.84/6.03 tff(633,plain,
% 5.84/6.03 ((non_ordered_pair(a, a) = non_ordered_pair(c, d)) | (non_ordered_pair(a, a) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[632, 628])).
% 5.84/6.03 tff(634,plain,
% 5.84/6.03 (non_ordered_pair(a, a) = non_ordered_pair(c, d)),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[633, 624])).
% 5.84/6.03 tff(635,plain,
% 5.84/6.03 (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.84/6.03 inference(symmetry,[status(thm)],[451])).
% 5.84/6.03 tff(636,plain,
% 5.84/6.03 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(c, d)),
% 5.84/6.03 inference(transitivity,[status(thm)],[12, 635, 634])).
% 5.84/6.03 tff(637,plain,
% 5.84/6.03 (f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f23(non_ordered_pair(c, d), non_ordered_pair(c, c))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[636, 614])).
% 5.84/6.03 tff(638,plain,
% 5.84/6.03 (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = f23(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.03 inference(symmetry,[status(thm)],[637])).
% 5.84/6.03 tff(639,plain,
% 5.84/6.03 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, d))) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(640,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(quant_inst,[status(thm)],[])).
% 5.84/6.03 tff(641,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, d))) | (~member(c, non_ordered_pair(c, c))) | (~disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c)))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[640, 639])).
% 5.84/6.03 tff(642,plain,
% 5.84/6.03 (~disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[641, 58, 377, 245])).
% 5.84/6.03 tff(643,plain,
% 5.84/6.03 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c)) | member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c)) | member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(644,plain,
% 5.84/6.03 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c)) | member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))),
% 5.84/6.03 inference(quant_inst,[status(thm)],[])).
% 5.84/6.03 tff(645,plain,
% 5.84/6.03 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(c, d), non_ordered_pair(c, c)) | member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[644, 643])).
% 5.84/6.03 tff(646,plain,
% 5.84/6.03 (member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[645, 69, 642])).
% 5.84/6.03 tff(647,plain,
% 5.84/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(648,plain,
% 5.84/6.03 (((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))) <=> ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(649,plain,
% 5.84/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[648])).
% 5.84/6.03 tff(650,plain,
% 5.84/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(transitivity,[status(thm)],[649, 647])).
% 5.84/6.03 tff(651,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c))))),
% 5.84/6.03 inference(quant_inst,[status(thm)],[])).
% 5.84/6.03 tff(652,plain,
% 5.84/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c) | (~member(f23(non_ordered_pair(c, d), non_ordered_pair(c, c)), non_ordered_pair(c, c)))),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[651, 650])).
% 5.84/6.03 tff(653,plain,
% 5.84/6.03 (f23(non_ordered_pair(c, d), non_ordered_pair(c, c)) = c),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[652, 83, 646])).
% 5.84/6.03 tff(654,plain,
% 5.84/6.03 (c = f23(non_ordered_pair(c, d), non_ordered_pair(c, c))),
% 5.84/6.03 inference(symmetry,[status(thm)],[653])).
% 5.84/6.03 tff(655,plain,
% 5.84/6.03 (f23(universal_set, f16(a, ordered_pair(c, d))) = f23(universal_set, non_ordered_pair(c, c))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[494])).
% 5.84/6.03 tff(656,plain,
% 5.84/6.03 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f23(universal_set, f16(a, ordered_pair(c, d)))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[543])).
% 5.84/6.03 tff(657,plain,
% 5.84/6.03 (f23(universal_set, non_ordered_pair(a, b)) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[541])).
% 5.84/6.03 tff(658,plain,
% 5.84/6.03 (f23(universal_set, non_ordered_pair(a, b)) = a),
% 5.84/6.03 inference(transitivity,[status(thm)],[657, 656, 655, 274, 654, 638, 613, 591, 552, 349])).
% 5.84/6.03 tff(659,plain,
% 5.84/6.03 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) = f23(universal_set, non_ordered_pair(a, b))),
% 5.84/6.03 inference(symmetry,[status(thm)],[657])).
% 5.84/6.03 tff(660,plain,
% 5.84/6.03 (f23(universal_set, f16(a, ordered_pair(c, d))) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.84/6.03 inference(symmetry,[status(thm)],[656])).
% 5.84/6.03 tff(661,plain,
% 5.84/6.03 (f23(universal_set, non_ordered_pair(c, c)) = f23(universal_set, f16(a, ordered_pair(c, d)))),
% 5.84/6.03 inference(symmetry,[status(thm)],[655])).
% 5.84/6.03 tff(662,plain,
% 5.84/6.03 (c = f23(universal_set, non_ordered_pair(c, c))),
% 5.84/6.03 inference(symmetry,[status(thm)],[274])).
% 5.84/6.03 tff(663,plain,
% 5.84/6.03 (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = f23(universal_set, non_ordered_pair(a, b))),
% 5.84/6.03 inference(transitivity,[status(thm)],[545, 544, 495, 493, 662, 661, 660, 659])).
% 5.84/6.03 tff(664,plain,
% 5.84/6.03 ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) <=> (f23(universal_set, non_ordered_pair(a, b)) = a)),
% 5.84/6.03 inference(monotonicity,[status(thm)],[663])).
% 5.84/6.03 tff(665,plain,
% 5.84/6.03 ((~(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)) <=> (~(f23(universal_set, non_ordered_pair(a, b)) = a))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[664])).
% 5.84/6.03 tff(666,plain,
% 5.84/6.03 (~(f23(universal_set, non_ordered_pair(a, b)) = a)),
% 5.84/6.03 inference(modus_ponens,[status(thm)],[549, 665])).
% 5.84/6.03 tff(667,plain,
% 5.84/6.03 ($false),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[666, 658])).
% 5.84/6.03 tff(668,plain,((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))) | (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b))) | (~(non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))), inference(lemma,lemma(discharge,[]))).
% 5.84/6.03 tff(669,plain,
% 5.84/6.03 (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[668, 549, 451, 496, 546])).
% 5.84/6.03 tff(670,plain,
% 5.84/6.03 (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)),
% 5.84/6.03 inference(unit_resolution,[status(thm)],[324, 669])).
% 5.84/6.03 tff(671,plain,
% 5.84/6.03 (f23(f16(a, ordered_pair(c, d)), sigma(sigma(universal_set))) = f23(non_ordered_pair(c, d), sigma(sigma(universal_set)))),
% 5.84/6.03 inference(monotonicity,[status(thm)],[670])).
% 5.84/6.03 tff(672,plain,
% 5.84/6.03 (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = f23(f16(a, ordered_pair(c, d)), sigma(sigma(universal_set)))),
% 5.84/6.03 inference(symmetry,[status(thm)],[671])).
% 5.84/6.03 tff(673,plain,
% 5.84/6.03 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(a, b), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(a, b), sigma(universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(a, b), sigma(universal_set)))),
% 5.84/6.03 inference(rewrite,[status(thm)],[])).
% 5.84/6.03 tff(674,plain,
% 5.84/6.03 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(a, b), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(a, b), sigma(universal_set)))),
% 5.84/6.03 inference(quant_inst,[status(thm)],[])).
% 5.84/6.03 tff(675,plain,
% 5.88/6.03 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(a, b), ordered_pair(c, d))) | (~member(ordered_pair(c, d), universal_set)) | member(non_ordered_pair(a, b), sigma(universal_set))),
% 5.88/6.03 inference(modus_ponens,[status(thm)],[674, 673])).
% 5.88/6.03 tff(676,plain,
% 5.88/6.03 (member(non_ordered_pair(a, b), sigma(universal_set))),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[675, 302, 292, 460])).
% 5.88/6.03 tff(677,plain,
% 5.88/6.03 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), sigma(universal_set))) | member(a, sigma(sigma(universal_set))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), sigma(universal_set))) | member(a, sigma(sigma(universal_set))))),
% 5.88/6.03 inference(rewrite,[status(thm)],[])).
% 5.88/6.03 tff(678,plain,
% 5.88/6.03 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), sigma(universal_set))) | member(a, sigma(sigma(universal_set))))),
% 5.88/6.03 inference(quant_inst,[status(thm)],[])).
% 5.88/6.03 tff(679,plain,
% 5.88/6.03 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(a, non_ordered_pair(a, b))) | (~member(non_ordered_pair(a, b), sigma(universal_set))) | member(a, sigma(sigma(universal_set)))),
% 5.88/6.03 inference(modus_ponens,[status(thm)],[678, 677])).
% 5.88/6.03 tff(680,plain,
% 5.88/6.03 (member(a, sigma(sigma(universal_set)))),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[679, 302, 48, 676])).
% 5.88/6.03 tff(681,plain,
% 5.88/6.03 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(a, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, non_ordered_pair(a, b))) | (~member(a, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set)))))),
% 5.88/6.03 inference(rewrite,[status(thm)],[])).
% 5.88/6.03 tff(682,plain,
% 5.88/6.03 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, b))) | (~member(a, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set)))))),
% 5.88/6.03 inference(quant_inst,[status(thm)],[])).
% 5.88/6.03 tff(683,plain,
% 5.88/6.03 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, non_ordered_pair(a, b))) | (~member(a, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set))))),
% 5.88/6.03 inference(modus_ponens,[status(thm)],[682, 681])).
% 5.88/6.03 tff(684,plain,
% 5.88/6.03 (~disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set)))),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[683, 58, 48, 680])).
% 5.88/6.03 tff(685,plain,
% 5.88/6.03 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b)))),
% 5.88/6.03 inference(rewrite,[status(thm)],[])).
% 5.88/6.03 tff(686,plain,
% 5.88/6.03 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b)))),
% 5.88/6.03 inference(quant_inst,[status(thm)],[])).
% 5.88/6.03 tff(687,plain,
% 5.88/6.03 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(a, b), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))),
% 5.88/6.03 inference(modus_ponens,[status(thm)],[686, 685])).
% 5.88/6.03 tff(688,plain,
% 5.88/6.03 (member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[687, 482, 684])).
% 5.88/6.03 tff(689,plain,
% 5.88/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a))),
% 5.88/6.03 inference(rewrite,[status(thm)],[])).
% 5.88/6.03 tff(690,plain,
% 5.88/6.03 (((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b)))) <=> ((~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a))),
% 5.88/6.03 inference(rewrite,[status(thm)],[])).
% 5.88/6.03 tff(691,plain,
% 5.88/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)))),
% 5.88/6.03 inference(monotonicity,[status(thm)],[690])).
% 5.88/6.03 tff(692,plain,
% 5.88/6.03 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a))),
% 5.88/6.03 inference(transitivity,[status(thm)],[691, 689])).
% 5.88/6.03 tff(693,plain,
% 5.88/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))))),
% 5.88/6.03 inference(quant_inst,[status(thm)],[])).
% 5.88/6.03 tff(694,plain,
% 5.88/6.03 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))), non_ordered_pair(a, b))) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)),
% 5.88/6.03 inference(modus_ponens,[status(thm)],[693, 692])).
% 5.88/6.03 tff(695,plain,
% 5.88/6.03 ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b) | (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[694, 83, 688])).
% 5.88/6.03 tff(696,plain,
% 5.88/6.03 (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = b),
% 5.88/6.03 inference(unit_resolution,[status(thm)],[695, 549])).
% 5.88/6.03 tff(697,plain,
% 5.88/6.03 (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = b),
% 5.88/6.03 inference(transitivity,[status(thm)],[672, 548, 547, 696])).
% 5.88/6.03 tff(698,plain,
% 5.88/6.03 ((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) <=> (b = d)),
% 5.88/6.04 inference(monotonicity,[status(thm)],[697])).
% 5.88/6.04 tff(699,plain,
% 5.88/6.04 ((b = d) <=> (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d)),
% 5.88/6.04 inference(symmetry,[status(thm)],[698])).
% 5.88/6.04 tff(700,plain,
% 5.88/6.04 ((~(b = d)) <=> (~(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[699])).
% 5.88/6.04 tff(701,plain,
% 5.88/6.04 (~(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d)),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[223, 700])).
% 5.88/6.04 tff(702,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, d))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set)))))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(703,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(c, non_ordered_pair(c, d))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set)))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(704,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(c, non_ordered_pair(c, d))) | (~member(c, sigma(sigma(universal_set)))) | (~disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set))))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[703, 702])).
% 5.88/6.04 tff(705,plain,
% 5.88/6.04 (~disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set)))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[704, 58, 377, 471])).
% 5.88/6.04 tff(706,plain,
% 5.88/6.04 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(707,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(708,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(c, d), sigma(sigma(universal_set))) | member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[707, 706])).
% 5.88/6.04 tff(709,plain,
% 5.88/6.04 (member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[708, 482, 705])).
% 5.88/6.04 tff(710,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(711,plain,
% 5.88/6.04 (((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d)))) <=> ((~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(712,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[711])).
% 5.88/6.04 tff(713,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c))),
% 5.88/6.04 inference(transitivity,[status(thm)],[712, 710])).
% 5.88/6.04 tff(714,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(715,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(c, d), sigma(sigma(universal_set))), non_ordered_pair(c, d))) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c)),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[714, 713])).
% 5.88/6.04 tff(716,plain,
% 5.88/6.04 ((f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = d) | (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[715, 83, 709])).
% 5.88/6.04 tff(717,plain,
% 5.88/6.04 (f23(non_ordered_pair(c, d), sigma(sigma(universal_set))) = c),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[716, 701])).
% 5.88/6.04 tff(718,plain,
% 5.88/6.04 (c = f23(non_ordered_pair(c, d), sigma(sigma(universal_set)))),
% 5.88/6.04 inference(symmetry,[status(thm)],[717])).
% 5.88/6.04 tff(719,plain,
% 5.88/6.04 (c = f23(non_ordered_pair(a, b), sigma(sigma(universal_set)))),
% 5.88/6.04 inference(transitivity,[status(thm)],[718, 672, 548, 547])).
% 5.88/6.04 tff(720,plain,
% 5.88/6.04 ((c = a) <=> (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)),
% 5.88/6.04 inference(monotonicity,[status(thm)],[719])).
% 5.88/6.04 tff(721,plain,
% 5.88/6.04 ((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) <=> (c = a)),
% 5.88/6.04 inference(symmetry,[status(thm)],[720])).
% 5.88/6.04 tff(722,plain,
% 5.88/6.04 ((~(f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a)) <=> (~(c = a))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[721])).
% 5.88/6.04 tff(723,plain,
% 5.88/6.04 (~(c = a)),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[549, 722])).
% 5.88/6.04 tff(724,plain,
% 5.88/6.04 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(transitivity,[status(thm)],[12, 635])).
% 5.88/6.04 tff(725,plain,
% 5.88/6.04 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f23(universal_set, non_ordered_pair(a, a))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[724])).
% 5.88/6.04 tff(726,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(a, b)) <=> (non_ordered_pair(a, b) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(commutativity,[status(thm)],[])).
% 5.88/6.04 tff(727,plain,
% 5.88/6.04 ((non_ordered_pair(a, b) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(a, b))),
% 5.88/6.04 inference(symmetry,[status(thm)],[726])).
% 5.88/6.04 tff(728,plain,
% 5.88/6.04 ((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.88/6.04 inference(commutativity,[status(thm)],[])).
% 5.88/6.04 tff(729,plain,
% 5.88/6.04 ((non_ordered_pair(a, b) = non_ordered_pair(c, c)) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[541])).
% 5.88/6.04 tff(730,plain,
% 5.88/6.04 ((non_ordered_pair(a, b) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.88/6.04 inference(transitivity,[status(thm)],[729, 728])).
% 5.88/6.04 tff(731,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(a, b) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(symmetry,[status(thm)],[730])).
% 5.88/6.04 tff(732,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = f16(a, ordered_pair(c, d))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(commutativity,[status(thm)],[])).
% 5.88/6.04 tff(733,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(c, c) = f16(a, ordered_pair(c, d)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[543])).
% 5.88/6.04 tff(734,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(transitivity,[status(thm)],[733, 732])).
% 5.88/6.04 tff(735,plain,
% 5.88/6.04 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.88/6.04 inference(symmetry,[status(thm)],[734])).
% 5.88/6.04 tff(736,plain,
% 5.88/6.04 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(a, b))),
% 5.88/6.04 inference(transitivity,[status(thm)],[735, 731, 727])).
% 5.88/6.04 tff(737,plain,
% 5.88/6.04 ((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))) <=> (~(non_ordered_pair(c, c) = non_ordered_pair(a, b)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[736])).
% 5.88/6.04 tff(738,plain,
% 5.88/6.04 (~(non_ordered_pair(c, c) = non_ordered_pair(a, b))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[669, 737])).
% 5.88/6.04 tff(739,plain,
% 5.88/6.04 (member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))) <=> member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[277, 167])).
% 5.88/6.04 tff(740,plain,
% 5.88/6.04 (member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))) <=> member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.88/6.04 inference(symmetry,[status(thm)],[739])).
% 5.88/6.04 tff(741,plain,
% 5.88/6.04 (little_set(non_ordered_pair(c, c)) <=> little_set(singleton_set(c))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[277])).
% 5.88/6.04 tff(742,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(c, c))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(743,plain,
% 5.88/6.04 (little_set(non_ordered_pair(c, c))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[742, 176])).
% 5.88/6.04 tff(744,plain,
% 5.88/6.04 (little_set(singleton_set(c))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[743, 741])).
% 5.88/6.04 tff(745,plain,
% 5.88/6.04 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(c))) | member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(c))) | member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(746,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(c))) | member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(747,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(c))) | member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[746, 745])).
% 5.88/6.04 tff(748,plain,
% 5.88/6.04 ((~little_set(singleton_set(c))) | member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[747, 40])).
% 5.88/6.04 tff(749,plain,
% 5.88/6.04 (member(singleton_set(c), non_ordered_pair(singleton_set(c), non_ordered_pair(c, d)))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[748, 744])).
% 5.88/6.04 tff(750,plain,
% 5.88/6.04 (member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[749, 740])).
% 5.88/6.04 tff(751,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(752,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(753,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[752, 751])).
% 5.88/6.04 tff(754,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(c, c), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[753, 83])).
% 5.88/6.04 tff(755,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(a, b)) | (non_ordered_pair(c, c) = non_ordered_pair(a, a))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[754, 750])).
% 5.88/6.04 tff(756,plain,
% 5.88/6.04 (non_ordered_pair(c, c) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[755, 738])).
% 5.88/6.04 tff(757,plain,
% 5.88/6.04 (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.88/6.04 inference(transitivity,[status(thm)],[756, 451, 11])).
% 5.88/6.04 tff(758,plain,
% 5.88/6.04 (f23(universal_set, non_ordered_pair(c, c)) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[757])).
% 5.88/6.04 tff(759,plain,
% 5.88/6.04 (c = a),
% 5.88/6.04 inference(transitivity,[status(thm)],[662, 758, 725, 349])).
% 5.88/6.04 tff(760,plain,
% 5.88/6.04 ($false),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[759, 723])).
% 5.88/6.04 tff(761,plain,((f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a) | (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b))) | (~(non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))), inference(lemma,lemma(discharge,[]))).
% 5.88/6.04 tff(762,plain,
% 5.88/6.04 (f23(non_ordered_pair(a, b), sigma(sigma(universal_set))) = a),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[761, 496, 451, 546])).
% 5.88/6.04 tff(763,plain,
% 5.88/6.04 (a = f23(non_ordered_pair(a, b), sigma(sigma(universal_set)))),
% 5.88/6.04 inference(symmetry,[status(thm)],[762])).
% 5.88/6.04 tff(764,plain,
% 5.88/6.04 (a = c),
% 5.88/6.04 inference(transitivity,[status(thm)],[763, 545, 544, 495, 493])).
% 5.88/6.04 tff(765,plain,
% 5.88/6.04 (singleton_set(a) = singleton_set(c)),
% 5.88/6.04 inference(monotonicity,[status(thm)],[764])).
% 5.88/6.04 tff(766,plain,
% 5.88/6.04 (singleton_set(c) = singleton_set(a)),
% 5.88/6.04 inference(symmetry,[status(thm)],[765])).
% 5.88/6.04 tff(767,plain,
% 5.88/6.04 (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.88/6.04 inference(transitivity,[status(thm)],[494, 277, 766, 164, 451, 11])).
% 5.88/6.04 tff(768,plain,
% 5.88/6.04 ($false),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[546, 767])).
% 5.88/6.04 tff(769,plain,((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))) | (f16(a, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~(non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))) | (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(a, b)))), inference(lemma,lemma(discharge,[]))).
% 5.88/6.04 tff(770,plain,
% 5.88/6.04 (~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[769, 450, 446, 423])).
% 5.88/6.04 tff(771,plain,
% 5.88/6.04 (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, d)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[324, 770])).
% 5.88/6.04 tff(772,plain,
% 5.88/6.04 (non_ordered_pair(a, b) = f16(a, ordered_pair(c, d))),
% 5.88/6.04 inference(symmetry,[status(thm)],[423])).
% 5.88/6.04 tff(773,plain,
% 5.88/6.04 (non_ordered_pair(a, b) = non_ordered_pair(c, d)),
% 5.88/6.04 inference(transitivity,[status(thm)],[772, 771])).
% 5.88/6.04 tff(774,plain,
% 5.88/6.04 (member(d, non_ordered_pair(a, b)) <=> member(d, non_ordered_pair(c, d))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[773])).
% 5.88/6.04 tff(775,plain,
% 5.88/6.04 (member(d, non_ordered_pair(c, d)) <=> member(d, non_ordered_pair(a, b))),
% 5.88/6.04 inference(symmetry,[status(thm)],[774])).
% 5.88/6.04 tff(776,plain,
% 5.88/6.04 (member(d, non_ordered_pair(a, b))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[217, 775])).
% 5.88/6.04 tff(777,plain,
% 5.88/6.04 ((~member(d, non_ordered_pair(a, b))) | (d = b) | (d = a)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[230, 83])).
% 5.88/6.04 tff(778,plain,
% 5.88/6.04 (d = a),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[777, 224, 776])).
% 5.88/6.04 tff(779,plain,
% 5.88/6.04 (d = f23(non_ordered_pair(a, b), non_ordered_pair(a, a))),
% 5.88/6.04 inference(transitivity,[status(thm)],[778, 91])).
% 5.88/6.04 tff(780,plain,
% 5.88/6.04 ((b = d) <=> (b = f23(non_ordered_pair(a, b), non_ordered_pair(a, a)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[779])).
% 5.88/6.04 tff(781,plain,
% 5.88/6.04 ((b = d) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.88/6.04 inference(transitivity,[status(thm)],[780, 23])).
% 5.88/6.04 tff(782,plain,
% 5.88/6.04 ((f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b) <=> (b = d)),
% 5.88/6.04 inference(symmetry,[status(thm)],[781])).
% 5.88/6.04 tff(783,plain,
% 5.88/6.04 (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(symmetry,[status(thm)],[446])).
% 5.88/6.04 tff(784,plain,
% 5.88/6.04 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(transitivity,[status(thm)],[12, 783])).
% 5.88/6.04 tff(785,plain,
% 5.88/6.04 (f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = f23(universal_set, non_ordered_pair(a, a))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[784])).
% 5.88/6.04 tff(786,plain,
% 5.88/6.04 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = f16(a, ordered_pair(c, d))),
% 5.88/6.04 inference(transitivity,[status(thm)],[542, 772])).
% 5.88/6.04 tff(787,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (non_ordered_pair(c, c) = f16(a, ordered_pair(c, d)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[786])).
% 5.88/6.04 tff(788,plain,
% 5.88/6.04 ((non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))) <=> (f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))),
% 5.88/6.04 inference(transitivity,[status(thm)],[787, 732])).
% 5.88/6.04 tff(789,plain,
% 5.88/6.04 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.88/6.04 inference(symmetry,[status(thm)],[788])).
% 5.88/6.04 tff(790,plain,
% 5.88/6.04 ((f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c)) <=> (non_ordered_pair(c, c) = non_ordered_pair(a, b))),
% 5.88/6.04 inference(transitivity,[status(thm)],[789, 731, 727])).
% 5.88/6.04 tff(791,plain,
% 5.88/6.04 ((~(f16(a, ordered_pair(c, d)) = non_ordered_pair(c, c))) <=> (~(non_ordered_pair(c, c) = non_ordered_pair(a, b)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[790])).
% 5.88/6.04 tff(792,plain,
% 5.88/6.04 (~(non_ordered_pair(c, c) = non_ordered_pair(a, b))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[770, 791])).
% 5.88/6.04 tff(793,plain,
% 5.88/6.04 (non_ordered_pair(c, c) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[755, 792])).
% 5.88/6.04 tff(794,plain,
% 5.88/6.04 (non_ordered_pair(c, c) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.88/6.04 inference(transitivity,[status(thm)],[793, 446, 11])).
% 5.88/6.04 tff(795,plain,
% 5.88/6.04 (f23(universal_set, non_ordered_pair(c, c)) = f23(universal_set, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[794])).
% 5.88/6.04 tff(796,plain,
% 5.88/6.04 (c = f23(non_ordered_pair(a, b), non_ordered_pair(a, a))),
% 5.88/6.04 inference(transitivity,[status(thm)],[662, 795, 785, 349, 91])).
% 5.88/6.04 tff(797,plain,
% 5.88/6.04 ((c = b) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.88/6.04 inference(monotonicity,[status(thm)],[796])).
% 5.88/6.04 tff(798,plain,
% 5.88/6.04 ((b = c) <=> (c = b)),
% 5.88/6.04 inference(commutativity,[status(thm)],[])).
% 5.88/6.04 tff(799,plain,
% 5.88/6.04 ((b = c) <=> (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b)),
% 5.88/6.04 inference(transitivity,[status(thm)],[798, 797])).
% 5.88/6.04 tff(800,plain,
% 5.88/6.04 (non_ordered_pair(c, d) = f16(a, ordered_pair(c, d))),
% 5.88/6.04 inference(symmetry,[status(thm)],[771])).
% 5.88/6.04 tff(801,plain,
% 5.88/6.04 (non_ordered_pair(c, d) = non_ordered_pair(a, b)),
% 5.88/6.04 inference(transitivity,[status(thm)],[800, 423])).
% 5.88/6.04 tff(802,plain,
% 5.88/6.04 (member(b, non_ordered_pair(c, d)) <=> member(b, non_ordered_pair(a, b))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[801])).
% 5.88/6.04 tff(803,plain,
% 5.88/6.04 (member(b, non_ordered_pair(a, b)) <=> member(b, non_ordered_pair(c, d))),
% 5.88/6.04 inference(symmetry,[status(thm)],[802])).
% 5.88/6.04 tff(804,plain,
% 5.88/6.04 (member(b, non_ordered_pair(c, d))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[359, 803])).
% 5.88/6.04 tff(805,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(806,plain,
% 5.88/6.04 (((b = d) | (b = c) | (~member(b, non_ordered_pair(c, d)))) <=> ((b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(807,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (b = c) | (~member(b, non_ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[806])).
% 5.88/6.04 tff(808,plain,
% 5.88/6.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (b = c) | (~member(b, non_ordered_pair(c, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c))),
% 5.88/6.04 inference(transitivity,[status(thm)],[807, 805])).
% 5.88/6.04 tff(809,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = d) | (b = c) | (~member(b, non_ordered_pair(c, d))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(810,plain,
% 5.88/6.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = d) | (~member(b, non_ordered_pair(c, d))) | (b = c)),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[809, 808])).
% 5.88/6.04 tff(811,plain,
% 5.88/6.04 ((~member(b, non_ordered_pair(c, d))) | (b = c)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[810, 83, 223])).
% 5.88/6.04 tff(812,plain,
% 5.88/6.04 (b = c),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[811, 804])).
% 5.88/6.04 tff(813,plain,
% 5.88/6.04 (f23(non_ordered_pair(a, b), non_ordered_pair(a, a)) = b),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[812, 799])).
% 5.88/6.04 tff(814,plain,
% 5.88/6.04 (b = d),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[813, 782])).
% 5.88/6.04 tff(815,plain,
% 5.88/6.04 ($false),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[223, 814])).
% 5.88/6.04 tff(816,plain,((non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))), inference(lemma,lemma(discharge,[]))).
% 5.88/6.04 tff(817,plain,
% 5.88/6.04 (non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[816, 17])).
% 5.88/6.04 tff(818,plain,
% 5.88/6.04 (non_ordered_pair(a, b) = non_ordered_pair(a, a)),
% 5.88/6.04 inference(transitivity,[status(thm)],[541, 817])).
% 5.88/6.04 tff(819,plain,
% 5.88/6.04 ((non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) <=> (non_ordered_pair(a, a) = singleton_set(f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[818])).
% 5.88/6.04 tff(820,plain,
% 5.88/6.04 ((non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))) <=> (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.88/6.04 inference(transitivity,[status(thm)],[819, 22])).
% 5.88/6.04 tff(821,plain,
% 5.88/6.04 ((~(non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d))))) <=> (~(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[820])).
% 5.88/6.04 tff(822,plain,
% 5.88/6.04 (~(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[17, 821])).
% 5.88/6.04 tff(823,plain,
% 5.88/6.04 (member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))) <=> member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[12, 529])).
% 5.88/6.04 tff(824,plain,
% 5.88/6.04 (member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))) <=> member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.88/6.04 inference(symmetry,[status(thm)],[823])).
% 5.88/6.04 tff(825,plain,
% 5.88/6.04 (little_set(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> little_set(singleton_set(f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(monotonicity,[status(thm)],[12])).
% 5.88/6.04 tff(826,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(827,plain,
% 5.88/6.04 (little_set(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(unit_resolution,[status(thm)],[826, 176])).
% 5.88/6.04 tff(828,plain,
% 5.88/6.04 (little_set(singleton_set(f2(ordered_pair(c, d))))),
% 5.88/6.04 inference(modus_ponens,[status(thm)],[827, 825])).
% 5.88/6.04 tff(829,plain,
% 5.88/6.04 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f2(ordered_pair(c, d))))) | member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f2(ordered_pair(c, d))))) | member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.88/6.04 inference(rewrite,[status(thm)],[])).
% 5.88/6.04 tff(830,plain,
% 5.88/6.04 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f2(ordered_pair(c, d))))) | member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))))),
% 5.88/6.04 inference(quant_inst,[status(thm)],[])).
% 5.88/6.04 tff(831,plain,
% 5.88/6.05 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f2(ordered_pair(c, d))))) | member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[830, 829])).
% 5.88/6.05 tff(832,plain,
% 5.88/6.05 ((~little_set(singleton_set(f2(ordered_pair(c, d))))) | member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[831, 40])).
% 5.88/6.05 tff(833,plain,
% 5.88/6.05 (member(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[832, 828])).
% 5.88/6.05 tff(834,plain,
% 5.88/6.05 (member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[833, 824])).
% 5.88/6.05 tff(835,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(836,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b)))))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(837,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[836, 835])).
% 5.88/6.05 tff(838,plain,
% 5.88/6.05 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, b))))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[837, 83])).
% 5.88/6.05 tff(839,plain,
% 5.88/6.05 ((non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)) | (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, a))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[838, 834])).
% 5.88/6.05 tff(840,plain,
% 5.88/6.05 ($false),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[839, 822, 18])).
% 5.88/6.05 tff(841,plain,(non_ordered_pair(a, b) = singleton_set(f2(ordered_pair(c, d)))), inference(lemma,lemma(discharge,[]))).
% 5.88/6.05 tff(842,plain,
% 5.88/6.05 (singleton_set(f2(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.88/6.05 inference(symmetry,[status(thm)],[841])).
% 5.88/6.05 tff(843,plain,
% 5.88/6.05 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(a, b)),
% 5.88/6.05 inference(transitivity,[status(thm)],[12, 842])).
% 5.88/6.05 tff(844,plain,
% 5.88/6.05 (member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> member(b, non_ordered_pair(a, b))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[843])).
% 5.88/6.05 tff(845,plain,
% 5.88/6.05 (member(b, non_ordered_pair(a, b)) <=> member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.05 inference(symmetry,[status(thm)],[844])).
% 5.88/6.05 tff(846,plain,
% 5.88/6.05 (member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[359, 845])).
% 5.88/6.05 tff(847,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(848,plain,
% 5.88/6.05 (((b = f2(ordered_pair(c, d))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(849,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = f2(ordered_pair(c, d))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[848])).
% 5.88/6.05 tff(850,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = f2(ordered_pair(c, d))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(transitivity,[status(thm)],[849, 847])).
% 5.88/6.05 tff(851,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((b = f2(ordered_pair(c, d))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(852,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[851, 850])).
% 5.88/6.05 tff(853,plain,
% 5.88/6.05 ((b = f2(ordered_pair(c, d))) | (~member(b, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[852, 83])).
% 5.88/6.05 tff(854,plain,
% 5.88/6.05 (b = f2(ordered_pair(c, d))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[853, 846])).
% 5.88/6.05 tff(855,plain,
% 5.88/6.05 (f2(ordered_pair(c, d)) = b),
% 5.88/6.05 inference(symmetry,[status(thm)],[854])).
% 5.88/6.05 tff(856,plain,
% 5.88/6.05 ((d = f2(ordered_pair(c, d))) <=> (d = b)),
% 5.88/6.05 inference(monotonicity,[status(thm)],[855])).
% 5.88/6.05 tff(857,plain,
% 5.88/6.05 ((d = f2(ordered_pair(c, d))) <=> (b = d)),
% 5.88/6.05 inference(transitivity,[status(thm)],[856, 1])).
% 5.88/6.05 tff(858,plain,
% 5.88/6.05 ((b = d) <=> (d = f2(ordered_pair(c, d)))),
% 5.88/6.05 inference(symmetry,[status(thm)],[857])).
% 5.88/6.05 tff(859,plain,
% 5.88/6.05 ((~(b = d)) <=> (~(d = f2(ordered_pair(c, d))))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[858])).
% 5.88/6.05 tff(860,plain,
% 5.88/6.05 (~(d = f2(ordered_pair(c, d)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[223, 859])).
% 5.88/6.05 tff(861,plain,
% 5.88/6.05 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d)))),
% 5.88/6.05 inference(transitivity,[status(thm)],[12, 842, 541])).
% 5.88/6.05 tff(862,plain,
% 5.88/6.05 (non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = non_ordered_pair(singleton_set(f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f3(ordered_pair(c, d))))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[12, 861])).
% 5.88/6.05 tff(863,plain,
% 5.88/6.05 (non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) = ordered_pair(c, d)),
% 5.88/6.05 inference(transitivity,[status(thm)],[862, 427, 426])).
% 5.88/6.05 tff(864,plain,
% 5.88/6.05 (member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))) <=> member(f16(d, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[863])).
% 5.88/6.05 tff(865,plain,
% 5.88/6.05 (member(f16(d, ordered_pair(c, d)), ordered_pair(c, d)) <=> member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.05 inference(symmetry,[status(thm)],[864])).
% 5.88/6.05 tff(866,plain,
% 5.88/6.05 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(d, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | member(d, sigma(ordered_pair(c, d))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(d, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | member(d, sigma(ordered_pair(c, d))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(867,plain,
% 5.88/6.05 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(d, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | member(d, sigma(ordered_pair(c, d))))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(868,plain,
% 5.88/6.05 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(d, non_ordered_pair(c, d))) | (~member(non_ordered_pair(c, d), ordered_pair(c, d))) | member(d, sigma(ordered_pair(c, d)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[867, 866])).
% 5.88/6.05 tff(869,plain,
% 5.88/6.05 ((~member(non_ordered_pair(c, d), ordered_pair(c, d))) | member(d, sigma(ordered_pair(c, d)))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[868, 302, 217])).
% 5.88/6.05 tff(870,plain,
% 5.88/6.05 (member(d, sigma(ordered_pair(c, d)))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[869, 463])).
% 5.88/6.05 tff(871,plain,
% 5.88/6.05 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(d, sigma(ordered_pair(c, d)))) | member(f16(d, ordered_pair(c, d)), ordered_pair(c, d)))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(d, sigma(ordered_pair(c, d)))) | member(f16(d, ordered_pair(c, d)), ordered_pair(c, d)))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(872,plain,
% 5.88/6.05 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(d, sigma(ordered_pair(c, d)))) | member(f16(d, ordered_pair(c, d)), ordered_pair(c, d)))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(873,plain,
% 5.88/6.05 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(d, sigma(ordered_pair(c, d)))) | member(f16(d, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[872, 871])).
% 5.88/6.05 tff(874,plain,
% 5.88/6.05 (member(f16(d, ordered_pair(c, d)), ordered_pair(c, d))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[873, 314, 870])).
% 5.88/6.05 tff(875,plain,
% 5.88/6.05 (member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[874, 865])).
% 5.88/6.05 tff(876,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(877,plain,
% 5.88/6.05 (((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(878,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[877])).
% 5.88/6.05 tff(879,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.05 inference(transitivity,[status(thm)],[878, 876])).
% 5.88/6.05 tff(880,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(881,plain,
% 5.88/6.05 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[880, 879])).
% 5.88/6.05 tff(882,plain,
% 5.88/6.05 ((f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) | (~member(f16(d, ordered_pair(c, d)), non_ordered_pair(non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))), non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[881, 83])).
% 5.88/6.05 tff(883,plain,
% 5.88/6.05 (f16(d, ordered_pair(c, d)) = non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[882, 875])).
% 5.88/6.05 tff(884,plain,
% 5.88/6.05 (non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))) = f16(d, ordered_pair(c, d))),
% 5.88/6.05 inference(symmetry,[status(thm)],[883])).
% 5.88/6.05 tff(885,plain,
% 5.88/6.05 (member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))) <=> member(d, f16(d, ordered_pair(c, d)))),
% 5.88/6.05 inference(monotonicity,[status(thm)],[884])).
% 5.88/6.05 tff(886,plain,
% 5.88/6.05 (member(d, f16(d, ordered_pair(c, d))) <=> member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.05 inference(symmetry,[status(thm)],[885])).
% 5.88/6.05 tff(887,plain,
% 5.88/6.05 (^[Z: $i, X: $i] : refl(((~member(Z, sigma(X))) | member(Z, f16(Z, X))) <=> ((~member(Z, sigma(X))) | member(Z, f16(Z, X))))),
% 5.88/6.05 inference(bind,[status(th)],[])).
% 5.88/6.05 tff(888,plain,
% 5.88/6.05 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 5.88/6.05 inference(quant_intro,[status(thm)],[887])).
% 5.88/6.05 tff(889,plain,
% 5.88/6.05 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(890,axiom,(![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax','sigma2')).
% 5.88/6.05 tff(891,plain,
% 5.88/6.05 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[890, 889])).
% 5.88/6.05 tff(892,plain,(
% 5.88/6.05 ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 5.88/6.05 inference(skolemize,[status(sab)],[891])).
% 5.88/6.05 tff(893,plain,
% 5.88/6.05 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[892, 888])).
% 5.88/6.05 tff(894,plain,
% 5.88/6.05 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(d, sigma(ordered_pair(c, d)))) | member(d, f16(d, ordered_pair(c, d))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(d, sigma(ordered_pair(c, d)))) | member(d, f16(d, ordered_pair(c, d))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(895,plain,
% 5.88/6.05 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(d, sigma(ordered_pair(c, d)))) | member(d, f16(d, ordered_pair(c, d))))),
% 5.88/6.05 inference(quant_inst,[status(thm)],[])).
% 5.88/6.05 tff(896,plain,
% 5.88/6.05 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(d, sigma(ordered_pair(c, d)))) | member(d, f16(d, ordered_pair(c, d)))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[895, 894])).
% 5.88/6.05 tff(897,plain,
% 5.88/6.05 (member(d, f16(d, ordered_pair(c, d)))),
% 5.88/6.05 inference(unit_resolution,[status(thm)],[896, 893, 870])).
% 5.88/6.05 tff(898,plain,
% 5.88/6.05 (member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))),
% 5.88/6.05 inference(modus_ponens,[status(thm)],[897, 886])).
% 5.88/6.05 tff(899,plain,
% 5.88/6.05 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.05 inference(rewrite,[status(thm)],[])).
% 5.88/6.05 tff(900,plain,
% 5.88/6.06 (((d = f2(ordered_pair(c, d))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))) <=> ((d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.06 inference(rewrite,[status(thm)],[])).
% 5.88/6.06 tff(901,plain,
% 5.88/6.06 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = f2(ordered_pair(c, d))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))))),
% 5.88/6.06 inference(monotonicity,[status(thm)],[900])).
% 5.88/6.06 tff(902,plain,
% 5.88/6.06 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = f2(ordered_pair(c, d))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.06 inference(transitivity,[status(thm)],[901, 899])).
% 5.88/6.06 tff(903,plain,
% 5.88/6.06 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((d = f2(ordered_pair(c, d))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d))))))),
% 5.88/6.06 inference(quant_inst,[status(thm)],[])).
% 5.88/6.06 tff(904,plain,
% 5.88/6.06 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.06 inference(modus_ponens,[status(thm)],[903, 902])).
% 5.88/6.06 tff(905,plain,
% 5.88/6.06 ((d = f2(ordered_pair(c, d))) | (~member(d, non_ordered_pair(f2(ordered_pair(c, d)), f2(ordered_pair(c, d)))))),
% 5.88/6.06 inference(unit_resolution,[status(thm)],[904, 83])).
% 5.88/6.06 tff(906,plain,
% 5.88/6.06 ($false),
% 5.88/6.06 inference(unit_resolution,[status(thm)],[905, 898, 860])).
% 5.88/6.06 % SZS output end Proof
% 5.88/6.07 % E exiting
%------------------------------------------------------------------------------