%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET016-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:48 AM UTC 2025
% Result : Unsatisfiable 61.21s 61.44s
% Output : Proof 61.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET016-3 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:01:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 61.21/61.44 % SZS status Unsatisfiable
% 61.21/61.44 % SZS output start Proof
% 61.21/61.44 tff(b_type, type, (
% 61.21/61.44 b: $i)).
% 61.21/61.44 tff(a_type, type, (
% 61.21/61.44 a: $i)).
% 61.21/61.44 tff(f23_type, type, (
% 61.21/61.44 f23: ( $i * $i ) > $i)).
% 61.21/61.44 tff(non_ordered_pair_type, type, (
% 61.21/61.44 non_ordered_pair: ( $i * $i ) > $i)).
% 61.21/61.44 tff(universal_set_type, type, (
% 61.21/61.44 universal_set: $i)).
% 61.21/61.44 tff(member_type, type, (
% 61.21/61.44 member: ( $i * $i ) > $o)).
% 61.21/61.44 tff(disjoint_type, type, (
% 61.21/61.44 disjoint: ( $i * $i ) > $o)).
% 61.21/61.44 tff(little_set_type, type, (
% 61.21/61.44 little_set: $i > $o)).
% 61.21/61.44 tff(c_type, type, (
% 61.21/61.44 c: $i)).
% 61.21/61.44 tff(ordered_pair_type, type, (
% 61.21/61.44 ordered_pair: ( $i * $i ) > $i)).
% 61.21/61.44 tff(d_type, type, (
% 61.21/61.44 d: $i)).
% 61.21/61.44 tff(f16_type, type, (
% 61.21/61.44 f16: ( $i * $i ) > $i)).
% 61.21/61.44 tff(singleton_set_type, type, (
% 61.21/61.44 singleton_set: $i > $i)).
% 61.21/61.44 tff(sigma_type, type, (
% 61.21/61.44 sigma: $i > $i)).
% 61.21/61.44 tff(1,plain,
% 61.21/61.44 (little_set(b) <=> little_set(b)),
% 61.21/61.44 inference(rewrite,[status(thm)],[])).
% 61.21/61.44 tff(2,axiom,(little_set(b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','little_set_b')).
% 61.21/61.44 tff(3,plain,
% 61.21/61.44 (little_set(b)),
% 61.21/61.44 inference(modus_ponens,[status(thm)],[2, 1])).
% 61.21/61.44 tff(4,plain,
% 61.21/61.44 (^[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))))),
% 61.21/61.44 inference(bind,[status(th)],[])).
% 61.21/61.44 tff(5,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(quant_intro,[status(thm)],[4])).
% 61.21/61.44 tff(6,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(rewrite,[status(thm)],[])).
% 61.21/61.44 tff(7,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(elim_unused_vars,[status(thm)],[])).
% 61.21/61.44 tff(8,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 61.21/61.44 tff(9,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(transitivity,[status(thm)],[8, 7])).
% 61.21/61.44 tff(10,plain,
% 61.21/61.44 (^[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)))))),
% 61.21/61.44 inference(bind,[status(th)],[])).
% 61.21/61.44 tff(11,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(quant_intro,[status(thm)],[10])).
% 61.21/61.44 tff(12,plain,
% 61.21/61.44 (![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)))),
% 61.21/61.44 inference(transitivity,[status(thm)],[11, 9])).
% 61.21/61.44 tff(13,axiom,(![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','non_ordered_pair2')).
% 61.21/61.44 tff(14,plain,
% 61.21/61.44 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 61.21/61.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 61.21/61.44 tff(15,plain,
% 61.21/61.44 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 61.21/61.44 inference(modus_ponens,[status(thm)],[14, 6])).
% 61.21/61.44 tff(16,plain,(
% 61.21/61.44 ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 61.21/61.45 inference(skolemize,[status(sab)],[15])).
% 61.21/61.45 tff(17,plain,
% 61.21/61.45 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[16, 5])).
% 61.21/61.45 tff(18,plain,
% 61.21/61.45 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(b, b)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(b, b)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(19,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(b, b)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(20,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(b, b))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[19, 18])).
% 61.21/61.45 tff(21,plain,
% 61.21/61.45 (member(b, non_ordered_pair(b, b))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[20, 17, 3])).
% 61.21/61.45 tff(22,plain,
% 61.21/61.45 (^[Z: $i] : refl(((~little_set(Z)) | member(Z, universal_set)) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(23,plain,
% 61.21/61.45 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[22])).
% 61.21/61.45 tff(24,plain,
% 61.21/61.45 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(25,plain,
% 61.21/61.45 (^[Z: $i] : rewrite((member(Z, universal_set) | (~little_set(Z))) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(26,plain,
% 61.21/61.45 (![Z: $i] : (member(Z, universal_set) | (~little_set(Z))) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[25])).
% 61.21/61.45 tff(27,axiom,(![Z: $i] : (member(Z, universal_set) | (~little_set(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','universal_set')).
% 61.21/61.45 tff(28,plain,
% 61.21/61.45 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 61.21/61.45 tff(29,plain,
% 61.21/61.45 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 61.21/61.45 tff(30,plain,(
% 61.21/61.45 ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(skolemize,[status(sab)],[29])).
% 61.21/61.45 tff(31,plain,
% 61.21/61.45 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[30, 23])).
% 61.21/61.45 tff(32,plain,
% 61.21/61.45 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(b)) | member(b, universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(b)) | member(b, universal_set))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(33,plain,
% 61.21/61.45 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(b)) | member(b, universal_set))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(34,plain,
% 61.21/61.45 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(b)) | member(b, universal_set)),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 61.21/61.45 tff(35,plain,
% 61.21/61.45 (member(b, universal_set)),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[34, 31, 3])).
% 61.21/61.45 tff(36,plain,
% 61.21/61.45 (^[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))))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(37,plain,
% 61.21/61.45 (![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)))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[36])).
% 61.21/61.45 tff(38,plain,
% 61.21/61.45 (![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)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(39,plain,
% 61.21/61.45 (^[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))))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(40,plain,
% 61.21/61.45 (![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)))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[39])).
% 61.21/61.45 tff(41,axiom,(![Y: $i, U: $i, X: $i] : (((~disjoint(X, Y)) | (~member(U, X))) | (~member(U, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','disjoint1')).
% 61.21/61.45 tff(42,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 61.21/61.45 tff(43,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[42, 38])).
% 61.21/61.45 tff(44,plain,(
% 61.21/61.45 ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 61.21/61.45 inference(skolemize,[status(sab)],[43])).
% 61.21/61.45 tff(45,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[44, 37])).
% 61.21/61.45 tff(46,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, universal_set)) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(universal_set, non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(b, universal_set)) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(universal_set, non_ordered_pair(b, b))))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(47,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, universal_set)) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(universal_set, non_ordered_pair(b, b))))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(48,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(b, universal_set)) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(universal_set, non_ordered_pair(b, b)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 61.21/61.45 tff(49,plain,
% 61.21/61.45 (~disjoint(universal_set, non_ordered_pair(b, b))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[48, 45, 35, 21])).
% 61.21/61.45 tff(50,plain,
% 61.21/61.45 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), Y)) <=> (disjoint(X, Y) | member(f23(X, Y), Y)))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(51,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[50])).
% 61.21/61.45 tff(52,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(53,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','disjoint3')).
% 61.21/61.45 tff(54,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 61.21/61.45 tff(55,plain,(
% 61.21/61.45 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 61.21/61.45 inference(skolemize,[status(sab)],[54])).
% 61.21/61.45 tff(56,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 61.21/61.45 tff(57,plain,
% 61.21/61.45 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(b, b)) | member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(b, b)) | member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(58,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(b, b)) | member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(59,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(b, b)) | member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 61.21/61.45 tff(60,plain,
% 61.21/61.45 (member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[59, 56, 49])).
% 61.21/61.45 tff(61,plain,
% 61.21/61.45 (^[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)))))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(62,plain,
% 61.21/61.45 (![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))))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[61])).
% 61.21/61.45 tff(63,plain,
% 61.21/61.45 (![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))))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(64,plain,
% 61.21/61.45 (^[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)))))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(65,plain,
% 61.21/61.45 (![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))))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[64])).
% 61.21/61.45 tff(66,axiom,(![Y: $i, U: $i, X: $i] : (((~member(U, non_ordered_pair(X, Y))) | (U = X)) | (U = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','non_ordered_pair1')).
% 61.21/61.45 tff(67,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 61.21/61.45 tff(68,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 61.21/61.45 tff(69,plain,(
% 61.21/61.45 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 61.21/61.45 inference(skolemize,[status(sab)],[68])).
% 61.21/61.45 tff(70,plain,
% 61.21/61.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 61.21/61.45 tff(71,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(72,plain,
% 61.21/61.45 (((f23(universal_set, non_ordered_pair(b, b)) = b) | (f23(universal_set, non_ordered_pair(b, b)) = b) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b)))) <=> ((~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(73,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(b, b)) = b) | (f23(universal_set, non_ordered_pair(b, b)) = b) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b)))),
% 61.21/61.45 inference(monotonicity,[status(thm)],[72])).
% 61.21/61.45 tff(74,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(b, b)) = b) | (f23(universal_set, non_ordered_pair(b, b)) = b) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b))),
% 61.21/61.45 inference(transitivity,[status(thm)],[73, 71])).
% 61.21/61.45 tff(75,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(b, b)) = b) | (f23(universal_set, non_ordered_pair(b, b)) = b) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(76,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(b, b)), non_ordered_pair(b, b))) | (f23(universal_set, non_ordered_pair(b, b)) = b)),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 61.21/61.45 tff(77,plain,
% 61.21/61.45 (f23(universal_set, non_ordered_pair(b, b)) = b),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 61.21/61.45 tff(78,plain,
% 61.21/61.45 ((non_ordered_pair(b, b) = non_ordered_pair(a, c)) <=> (non_ordered_pair(a, c) = non_ordered_pair(b, b))),
% 61.21/61.45 inference(commutativity,[status(thm)],[])).
% 61.21/61.45 tff(79,plain,
% 61.21/61.45 ((non_ordered_pair(a, c) = non_ordered_pair(b, b)) <=> (non_ordered_pair(b, b) = non_ordered_pair(a, c))),
% 61.21/61.45 inference(symmetry,[status(thm)],[78])).
% 61.21/61.45 tff(80,assumption,(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)), introduced(assumption)).
% 61.21/61.45 tff(81,plain,
% 61.21/61.45 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(b, d)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(b, d)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(82,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(b)) | member(b, non_ordered_pair(b, d)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(83,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(b)) | member(b, non_ordered_pair(b, d))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 61.21/61.45 tff(84,plain,
% 61.21/61.45 (member(b, non_ordered_pair(b, d))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[83, 17, 3])).
% 61.21/61.45 tff(85,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(86,plain,
% 61.21/61.45 (((~member(b, non_ordered_pair(b, b))) | (~member(b, non_ordered_pair(b, d))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)))) <=> ((~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(87,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, non_ordered_pair(b, b))) | (~member(b, non_ordered_pair(b, d))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)))))),
% 61.21/61.45 inference(monotonicity,[status(thm)],[86])).
% 61.21/61.45 tff(88,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, non_ordered_pair(b, b))) | (~member(b, non_ordered_pair(b, d))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.21/61.45 inference(transitivity,[status(thm)],[87, 85])).
% 61.21/61.45 tff(89,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(b, non_ordered_pair(b, b))) | (~member(b, non_ordered_pair(b, d))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(90,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(b, non_ordered_pair(b, d))) | (~member(b, non_ordered_pair(b, b))) | (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 61.21/61.45 tff(91,plain,
% 61.21/61.45 (~disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[90, 45, 84, 21])).
% 61.21/61.45 tff(92,plain,
% 61.21/61.45 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), X)) <=> (disjoint(X, Y) | member(f23(X, Y), X)))),
% 61.21/61.45 inference(bind,[status(th)],[])).
% 61.21/61.45 tff(93,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 61.21/61.45 inference(quant_intro,[status(thm)],[92])).
% 61.21/61.45 tff(94,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(95,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','disjoint2')).
% 61.21/61.45 tff(96,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[95, 94])).
% 61.21/61.45 tff(97,plain,(
% 61.21/61.45 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 61.21/61.45 inference(skolemize,[status(sab)],[96])).
% 61.21/61.45 tff(98,plain,
% 61.21/61.45 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[97, 93])).
% 61.21/61.45 tff(99,plain,
% 61.21/61.45 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)) | member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)) | member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(100,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)) | member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(101,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(b, b), non_ordered_pair(b, d)) | member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[100, 99])).
% 61.21/61.45 tff(102,plain,
% 61.21/61.45 (member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[101, 98, 91])).
% 61.21/61.45 tff(103,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(104,plain,
% 61.21/61.45 (((f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b)))) <=> ((~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(105,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b)))),
% 61.21/61.45 inference(monotonicity,[status(thm)],[104])).
% 61.21/61.45 tff(106,plain,
% 61.21/61.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b))),
% 61.21/61.45 inference(transitivity,[status(thm)],[105, 103])).
% 61.21/61.45 tff(107,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(108,plain,
% 61.21/61.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(b, b), non_ordered_pair(b, d)), non_ordered_pair(b, b))) | (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b)),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 61.21/61.45 tff(109,plain,
% 61.21/61.45 (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = b),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[108, 70, 102])).
% 61.21/61.45 tff(110,assumption,(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)), introduced(assumption)).
% 61.21/61.45 tff(111,plain,
% 61.21/61.45 (non_ordered_pair(b, d) = f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))),
% 61.21/61.45 inference(symmetry,[status(thm)],[110])).
% 61.21/61.45 tff(112,plain,
% 61.21/61.45 (non_ordered_pair(b, d) = non_ordered_pair(a, a)),
% 61.21/61.45 inference(transitivity,[status(thm)],[111, 80])).
% 61.21/61.45 tff(113,plain,
% 61.21/61.45 ((non_ordered_pair(b, b) = non_ordered_pair(a, a)) <=> (non_ordered_pair(a, a) = non_ordered_pair(b, b))),
% 61.21/61.45 inference(commutativity,[status(thm)],[])).
% 61.21/61.45 tff(114,plain,
% 61.21/61.45 ((non_ordered_pair(a, a) = non_ordered_pair(b, b)) <=> (non_ordered_pair(b, b) = non_ordered_pair(a, a))),
% 61.21/61.45 inference(symmetry,[status(thm)],[113])).
% 61.21/61.45 tff(115,assumption,(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)), introduced(assumption)).
% 61.21/61.45 tff(116,assumption,(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)), introduced(assumption)).
% 61.21/61.45 tff(117,plain,
% 61.21/61.45 (non_ordered_pair(b, b) = f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))),
% 61.21/61.45 inference(symmetry,[status(thm)],[115])).
% 61.21/61.45 tff(118,plain,
% 61.21/61.45 (non_ordered_pair(b, b) = non_ordered_pair(a, a)),
% 61.21/61.45 inference(transitivity,[status(thm)],[117, 116])).
% 61.21/61.45 tff(119,plain,
% 61.21/61.45 (f23(universal_set, non_ordered_pair(b, b)) = f23(universal_set, non_ordered_pair(a, a))),
% 61.21/61.45 inference(monotonicity,[status(thm)],[118])).
% 61.21/61.45 tff(120,plain,
% 61.21/61.45 (f23(universal_set, non_ordered_pair(a, a)) = f23(universal_set, non_ordered_pair(b, b))),
% 61.21/61.45 inference(symmetry,[status(thm)],[119])).
% 61.21/61.45 tff(121,plain,
% 61.21/61.45 (little_set(a) <=> little_set(a)),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(122,axiom,(little_set(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','little_set_a')).
% 61.21/61.45 tff(123,plain,
% 61.21/61.45 (little_set(a)),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 61.21/61.45 tff(124,plain,
% 61.21/61.45 (((~![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)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(125,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, a)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(126,plain,
% 61.21/61.45 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, a))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 61.21/61.45 tff(127,plain,
% 61.21/61.45 (member(a, non_ordered_pair(a, a))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[126, 17, 123])).
% 61.21/61.45 tff(128,plain,
% 61.21/61.45 (((~![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))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(129,plain,
% 61.21/61.45 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(a)) | member(a, universal_set))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(130,plain,
% 61.21/61.45 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(a)) | member(a, universal_set)),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[129, 128])).
% 61.21/61.45 tff(131,plain,
% 61.21/61.45 (member(a, universal_set)),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[130, 31, 123])).
% 61.21/61.45 tff(132,plain,
% 61.21/61.45 (((~![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))))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(133,plain,
% 61.21/61.45 ((~![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))))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(134,plain,
% 61.21/61.45 ((~![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)))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[133, 132])).
% 61.21/61.45 tff(135,plain,
% 61.21/61.45 (~disjoint(universal_set, non_ordered_pair(a, a))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[134, 45, 131, 127])).
% 61.21/61.45 tff(136,plain,
% 61.21/61.45 (((~![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)))),
% 61.21/61.45 inference(rewrite,[status(thm)],[])).
% 61.21/61.45 tff(137,plain,
% 61.21/61.45 ((~![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)))),
% 61.21/61.45 inference(quant_inst,[status(thm)],[])).
% 61.21/61.45 tff(138,plain,
% 61.21/61.45 ((~![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))),
% 61.21/61.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 61.21/61.45 tff(139,plain,
% 61.21/61.45 (member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 61.21/61.45 inference(unit_resolution,[status(thm)],[138, 56, 135])).
% 61.21/61.45 tff(140,plain,
% 61.21/61.45 (((~![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))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(141,plain,
% 61.21/61.46 (((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))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(142,plain,
% 61.21/61.46 (((~![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)))),
% 61.21/61.46 inference(monotonicity,[status(thm)],[141])).
% 61.21/61.46 tff(143,plain,
% 61.21/61.46 (((~![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))),
% 61.21/61.46 inference(transitivity,[status(thm)],[142, 140])).
% 61.21/61.46 tff(144,plain,
% 61.21/61.46 ((~![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))))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(145,plain,
% 61.21/61.46 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(a, a)), non_ordered_pair(a, a))) | (f23(universal_set, non_ordered_pair(a, a)) = a)),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 61.21/61.46 tff(146,plain,
% 61.21/61.46 (f23(universal_set, non_ordered_pair(a, a)) = a),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[145, 70, 139])).
% 61.21/61.46 tff(147,plain,
% 61.21/61.46 (a = f23(universal_set, non_ordered_pair(a, a))),
% 61.21/61.46 inference(symmetry,[status(thm)],[146])).
% 61.21/61.46 tff(148,plain,
% 61.21/61.46 (a = b),
% 61.21/61.46 inference(transitivity,[status(thm)],[147, 120, 77])).
% 61.21/61.46 tff(149,plain,
% 61.21/61.46 ((~(a = b)) <=> (~(a = b))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(150,axiom,(~(a = b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_first_components_equal')).
% 61.21/61.46 tff(151,plain,
% 61.21/61.46 (~(a = b)),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[150, 149])).
% 61.21/61.46 tff(152,plain,
% 61.21/61.46 ($false),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[151, 148])).
% 61.21/61.46 tff(153,plain,((~(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a))) | (~(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)))), inference(lemma,lemma(discharge,[]))).
% 61.21/61.46 tff(154,plain,
% 61.21/61.46 (~(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a))),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[153, 115])).
% 61.21/61.46 tff(155,plain,
% 61.21/61.46 ((ordered_pair(a, c) = ordered_pair(b, d)) <=> (ordered_pair(a, c) = ordered_pair(b, d))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(156,axiom,(ordered_pair(a, c) = ordered_pair(b, d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_ordered_pairs')).
% 61.21/61.46 tff(157,plain,
% 61.21/61.46 (ordered_pair(a, c) = ordered_pair(b, d)),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[156, 155])).
% 61.21/61.46 tff(158,plain,
% 61.21/61.46 (^[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))))),
% 61.21/61.46 inference(bind,[status(th)],[])).
% 61.21/61.46 tff(159,plain,
% 61.21/61.46 (![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)))),
% 61.21/61.46 inference(quant_intro,[status(thm)],[158])).
% 61.21/61.46 tff(160,plain,
% 61.21/61.46 (![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)))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(161,axiom,(![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','ordered_pair')).
% 61.21/61.46 tff(162,plain,
% 61.21/61.46 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 61.21/61.46 tff(163,plain,(
% 61.21/61.46 ![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 61.21/61.46 inference(skolemize,[status(sab)],[162])).
% 61.21/61.46 tff(164,plain,
% 61.21/61.46 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[163, 159])).
% 61.21/61.46 tff(165,plain,
% 61.21/61.46 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(a, c) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, c)))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(166,plain,
% 61.21/61.46 (ordered_pair(a, c) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, c))),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[165, 164])).
% 61.21/61.46 tff(167,plain,
% 61.21/61.46 (non_ordered_pair(singleton_set(a), non_ordered_pair(a, c)) = ordered_pair(a, c)),
% 61.21/61.46 inference(symmetry,[status(thm)],[166])).
% 61.21/61.46 tff(168,plain,
% 61.21/61.46 (^[X: $i] : refl((singleton_set(X) = non_ordered_pair(X, X)) <=> (singleton_set(X) = non_ordered_pair(X, X)))),
% 61.21/61.46 inference(bind,[status(th)],[])).
% 61.21/61.46 tff(169,plain,
% 61.21/61.46 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 61.21/61.46 inference(quant_intro,[status(thm)],[168])).
% 61.21/61.46 tff(170,plain,
% 61.21/61.46 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(171,axiom,(![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','singleton_set')).
% 61.21/61.46 tff(172,plain,
% 61.21/61.46 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 61.21/61.46 tff(173,plain,(
% 61.21/61.46 ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 61.21/61.46 inference(skolemize,[status(sab)],[172])).
% 61.21/61.46 tff(174,plain,
% 61.21/61.46 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[173, 169])).
% 61.21/61.46 tff(175,plain,
% 61.21/61.46 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(a) = non_ordered_pair(a, a))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(176,plain,
% 61.21/61.46 (singleton_set(a) = non_ordered_pair(a, a)),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[175, 174])).
% 61.21/61.46 tff(177,plain,
% 61.21/61.46 (non_ordered_pair(a, a) = singleton_set(a)),
% 61.21/61.46 inference(symmetry,[status(thm)],[176])).
% 61.21/61.46 tff(178,plain,
% 61.21/61.46 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, c))),
% 61.21/61.46 inference(monotonicity,[status(thm)],[177])).
% 61.21/61.46 tff(179,plain,
% 61.21/61.46 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)) = ordered_pair(b, d)),
% 61.21/61.46 inference(transitivity,[status(thm)],[178, 167, 157])).
% 61.21/61.46 tff(180,plain,
% 61.21/61.46 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))) <=> member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.21/61.46 inference(monotonicity,[status(thm)],[179])).
% 61.21/61.46 tff(181,plain,
% 61.21/61.46 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d)) <=> member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.21/61.46 inference(symmetry,[status(thm)],[180])).
% 61.21/61.46 tff(182,plain,
% 61.21/61.46 (ordered_pair(b, d) = ordered_pair(a, c)),
% 61.21/61.46 inference(symmetry,[status(thm)],[157])).
% 61.21/61.46 tff(183,plain,
% 61.21/61.46 (ordered_pair(b, d) = non_ordered_pair(singleton_set(a), non_ordered_pair(a, c))),
% 61.21/61.46 inference(transitivity,[status(thm)],[182, 166])).
% 61.21/61.46 tff(184,plain,
% 61.21/61.46 (little_set(ordered_pair(b, d)) <=> little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, c)))),
% 61.21/61.46 inference(monotonicity,[status(thm)],[183])).
% 61.21/61.46 tff(185,plain,
% 61.21/61.46 (little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, c))) <=> little_set(ordered_pair(b, d))),
% 61.21/61.46 inference(symmetry,[status(thm)],[184])).
% 61.21/61.46 tff(186,plain,
% 61.21/61.46 (^[Y: $i, X: $i] : refl(little_set(non_ordered_pair(X, Y)) <=> little_set(non_ordered_pair(X, Y)))),
% 61.21/61.46 inference(bind,[status(th)],[])).
% 61.21/61.46 tff(187,plain,
% 61.21/61.46 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 61.21/61.46 inference(quant_intro,[status(thm)],[186])).
% 61.21/61.46 tff(188,plain,
% 61.21/61.46 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(189,axiom,(![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','non_ordered_pair4')).
% 61.21/61.46 tff(190,plain,
% 61.21/61.46 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[189, 188])).
% 61.21/61.46 tff(191,plain,(
% 61.21/61.46 ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 61.21/61.46 inference(skolemize,[status(sab)],[190])).
% 61.21/61.46 tff(192,plain,
% 61.21/61.46 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[191, 187])).
% 61.21/61.46 tff(193,plain,
% 61.21/61.46 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, c)))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(194,plain,
% 61.21/61.46 (little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, c)))),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[193, 192])).
% 61.21/61.46 tff(195,plain,
% 61.21/61.46 (little_set(ordered_pair(b, d))),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[194, 185])).
% 61.21/61.46 tff(196,plain,
% 61.21/61.46 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(b, d))) | member(ordered_pair(b, d), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(b, d))) | member(ordered_pair(b, d), universal_set))),
% 61.21/61.46 inference(rewrite,[status(thm)],[])).
% 61.21/61.46 tff(197,plain,
% 61.21/61.46 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(b, d))) | member(ordered_pair(b, d), universal_set))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(198,plain,
% 61.21/61.46 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(b, d))) | member(ordered_pair(b, d), universal_set)),
% 61.21/61.46 inference(modus_ponens,[status(thm)],[197, 196])).
% 61.21/61.46 tff(199,plain,
% 61.21/61.46 ((~little_set(ordered_pair(b, d))) | member(ordered_pair(b, d), universal_set)),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[198, 31])).
% 61.21/61.46 tff(200,plain,
% 61.21/61.46 (member(ordered_pair(b, d), universal_set)),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[199, 195])).
% 61.21/61.46 tff(201,plain,
% 61.21/61.46 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(b, d) = non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(202,plain,
% 61.21/61.46 (ordered_pair(b, d) = non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[201, 164])).
% 61.21/61.46 tff(203,plain,
% 61.21/61.46 (member(non_ordered_pair(b, d), ordered_pair(b, d)) <=> member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.21/61.46 inference(monotonicity,[status(thm)],[202])).
% 61.21/61.46 tff(204,plain,
% 61.21/61.46 (member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))) <=> member(non_ordered_pair(b, d), ordered_pair(b, d))),
% 61.21/61.46 inference(symmetry,[status(thm)],[203])).
% 61.21/61.46 tff(205,plain,
% 61.21/61.46 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(b, d))),
% 61.21/61.46 inference(quant_inst,[status(thm)],[])).
% 61.21/61.46 tff(206,plain,
% 61.21/61.46 (little_set(non_ordered_pair(b, d))),
% 61.21/61.46 inference(unit_resolution,[status(thm)],[205, 192])).
% 61.21/61.46 tff(207,plain,
% 61.21/61.46 (^[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))))),
% 61.21/61.46 inference(bind,[status(th)],[])).
% 61.21/61.46 tff(208,plain,
% 61.21/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[207])).
% 61.23/61.46 tff(209,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(210,plain,
% 61.23/61.46 (^[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))))),
% 61.23/61.46 inference(bind,[status(th)],[])).
% 61.23/61.46 tff(211,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[210])).
% 61.23/61.46 tff(212,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(elim_unused_vars,[status(thm)],[])).
% 61.23/61.46 tff(213,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 61.23/61.46 tff(214,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(transitivity,[status(thm)],[213, 212])).
% 61.23/61.46 tff(215,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(transitivity,[status(thm)],[214, 211])).
% 61.23/61.46 tff(216,plain,
% 61.23/61.46 (^[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)))))),
% 61.23/61.46 inference(bind,[status(th)],[])).
% 61.23/61.46 tff(217,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[216])).
% 61.23/61.46 tff(218,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(transitivity,[status(thm)],[217, 215])).
% 61.23/61.46 tff(219,axiom,(![Y: $i, U: $i, X: $i] : ((member(U, non_ordered_pair(X, Y)) | (~little_set(U))) | (~(U = Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','non_ordered_pair3')).
% 61.23/61.46 tff(220,plain,
% 61.23/61.46 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[219, 218])).
% 61.23/61.46 tff(221,plain,
% 61.23/61.46 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[220, 209])).
% 61.23/61.46 tff(222,plain,(
% 61.23/61.46 ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 61.23/61.46 inference(skolemize,[status(sab)],[221])).
% 61.23/61.46 tff(223,plain,
% 61.23/61.46 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[222, 208])).
% 61.23/61.46 tff(224,plain,
% 61.23/61.46 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(b, d))) | member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(b, d))) | member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(225,plain,
% 61.23/61.46 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(b, d))) | member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(226,plain,
% 61.23/61.46 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(b, d))) | member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[225, 224])).
% 61.23/61.46 tff(227,plain,
% 61.23/61.46 ((~little_set(non_ordered_pair(b, d))) | member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[226, 223])).
% 61.23/61.46 tff(228,plain,
% 61.23/61.46 (member(non_ordered_pair(b, d), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[227, 206])).
% 61.23/61.46 tff(229,plain,
% 61.23/61.46 (member(non_ordered_pair(b, d), ordered_pair(b, d))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[228, 204])).
% 61.23/61.46 tff(230,plain,
% 61.23/61.46 (^[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))))),
% 61.23/61.46 inference(bind,[status(th)],[])).
% 61.23/61.46 tff(231,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[230])).
% 61.23/61.46 tff(232,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(233,plain,
% 61.23/61.46 (^[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)))))),
% 61.23/61.46 inference(bind,[status(th)],[])).
% 61.23/61.46 tff(234,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[233])).
% 61.23/61.46 tff(235,axiom,(![Z: $i, Y: $i, X: $i] : ((member(Z, sigma(X)) | (~member(Y, X))) | (~member(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','sigma3')).
% 61.23/61.46 tff(236,plain,
% 61.23/61.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[235, 234])).
% 61.23/61.46 tff(237,plain,
% 61.23/61.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[236, 232])).
% 61.23/61.46 tff(238,plain,(
% 61.23/61.46 ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 61.23/61.46 inference(skolemize,[status(sab)],[237])).
% 61.23/61.46 tff(239,plain,
% 61.23/61.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[238, 231])).
% 61.23/61.46 tff(240,plain,
% 61.23/61.46 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, d), sigma(universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, d), sigma(universal_set)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(241,plain,
% 61.23/61.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, d), sigma(universal_set)))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(242,plain,
% 61.23/61.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, d), sigma(universal_set))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[241, 240])).
% 61.23/61.46 tff(243,plain,
% 61.23/61.46 (member(non_ordered_pair(b, d), sigma(universal_set))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[242, 239, 229, 200])).
% 61.23/61.46 tff(244,plain,
% 61.23/61.46 (^[Z: $i, X: $i] : refl(((~member(Z, sigma(X))) | member(Z, f16(Z, X))) <=> ((~member(Z, sigma(X))) | member(Z, f16(Z, X))))),
% 61.23/61.46 inference(bind,[status(th)],[])).
% 61.23/61.46 tff(245,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(quant_intro,[status(thm)],[244])).
% 61.23/61.46 tff(246,plain,
% 61.23/61.46 (![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)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(247,axiom,(![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','sigma2')).
% 61.23/61.46 tff(248,plain,
% 61.23/61.46 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[247, 246])).
% 61.23/61.46 tff(249,plain,(
% 61.23/61.46 ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 61.23/61.46 inference(skolemize,[status(sab)],[248])).
% 61.23/61.46 tff(250,plain,
% 61.23/61.46 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[249, 245])).
% 61.23/61.46 tff(251,plain,
% 61.23/61.46 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(b, d), sigma(universal_set))) | member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set)))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(b, d), sigma(universal_set))) | member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(252,plain,
% 61.23/61.46 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(b, d), sigma(universal_set))) | member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set)))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(253,plain,
% 61.23/61.46 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(b, d), sigma(universal_set))) | member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[252, 251])).
% 61.23/61.46 tff(254,plain,
% 61.23/61.46 (member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[253, 250, 243])).
% 61.23/61.46 tff(255,plain,
% 61.23/61.46 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(256,plain,
% 61.23/61.46 (((~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)))) <=> ((~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(257,plain,
% 61.23/61.46 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)))))),
% 61.23/61.46 inference(monotonicity,[status(thm)],[256])).
% 61.23/61.46 tff(258,plain,
% 61.23/61.46 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))),
% 61.23/61.46 inference(transitivity,[status(thm)],[257, 255])).
% 61.23/61.46 tff(259,plain,
% 61.23/61.46 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(260,plain,
% 61.23/61.46 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, d), ordered_pair(b, d))) | (~member(non_ordered_pair(b, d), f16(non_ordered_pair(b, d), universal_set))) | (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[259, 258])).
% 61.23/61.46 tff(261,plain,
% 61.23/61.46 (~disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[260, 45, 229, 254])).
% 61.23/61.46 tff(262,plain,
% 61.23/61.46 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(263,plain,
% 61.23/61.46 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(264,plain,
% 61.23/61.46 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[263, 262])).
% 61.23/61.46 tff(265,plain,
% 61.23/61.46 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[264, 56, 261])).
% 61.23/61.46 tff(266,plain,
% 61.23/61.46 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[265, 181])).
% 61.23/61.46 tff(267,plain,
% 61.23/61.46 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.46 inference(rewrite,[status(thm)],[])).
% 61.23/61.46 tff(268,plain,
% 61.23/61.46 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.46 inference(quant_inst,[status(thm)],[])).
% 61.23/61.46 tff(269,plain,
% 61.23/61.46 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.46 inference(modus_ponens,[status(thm)],[268, 267])).
% 61.23/61.46 tff(270,plain,
% 61.23/61.46 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[269, 70])).
% 61.23/61.46 tff(271,plain,
% 61.23/61.46 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a))),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[270, 266])).
% 61.23/61.46 tff(272,plain,
% 61.23/61.46 (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)),
% 61.23/61.46 inference(unit_resolution,[status(thm)],[271, 154])).
% 61.23/61.46 tff(273,plain,
% 61.23/61.46 (non_ordered_pair(b, b) = non_ordered_pair(a, c)),
% 61.23/61.46 inference(transitivity,[status(thm)],[117, 272])).
% 61.23/61.46 tff(274,plain,
% 61.23/61.46 (member(a, non_ordered_pair(b, b)) <=> member(a, non_ordered_pair(a, c))),
% 61.23/61.46 inference(monotonicity,[status(thm)],[273])).
% 61.23/61.46 tff(275,plain,
% 61.23/61.46 (member(a, non_ordered_pair(a, c)) <=> member(a, non_ordered_pair(b, b))),
% 61.23/61.47 inference(symmetry,[status(thm)],[274])).
% 61.23/61.47 tff(276,plain,
% 61.23/61.47 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, c)))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, c)))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(277,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(a)) | member(a, non_ordered_pair(a, c)))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(278,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(a)) | member(a, non_ordered_pair(a, c))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[277, 276])).
% 61.23/61.47 tff(279,plain,
% 61.23/61.47 (member(a, non_ordered_pair(a, c))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[278, 17, 123])).
% 61.23/61.47 tff(280,plain,
% 61.23/61.47 (member(a, non_ordered_pair(b, b))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[279, 275])).
% 61.23/61.47 tff(281,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = b) | (~member(a, non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (a = b) | (~member(a, non_ordered_pair(b, b))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(282,plain,
% 61.23/61.47 (((a = b) | (a = b) | (~member(a, non_ordered_pair(b, b)))) <=> ((a = b) | (~member(a, non_ordered_pair(b, b))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(283,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = b) | (a = b) | (~member(a, non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = b) | (~member(a, non_ordered_pair(b, b)))))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[282])).
% 61.23/61.47 tff(284,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = b) | (a = b) | (~member(a, non_ordered_pair(b, b))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (a = b) | (~member(a, non_ordered_pair(b, b))))),
% 61.23/61.47 inference(transitivity,[status(thm)],[283, 281])).
% 61.23/61.47 tff(285,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((a = b) | (a = b) | (~member(a, non_ordered_pair(b, b))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(286,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (a = b) | (~member(a, non_ordered_pair(b, b)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[285, 284])).
% 61.23/61.47 tff(287,plain,
% 61.23/61.47 (~member(a, non_ordered_pair(b, b))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[286, 70, 151])).
% 61.23/61.47 tff(288,plain,
% 61.23/61.47 ($false),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[287, 280])).
% 61.23/61.47 tff(289,plain,(~(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))), inference(lemma,lemma(discharge,[]))).
% 61.23/61.47 tff(290,plain,
% 61.23/61.47 (non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)) = ordered_pair(b, d)),
% 61.23/61.47 inference(symmetry,[status(thm)],[202])).
% 61.23/61.47 tff(291,plain,
% 61.23/61.47 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(b) = non_ordered_pair(b, b))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(292,plain,
% 61.23/61.47 (singleton_set(b) = non_ordered_pair(b, b)),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[291, 174])).
% 61.23/61.47 tff(293,plain,
% 61.23/61.47 (non_ordered_pair(b, b) = singleton_set(b)),
% 61.23/61.47 inference(symmetry,[status(thm)],[292])).
% 61.23/61.47 tff(294,plain,
% 61.23/61.47 (non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)) = non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[293])).
% 61.23/61.47 tff(295,plain,
% 61.23/61.47 (non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)) = ordered_pair(b, d)),
% 61.23/61.47 inference(transitivity,[status(thm)],[294, 290])).
% 61.23/61.47 tff(296,plain,
% 61.23/61.47 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))) <=> member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[295])).
% 61.23/61.47 tff(297,plain,
% 61.23/61.47 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), ordered_pair(b, d)) <=> member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(symmetry,[status(thm)],[296])).
% 61.23/61.47 tff(298,plain,
% 61.23/61.47 (member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[265, 297])).
% 61.23/61.47 tff(299,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(300,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(301,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[300, 299])).
% 61.23/61.47 tff(302,plain,
% 61.23/61.47 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[301, 70])).
% 61.23/61.47 tff(303,plain,
% 61.23/61.47 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[302, 298])).
% 61.23/61.47 tff(304,plain,
% 61.23/61.47 (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[303, 289])).
% 61.23/61.47 tff(305,plain,
% 61.23/61.47 (f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)),
% 61.23/61.47 inference(transitivity,[status(thm)],[304, 111, 80])).
% 61.23/61.47 tff(306,plain,
% 61.23/61.47 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) <=> (non_ordered_pair(a, a) = non_ordered_pair(b, b))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[305])).
% 61.23/61.47 tff(307,plain,
% 61.23/61.47 ((f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) <=> (non_ordered_pair(b, b) = non_ordered_pair(a, a))),
% 61.23/61.47 inference(transitivity,[status(thm)],[306, 114])).
% 61.23/61.47 tff(308,plain,
% 61.23/61.47 ((~(f23(f16(non_ordered_pair(b, d), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))) <=> (~(non_ordered_pair(b, b) = non_ordered_pair(a, a)))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[307])).
% 61.23/61.47 tff(309,plain,
% 61.23/61.47 (~(non_ordered_pair(b, b) = non_ordered_pair(a, a))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[289, 308])).
% 61.23/61.47 tff(310,plain,
% 61.23/61.47 (non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)) = non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))),
% 61.23/61.47 inference(transitivity,[status(thm)],[178, 167, 157, 202])).
% 61.23/61.47 tff(311,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))) <=> member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[293, 310])).
% 61.23/61.47 tff(312,plain,
% 61.23/61.47 (member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))) <=> member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.23/61.47 inference(symmetry,[status(thm)],[311])).
% 61.23/61.47 tff(313,plain,
% 61.23/61.47 (little_set(non_ordered_pair(b, b)) <=> little_set(singleton_set(b))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[293])).
% 61.23/61.47 tff(314,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(b, b))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(315,plain,
% 61.23/61.47 (little_set(non_ordered_pair(b, b))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[314, 192])).
% 61.23/61.47 tff(316,plain,
% 61.23/61.47 (little_set(singleton_set(b))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[315, 313])).
% 61.23/61.47 tff(317,plain,
% 61.23/61.47 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(b))) | member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(b))) | member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(318,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(b))) | member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(319,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(b))) | member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[318, 317])).
% 61.23/61.47 tff(320,plain,
% 61.23/61.47 ((~little_set(singleton_set(b))) | member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[319, 17])).
% 61.23/61.47 tff(321,plain,
% 61.23/61.47 (member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[320, 316])).
% 61.23/61.47 tff(322,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[321, 312])).
% 61.23/61.47 tff(323,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(324,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(325,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[324, 323])).
% 61.23/61.47 tff(326,plain,
% 61.23/61.47 ((non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a)) | (~member(non_ordered_pair(b, b), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[325, 70])).
% 61.23/61.47 tff(327,plain,
% 61.23/61.47 ((non_ordered_pair(b, b) = non_ordered_pair(a, c)) | (non_ordered_pair(b, b) = non_ordered_pair(a, a))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[326, 322])).
% 61.23/61.47 tff(328,plain,
% 61.23/61.47 (non_ordered_pair(b, b) = non_ordered_pair(a, c)),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[327, 309])).
% 61.23/61.47 tff(329,plain,
% 61.23/61.47 (f23(non_ordered_pair(b, b), non_ordered_pair(b, d)) = f23(non_ordered_pair(a, c), non_ordered_pair(a, a))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[328, 112])).
% 61.23/61.47 tff(330,plain,
% 61.23/61.47 (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = f23(non_ordered_pair(b, b), non_ordered_pair(b, d))),
% 61.23/61.47 inference(symmetry,[status(thm)],[329])).
% 61.23/61.47 tff(331,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, c))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, c), 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, c))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(332,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(a, non_ordered_pair(a, c))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(333,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(a, non_ordered_pair(a, c))) | (~member(a, non_ordered_pair(a, a))) | (~disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[332, 331])).
% 61.23/61.47 tff(334,plain,
% 61.23/61.47 (~disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[333, 45, 279, 127])).
% 61.23/61.47 tff(335,plain,
% 61.23/61.47 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, c), 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, c), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(336,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(337,plain,
% 61.23/61.47 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(a, c), non_ordered_pair(a, a)) | member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[336, 335])).
% 61.23/61.47 tff(338,plain,
% 61.23/61.47 (member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[337, 56, 334])).
% 61.23/61.47 tff(339,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), 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, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(340,plain,
% 61.23/61.47 (((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a)))) <=> ((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(341,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), 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, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a)))))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[340])).
% 61.23/61.47 tff(342,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), 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, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(transitivity,[status(thm)],[341, 339])).
% 61.23/61.47 tff(343,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a))))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(344,plain,
% 61.23/61.47 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a) | (~member(f23(non_ordered_pair(a, c), non_ordered_pair(a, a)), non_ordered_pair(a, a)))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[343, 342])).
% 61.23/61.47 tff(345,plain,
% 61.23/61.47 (f23(non_ordered_pair(a, c), non_ordered_pair(a, a)) = a),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[344, 70, 338])).
% 61.23/61.47 tff(346,plain,
% 61.23/61.47 (a = f23(non_ordered_pair(a, c), non_ordered_pair(a, a))),
% 61.23/61.47 inference(symmetry,[status(thm)],[345])).
% 61.23/61.47 tff(347,plain,
% 61.23/61.47 (a = b),
% 61.23/61.47 inference(transitivity,[status(thm)],[346, 330, 109])).
% 61.23/61.47 tff(348,plain,
% 61.23/61.47 ($false),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[151, 347])).
% 61.23/61.47 tff(349,plain,((~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d))) | (~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)))), inference(lemma,lemma(discharge,[]))).
% 61.23/61.47 tff(350,plain,
% 61.23/61.47 (~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[349, 80])).
% 61.23/61.47 tff(351,plain,
% 61.23/61.47 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))) <=> member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[295])).
% 61.23/61.47 tff(352,plain,
% 61.23/61.47 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d)) <=> member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(symmetry,[status(thm)],[351])).
% 61.23/61.47 tff(353,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), ordered_pair(b, d)) <=> member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d)))),
% 61.23/61.47 inference(monotonicity,[status(thm)],[293, 202])).
% 61.23/61.47 tff(354,plain,
% 61.23/61.47 (member(singleton_set(b), non_ordered_pair(singleton_set(b), non_ordered_pair(b, d))) <=> member(non_ordered_pair(b, b), ordered_pair(b, d))),
% 61.23/61.47 inference(symmetry,[status(thm)],[353])).
% 61.23/61.47 tff(355,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), ordered_pair(b, d))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[321, 354])).
% 61.23/61.47 tff(356,plain,
% 61.23/61.47 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, b), sigma(universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, b), sigma(universal_set)))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(357,plain,
% 61.23/61.47 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, b), sigma(universal_set)))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(358,plain,
% 61.23/61.47 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(ordered_pair(b, d), universal_set)) | member(non_ordered_pair(b, b), sigma(universal_set))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[357, 356])).
% 61.23/61.47 tff(359,plain,
% 61.23/61.47 ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | member(non_ordered_pair(b, b), sigma(universal_set))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[358, 239, 200])).
% 61.23/61.47 tff(360,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), sigma(universal_set))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[359, 355])).
% 61.23/61.47 tff(361,plain,
% 61.23/61.47 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(b, b), sigma(universal_set))) | member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set)))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(b, b), sigma(universal_set))) | member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set)))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(362,plain,
% 61.23/61.47 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(b, b), sigma(universal_set))) | member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set)))),
% 61.23/61.47 inference(quant_inst,[status(thm)],[])).
% 61.23/61.47 tff(363,plain,
% 61.23/61.47 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(b, b), sigma(universal_set))) | member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))),
% 61.23/61.47 inference(modus_ponens,[status(thm)],[362, 361])).
% 61.23/61.47 tff(364,plain,
% 61.23/61.47 (member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))),
% 61.23/61.47 inference(unit_resolution,[status(thm)],[363, 250, 360])).
% 61.23/61.47 tff(365,plain,
% 61.23/61.47 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))),
% 61.23/61.47 inference(rewrite,[status(thm)],[])).
% 61.23/61.47 tff(366,plain,
% 61.23/61.47 (((~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)))) <=> ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))),
% 61.23/61.48 inference(rewrite,[status(thm)],[])).
% 61.23/61.48 tff(367,plain,
% 61.23/61.48 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)))))),
% 61.23/61.48 inference(monotonicity,[status(thm)],[366])).
% 61.23/61.48 tff(368,plain,
% 61.23/61.48 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))),
% 61.23/61.48 inference(transitivity,[status(thm)],[367, 365])).
% 61.23/61.48 tff(369,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))))),
% 61.23/61.48 inference(quant_inst,[status(thm)],[])).
% 61.23/61.48 tff(370,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(b, b), ordered_pair(b, d))) | (~member(non_ordered_pair(b, b), f16(non_ordered_pair(b, b), universal_set))) | (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[369, 368])).
% 61.23/61.48 tff(371,plain,
% 61.23/61.48 (~disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[370, 45, 355, 364])).
% 61.23/61.48 tff(372,plain,
% 61.23/61.48 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))),
% 61.23/61.48 inference(rewrite,[status(thm)],[])).
% 61.23/61.48 tff(373,plain,
% 61.23/61.48 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d)))),
% 61.23/61.48 inference(quant_inst,[status(thm)],[])).
% 61.23/61.48 tff(374,plain,
% 61.23/61.48 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) | member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[373, 372])).
% 61.23/61.48 tff(375,plain,
% 61.23/61.48 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[374, 56, 371])).
% 61.23/61.48 tff(376,plain,
% 61.23/61.48 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[375, 352])).
% 61.23/61.48 tff(377,plain,
% 61.23/61.48 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))),
% 61.23/61.48 inference(rewrite,[status(thm)],[])).
% 61.23/61.48 tff(378,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d)))))),
% 61.23/61.48 inference(quant_inst,[status(thm)],[])).
% 61.23/61.48 tff(379,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[378, 377])).
% 61.23/61.48 tff(380,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(b, b), non_ordered_pair(b, d))))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[379, 70])).
% 61.23/61.48 tff(381,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, d)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[380, 376])).
% 61.23/61.48 tff(382,plain,
% 61.23/61.48 (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[381, 350])).
% 61.23/61.48 tff(383,plain,
% 61.23/61.48 (non_ordered_pair(b, b) = f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))),
% 61.23/61.48 inference(symmetry,[status(thm)],[382])).
% 61.23/61.48 tff(384,plain,
% 61.23/61.48 (non_ordered_pair(b, b) = non_ordered_pair(a, a)),
% 61.23/61.48 inference(transitivity,[status(thm)],[383, 80])).
% 61.23/61.48 tff(385,plain,
% 61.23/61.48 (f23(universal_set, non_ordered_pair(b, b)) = f23(universal_set, non_ordered_pair(a, a))),
% 61.23/61.48 inference(monotonicity,[status(thm)],[384])).
% 61.23/61.48 tff(386,plain,
% 61.23/61.48 (f23(universal_set, non_ordered_pair(a, a)) = f23(universal_set, non_ordered_pair(b, b))),
% 61.23/61.48 inference(symmetry,[status(thm)],[385])).
% 61.23/61.48 tff(387,plain,
% 61.23/61.48 (a = b),
% 61.23/61.48 inference(transitivity,[status(thm)],[147, 386, 77])).
% 61.23/61.48 tff(388,plain,
% 61.23/61.48 ($false),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[151, 387])).
% 61.23/61.48 tff(389,plain,(~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a))), inference(lemma,lemma(discharge,[]))).
% 61.23/61.48 tff(390,plain,
% 61.23/61.48 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))) <=> member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d))),
% 61.23/61.48 inference(monotonicity,[status(thm)],[179])).
% 61.23/61.48 tff(391,plain,
% 61.23/61.48 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), ordered_pair(b, d)) <=> member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.23/61.48 inference(symmetry,[status(thm)],[390])).
% 61.23/61.48 tff(392,plain,
% 61.23/61.48 (member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[375, 391])).
% 61.23/61.48 tff(393,plain,
% 61.23/61.48 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.48 inference(rewrite,[status(thm)],[])).
% 61.23/61.48 tff(394,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c)))))),
% 61.23/61.48 inference(quant_inst,[status(thm)],[])).
% 61.23/61.48 tff(395,plain,
% 61.23/61.48 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.48 inference(modus_ponens,[status(thm)],[394, 393])).
% 61.23/61.48 tff(396,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a)) | (~member(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)), non_ordered_pair(non_ordered_pair(a, a), non_ordered_pair(a, c))))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[395, 70])).
% 61.23/61.48 tff(397,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)) | (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, a))),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[396, 392])).
% 61.23/61.48 tff(398,plain,
% 61.23/61.48 (f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(a, c)),
% 61.23/61.48 inference(unit_resolution,[status(thm)],[397, 389])).
% 61.23/61.48 tff(399,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) <=> (non_ordered_pair(a, c) = non_ordered_pair(b, b))),
% 61.23/61.48 inference(monotonicity,[status(thm)],[398])).
% 61.23/61.48 tff(400,plain,
% 61.23/61.48 ((f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)) <=> (non_ordered_pair(b, b) = non_ordered_pair(a, c))),
% 61.23/61.48 inference(transitivity,[status(thm)],[399, 79])).
% 61.23/61.48 tff(401,plain,
% 61.23/61.48 ((~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))) <=> (~(non_ordered_pair(b, b) = non_ordered_pair(a, c)))),
% 61.23/61.48 inference(monotonicity,[status(thm)],[400])).
% 61.23/61.51 tff(402,assumption,(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b)), introduced(assumption)).
% 61.23/61.51 tff(403,plain,
% 61.23/61.51 (non_ordered_pair(b, b) = f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d))),
% 61.23/61.51 inference(symmetry,[status(thm)],[402])).
% 61.23/61.51 tff(404,plain,
% 61.23/61.51 (non_ordered_pair(b, b) = non_ordered_pair(a, c)),
% 61.23/61.51 inference(transitivity,[status(thm)],[403, 398])).
% 61.23/61.51 tff(405,plain,
% 61.23/61.51 (member(a, non_ordered_pair(b, b)) <=> member(a, non_ordered_pair(a, c))),
% 61.23/61.51 inference(monotonicity,[status(thm)],[404])).
% 61.23/61.51 tff(406,plain,
% 61.23/61.51 (member(a, non_ordered_pair(a, c)) <=> member(a, non_ordered_pair(b, b))),
% 61.23/61.51 inference(symmetry,[status(thm)],[405])).
% 61.23/61.51 tff(407,plain,
% 61.23/61.51 (member(a, non_ordered_pair(b, b))),
% 61.23/61.51 inference(modus_ponens,[status(thm)],[279, 406])).
% 61.23/61.51 tff(408,plain,
% 61.23/61.51 ($false),
% 61.23/61.51 inference(unit_resolution,[status(thm)],[287, 407])).
% 61.23/61.51 tff(409,plain,(~(f23(f16(non_ordered_pair(b, b), universal_set), ordered_pair(b, d)) = non_ordered_pair(b, b))), inference(lemma,lemma(discharge,[]))).
% 61.23/61.51 tff(410,plain,
% 61.23/61.51 (~(non_ordered_pair(b, b) = non_ordered_pair(a, c))),
% 61.23/61.51 inference(modus_ponens,[status(thm)],[409, 401])).
% 61.23/61.51 tff(411,plain,
% 61.23/61.51 (non_ordered_pair(b, b) = non_ordered_pair(a, a)),
% 61.23/61.51 inference(unit_resolution,[status(thm)],[327, 410])).
% 61.23/61.51 tff(412,plain,
% 61.23/61.51 (f23(universal_set, non_ordered_pair(b, b)) = f23(universal_set, non_ordered_pair(a, a))),
% 61.23/61.51 inference(monotonicity,[status(thm)],[411])).
% 61.23/61.51 tff(413,plain,
% 61.23/61.51 (f23(universal_set, non_ordered_pair(a, a)) = f23(universal_set, non_ordered_pair(b, b))),
% 61.23/61.51 inference(symmetry,[status(thm)],[412])).
% 61.23/61.51 tff(414,plain,
% 61.23/61.51 (a = b),
% 61.23/61.51 inference(transitivity,[status(thm)],[147, 413, 77])).
% 61.23/61.51 tff(415,plain,
% 61.23/61.51 ($false),
% 61.23/61.51 inference(unit_resolution,[status(thm)],[151, 414])).
% 61.23/61.51 % SZS output end Proof
% 61.29/61.54 % E exiting
%------------------------------------------------------------------------------