%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET034-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:56 AM UTC 2025
% Result : Unsatisfiable 88.38s 88.59s
% Output : Proof 89.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET034-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 04:07:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 88.38/88.59 % SZS status Unsatisfiable
% 88.38/88.59 % SZS output start Proof
% 88.38/88.59 tff(non_ordered_pair_type, type, (
% 88.38/88.59 non_ordered_pair: ( $i * $i ) > $i)).
% 88.38/88.59 tff(f20_type, type, (
% 88.38/88.59 f20: $i > $i)).
% 88.38/88.59 tff(compose_type, type, (
% 88.38/88.59 compose: ( $i * $i ) > $i)).
% 88.38/88.59 tff(a_type, type, (
% 88.38/88.59 a: $i)).
% 88.38/88.59 tff(b_type, type, (
% 88.38/88.59 b: $i)).
% 88.38/88.59 tff(f19_type, type, (
% 88.38/88.59 f19: $i > $i)).
% 88.38/88.59 tff(f16_type, type, (
% 88.38/88.59 f16: ( $i * $i ) > $i)).
% 88.38/88.59 tff(ordered_pair_type, type, (
% 88.38/88.59 ordered_pair: ( $i * $i ) > $i)).
% 88.38/88.59 tff(f30_type, type, (
% 88.38/88.59 f30: ( $i * $i * $i ) > $i)).
% 88.38/88.59 tff(f29_type, type, (
% 88.38/88.59 f29: ( $i * $i * $i ) > $i)).
% 88.38/88.59 tff(member_type, type, (
% 88.38/88.59 member: ( $i * $i ) > $o)).
% 88.38/88.59 tff(f31_type, type, (
% 88.38/88.59 f31: ( $i * $i * $i ) > $i)).
% 88.38/88.59 tff(f21_type, type, (
% 88.38/88.59 f21: $i > $i)).
% 88.38/88.59 tff(f23_type, type, (
% 88.38/88.59 f23: ( $i * $i ) > $i)).
% 88.38/88.59 tff(universal_set_type, type, (
% 88.38/88.59 universal_set: $i)).
% 88.38/88.59 tff(disjoint_type, type, (
% 88.38/88.59 disjoint: ( $i * $i ) > $o)).
% 88.38/88.59 tff(little_set_type, type, (
% 88.38/88.59 little_set: $i > $o)).
% 88.38/88.59 tff(single_valued_set_type, type, (
% 88.38/88.59 single_valued_set: $i > $o)).
% 88.38/88.59 tff(relation_type, type, (
% 88.38/88.59 relation: $i > $o)).
% 88.38/88.59 tff(ordered_pair_predicate_type, type, (
% 88.38/88.59 ordered_pair_predicate: $i > $o)).
% 88.38/88.59 tff(f18_type, type, (
% 88.38/88.59 f18: $i > $i)).
% 88.38/88.59 tff(function_type, type, (
% 88.38/88.59 function: $i > $o)).
% 88.38/88.59 tff(singleton_set_type, type, (
% 88.38/88.59 singleton_set: $i > $i)).
% 88.38/88.59 tff(sigma_type, type, (
% 88.38/88.59 sigma: $i > $i)).
% 88.38/88.59 tff(1,plain,
% 88.38/88.59 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.59 inference(commutativity,[status(thm)],[])).
% 88.38/88.59 tff(2,assumption,(~relation(compose(b, a))), introduced(assumption)).
% 88.38/88.59 tff(3,plain,
% 88.38/88.59 (^[Z: $i] : refl((relation(Z) | member(f18(Z), Z)) <=> (relation(Z) | member(f18(Z), Z)))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(4,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | member(f18(Z), Z)) <=> ![Z: $i] : (relation(Z) | member(f18(Z), Z))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[3])).
% 88.38/88.59 tff(5,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | member(f18(Z), Z)) <=> ![Z: $i] : (relation(Z) | member(f18(Z), Z))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(6,axiom,(![Z: $i] : (relation(Z) | member(f18(Z), Z))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','relation2')).
% 88.38/88.59 tff(7,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | member(f18(Z), Z))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[6, 5])).
% 88.38/88.59 tff(8,plain,(
% 88.38/88.59 ![Z: $i] : (relation(Z) | member(f18(Z), Z))),
% 88.38/88.59 inference(skolemize,[status(sab)],[7])).
% 88.38/88.59 tff(9,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | member(f18(Z), Z))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[8, 4])).
% 88.38/88.59 tff(10,plain,
% 88.38/88.59 (((~![Z: $i] : (relation(Z) | member(f18(Z), Z))) | (relation(compose(b, a)) | member(f18(compose(b, a)), compose(b, a)))) <=> ((~![Z: $i] : (relation(Z) | member(f18(Z), Z))) | relation(compose(b, a)) | member(f18(compose(b, a)), compose(b, a)))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(11,plain,
% 88.38/88.59 ((~![Z: $i] : (relation(Z) | member(f18(Z), Z))) | (relation(compose(b, a)) | member(f18(compose(b, a)), compose(b, a)))),
% 88.38/88.59 inference(quant_inst,[status(thm)],[])).
% 88.38/88.59 tff(12,plain,
% 88.38/88.59 ((~![Z: $i] : (relation(Z) | member(f18(Z), Z))) | relation(compose(b, a)) | member(f18(compose(b, a)), compose(b, a))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[11, 10])).
% 88.38/88.59 tff(13,plain,
% 88.38/88.59 (member(f18(compose(b, a)), compose(b, a))),
% 88.38/88.59 inference(unit_resolution,[status(thm)],[12, 9, 2])).
% 88.38/88.59 tff(14,plain,
% 88.38/88.59 (^[Xg: $i, Z: $i, Xf: $i] : refl(((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg)))) <=> ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg)))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(15,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg)))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[14])).
% 88.38/88.59 tff(16,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg)))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(17,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose4')).
% 88.38/88.59 tff(18,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[17, 16])).
% 88.38/88.59 tff(19,plain,(
% 88.38/88.59 ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(skolemize,[status(sab)],[18])).
% 88.38/88.59 tff(20,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[19, 15])).
% 88.38/88.59 tff(21,plain,
% 88.38/88.59 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(f18(compose(b, a)), compose(b, a))) | (f18(compose(b, a)) = ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(f18(compose(b, a)), compose(b, a))) | (f18(compose(b, a)) = ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(22,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(f18(compose(b, a)), compose(b, a))) | (f18(compose(b, a)) = ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.59 inference(quant_inst,[status(thm)],[])).
% 88.38/88.59 tff(23,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(f18(compose(b, a)), compose(b, a))) | (f18(compose(b, a)) = ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[22, 21])).
% 88.38/88.59 tff(24,plain,
% 88.38/88.59 (f18(compose(b, a)) = ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))),
% 88.38/88.59 inference(unit_resolution,[status(thm)],[23, 20, 13])).
% 88.38/88.59 tff(25,plain,
% 88.38/88.59 (ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)) = f18(compose(b, a))),
% 88.38/88.59 inference(symmetry,[status(thm)],[24])).
% 88.38/88.59 tff(26,plain,
% 88.38/88.59 (ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))) <=> ordered_pair_predicate(f18(compose(b, a)))),
% 88.38/88.59 inference(monotonicity,[status(thm)],[25])).
% 88.38/88.59 tff(27,plain,
% 88.38/88.59 (ordered_pair_predicate(f18(compose(b, a))) <=> ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))),
% 88.38/88.59 inference(symmetry,[status(thm)],[26])).
% 88.38/88.59 tff(28,plain,
% 88.38/88.59 ((~ordered_pair_predicate(f18(compose(b, a)))) <=> (~ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.59 inference(monotonicity,[status(thm)],[27])).
% 88.38/88.59 tff(29,plain,
% 88.38/88.59 (^[Z: $i] : refl((relation(Z) | (~ordered_pair_predicate(f18(Z)))) <=> (relation(Z) | (~ordered_pair_predicate(f18(Z)))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(30,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z)))) <=> ![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[29])).
% 88.38/88.59 tff(31,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z)))) <=> ![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(32,axiom,(![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','relation3')).
% 88.38/88.59 tff(33,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 88.38/88.59 tff(34,plain,(
% 88.38/88.59 ![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))),
% 88.38/88.59 inference(skolemize,[status(sab)],[33])).
% 88.38/88.59 tff(35,plain,
% 88.38/88.59 (![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[34, 30])).
% 88.38/88.59 tff(36,plain,
% 88.38/88.59 (((~![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))) | (relation(compose(b, a)) | (~ordered_pair_predicate(f18(compose(b, a)))))) <=> ((~![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))) | relation(compose(b, a)) | (~ordered_pair_predicate(f18(compose(b, a)))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(37,plain,
% 88.38/88.59 ((~![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))) | (relation(compose(b, a)) | (~ordered_pair_predicate(f18(compose(b, a)))))),
% 88.38/88.59 inference(quant_inst,[status(thm)],[])).
% 88.38/88.59 tff(38,plain,
% 88.38/88.59 ((~![Z: $i] : (relation(Z) | (~ordered_pair_predicate(f18(Z))))) | relation(compose(b, a)) | (~ordered_pair_predicate(f18(compose(b, a))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[37, 36])).
% 88.38/88.59 tff(39,plain,
% 88.38/88.59 (~ordered_pair_predicate(f18(compose(b, a)))),
% 88.38/88.59 inference(unit_resolution,[status(thm)],[38, 35, 2])).
% 88.38/88.59 tff(40,plain,
% 88.38/88.59 (~ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[39, 28])).
% 88.38/88.59 tff(41,plain,
% 88.38/88.59 (^[Xg: $i, Z: $i, Xf: $i] : refl(((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg))) <=> ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(42,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[41])).
% 88.38/88.59 tff(43,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(44,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose2')).
% 88.38/88.59 tff(45,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[44, 43])).
% 88.38/88.59 tff(46,plain,(
% 88.38/88.59 ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))),
% 88.38/88.59 inference(skolemize,[status(sab)],[45])).
% 88.38/88.59 tff(47,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[46, 42])).
% 88.38/88.59 tff(48,plain,
% 88.38/88.59 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(f18(compose(b, a)), compose(b, a))) | little_set(f30(f18(compose(b, a)), b, a)))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(f18(compose(b, a)), compose(b, a))) | little_set(f30(f18(compose(b, a)), b, a)))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(49,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(f18(compose(b, a)), compose(b, a))) | little_set(f30(f18(compose(b, a)), b, a)))),
% 88.38/88.59 inference(quant_inst,[status(thm)],[])).
% 88.38/88.59 tff(50,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(f18(compose(b, a)), compose(b, a))) | little_set(f30(f18(compose(b, a)), b, a))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[49, 48])).
% 88.38/88.59 tff(51,plain,
% 88.38/88.59 (little_set(f30(f18(compose(b, a)), b, a))),
% 88.38/88.59 inference(unit_resolution,[status(thm)],[50, 47, 13])).
% 88.38/88.59 tff(52,plain,
% 88.38/88.59 (^[Xg: $i, Z: $i, Xf: $i] : refl((little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg)))) <=> (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg)))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(53,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg)))) <=> ![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[52])).
% 88.38/88.59 tff(54,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg)))) <=> ![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(55,plain,
% 88.38/88.59 (^[Xg: $i, Z: $i, Xf: $i] : rewrite(((~member(Z, compose(Xf, Xg))) | little_set(f29(Z, Xf, Xg))) <=> (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg)))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(56,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f29(Z, Xf, Xg))) <=> ![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[55])).
% 88.38/88.59 tff(57,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f29(Z, Xf, Xg)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose1')).
% 88.38/88.59 tff(58,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[57, 56])).
% 88.38/88.59 tff(59,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[58, 54])).
% 88.38/88.59 tff(60,plain,(
% 88.38/88.59 ![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(skolemize,[status(sab)],[59])).
% 88.38/88.59 tff(61,plain,
% 88.38/88.59 (![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[60, 53])).
% 88.38/88.59 tff(62,plain,
% 88.38/88.59 (((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(f18(compose(b, a)), b, a)) | (~member(f18(compose(b, a)), compose(b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(f18(compose(b, a)), b, a)) | (~member(f18(compose(b, a)), compose(b, a))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(63,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(f18(compose(b, a)), b, a)) | (~member(f18(compose(b, a)), compose(b, a))))),
% 88.38/88.59 inference(quant_inst,[status(thm)],[])).
% 88.38/88.59 tff(64,plain,
% 88.38/88.59 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(f18(compose(b, a)), b, a)) | (~member(f18(compose(b, a)), compose(b, a)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[63, 62])).
% 88.38/88.59 tff(65,plain,
% 88.38/88.59 (little_set(f29(f18(compose(b, a)), b, a))),
% 88.38/88.59 inference(unit_resolution,[status(thm)],[64, 61, 13])).
% 88.38/88.59 tff(66,plain,
% 88.38/88.59 (^[Z: $i, Y: $i] : refl(((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(67,plain,
% 88.38/88.59 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[66])).
% 88.38/88.59 tff(68,plain,
% 88.38/88.59 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(69,plain,
% 88.38/88.59 (![Z: $i, Y: $i, X: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(elim_unused_vars,[status(thm)],[])).
% 88.38/88.59 tff(70,plain,
% 88.38/88.59 (![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(destructive_equality_resolution,[status(thm)],[])).
% 88.38/88.59 tff(71,plain,
% 88.38/88.59 (![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(transitivity,[status(thm)],[70, 69])).
% 88.38/88.59 tff(72,plain,
% 88.38/88.59 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z)))), ((((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> (((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))))), rewrite((((~little_set(Y)) | ordered_pair_predicate(X) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))), ((((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))))),
% 88.38/88.59 inference(bind,[status(th)],[])).
% 88.38/88.59 tff(73,plain,
% 88.38/88.59 (![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((~little_set(Y)) | ordered_pair_predicate(X) | (~(X = ordered_pair(Y, Z))) | (~little_set(Z)))),
% 88.38/88.59 inference(quant_intro,[status(thm)],[72])).
% 88.38/88.59 tff(74,plain,
% 88.38/88.59 (![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(transitivity,[status(thm)],[73, 71])).
% 88.38/88.59 tff(75,axiom,(![Z: $i, Y: $i, X: $i] : (((ordered_pair_predicate(X) | (~little_set(Y))) | (~little_set(Z))) | (~(X = ordered_pair(Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','ordered_pair_predicate4')).
% 88.38/88.59 tff(76,plain,
% 88.38/88.59 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[75, 74])).
% 88.38/88.59 tff(77,plain,
% 88.38/88.59 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[76, 68])).
% 88.38/88.59 tff(78,plain,(
% 88.38/88.59 ![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(skolemize,[status(sab)],[77])).
% 88.38/88.59 tff(79,plain,
% 88.38/88.59 (![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))),
% 88.38/88.59 inference(modus_ponens,[status(thm)],[78, 67])).
% 88.38/88.59 tff(80,plain,
% 88.38/88.59 (((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))) <=> ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | (~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(81,plain,
% 88.38/88.59 (((~little_set(f30(f18(compose(b, a)), b, a))) | (~little_set(f29(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))) <=> ((~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.59 inference(rewrite,[status(thm)],[])).
% 88.38/88.59 tff(82,plain,
% 88.38/88.59 (((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(f30(f18(compose(b, a)), b, a))) | (~little_set(f29(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))) <=> ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))))),
% 88.38/88.60 inference(monotonicity,[status(thm)],[81])).
% 88.38/88.60 tff(83,plain,
% 88.38/88.60 (((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(f30(f18(compose(b, a)), b, a))) | (~little_set(f29(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))) <=> ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | (~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.60 inference(transitivity,[status(thm)],[82, 80])).
% 88.38/88.60 tff(84,plain,
% 88.38/88.60 ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | ((~little_set(f30(f18(compose(b, a)), b, a))) | (~little_set(f29(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(85,plain,
% 88.38/88.60 ((~![Z: $i, Y: $i] : ((~little_set(Z)) | (~little_set(Y)) | ordered_pair_predicate(ordered_pair(Y, Z)))) | (~little_set(f29(f18(compose(b, a)), b, a))) | (~little_set(f30(f18(compose(b, a)), b, a))) | ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[84, 83])).
% 88.38/88.60 tff(86,plain,
% 88.38/88.60 (ordered_pair_predicate(ordered_pair(f29(f18(compose(b, a)), b, a), f30(f18(compose(b, a)), b, a)))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[85, 79, 65, 51])).
% 88.38/88.60 tff(87,plain,
% 88.38/88.60 ($false),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[86, 40])).
% 88.38/88.60 tff(88,plain,(relation(compose(b, a))), inference(lemma,lemma(discharge,[]))).
% 88.38/88.60 tff(89,plain,
% 88.38/88.60 ((~function(compose(b, a))) <=> (~function(compose(b, a)))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(90,axiom,(~function(compose(b, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_their_composition_is_a_function')).
% 88.38/88.60 tff(91,plain,
% 88.38/88.60 (~function(compose(b, a))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[90, 89])).
% 88.38/88.60 tff(92,plain,
% 88.38/88.60 (^[Xf: $i] : refl((function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf))) <=> (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(93,plain,
% 88.38/88.60 (![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf))) <=> ![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[92])).
% 88.38/88.60 tff(94,plain,
% 88.38/88.60 (![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf))) <=> ![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(95,plain,
% 88.38/88.60 (^[Xf: $i] : rewrite(((function(Xf) | (~relation(Xf))) | (~single_valued_set(Xf))) <=> (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(96,plain,
% 88.38/88.60 (![Xf: $i] : ((function(Xf) | (~relation(Xf))) | (~single_valued_set(Xf))) <=> ![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[95])).
% 88.38/88.60 tff(97,axiom,(![Xf: $i] : ((function(Xf) | (~relation(Xf))) | (~single_valued_set(Xf)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','function3')).
% 88.38/88.60 tff(98,plain,
% 88.38/88.60 (![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[97, 96])).
% 88.38/88.60 tff(99,plain,
% 88.38/88.60 (![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[98, 94])).
% 88.38/88.60 tff(100,plain,(
% 88.38/88.60 ![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(skolemize,[status(sab)],[99])).
% 88.38/88.60 tff(101,plain,
% 88.38/88.60 (![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[100, 93])).
% 88.38/88.60 tff(102,plain,
% 88.38/88.60 (((~![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))) | (function(compose(b, a)) | (~single_valued_set(compose(b, a))) | (~relation(compose(b, a))))) <=> ((~![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))) | function(compose(b, a)) | (~single_valued_set(compose(b, a))) | (~relation(compose(b, a))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(103,plain,
% 88.38/88.60 ((~![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))) | (function(compose(b, a)) | (~single_valued_set(compose(b, a))) | (~relation(compose(b, a))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(104,plain,
% 88.38/88.60 ((~![Xf: $i] : (function(Xf) | (~single_valued_set(Xf)) | (~relation(Xf)))) | function(compose(b, a)) | (~single_valued_set(compose(b, a))) | (~relation(compose(b, a)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[103, 102])).
% 88.38/88.60 tff(105,plain,
% 88.38/88.60 ((~single_valued_set(compose(b, a))) | (~relation(compose(b, a)))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 88.38/88.60 tff(106,plain,
% 88.38/88.60 (~single_valued_set(compose(b, a))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[105, 88])).
% 88.38/88.60 tff(107,plain,
% 88.38/88.60 (^[X: $i] : refl((single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X)) <=> (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X)))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(108,plain,
% 88.38/88.60 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X)) <=> ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[107])).
% 88.38/88.60 tff(109,plain,
% 88.38/88.60 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X)) <=> ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(110,axiom,(![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set5')).
% 88.38/88.60 tff(111,plain,
% 88.38/88.60 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[110, 109])).
% 88.38/88.60 tff(112,plain,(
% 88.38/88.60 ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))),
% 88.38/88.60 inference(skolemize,[status(sab)],[111])).
% 88.38/88.60 tff(113,plain,
% 88.38/88.60 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[112, 108])).
% 88.38/88.60 tff(114,plain,
% 88.38/88.60 (((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))) | (single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a)))) <=> ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))) | single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a)))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(115,plain,
% 88.38/88.60 ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))) | (single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a)))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(116,plain,
% 88.38/88.60 ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X))) | single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[115, 114])).
% 88.38/88.60 tff(117,plain,
% 88.38/88.60 (member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[116, 113, 106])).
% 88.38/88.60 tff(118,plain,
% 88.38/88.60 (((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(119,plain,
% 88.38/88.60 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(120,plain,
% 88.38/88.60 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[119, 118])).
% 88.38/88.60 tff(121,plain,
% 88.38/88.60 (little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[120, 61, 117])).
% 88.38/88.60 tff(122,plain,
% 88.38/88.60 (^[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))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(123,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[122])).
% 88.38/88.60 tff(124,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(125,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(elim_unused_vars,[status(thm)],[])).
% 88.38/88.60 tff(126,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(destructive_equality_resolution,[status(thm)],[])).
% 88.38/88.60 tff(127,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(transitivity,[status(thm)],[126, 125])).
% 88.38/88.60 tff(128,plain,
% 88.38/88.60 (^[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)))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(129,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[128])).
% 88.38/88.60 tff(130,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(transitivity,[status(thm)],[129, 127])).
% 88.38/88.60 tff(131,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')).
% 88.38/88.60 tff(132,plain,
% 88.38/88.60 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[131, 130])).
% 88.38/88.60 tff(133,plain,
% 88.38/88.60 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[132, 124])).
% 88.38/88.60 tff(134,plain,(
% 88.38/88.60 ![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 88.38/88.60 inference(skolemize,[status(sab)],[133])).
% 88.38/88.60 tff(135,plain,
% 88.38/88.60 (![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[134, 123])).
% 88.38/88.60 tff(136,plain,
% 88.38/88.60 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(137,plain,
% 88.38/88.60 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(138,plain,
% 88.38/88.60 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[137, 136])).
% 88.38/88.60 tff(139,plain,
% 88.38/88.60 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[138, 135, 121])).
% 88.38/88.60 tff(140,plain,
% 88.38/88.60 (^[Z: $i] : refl(((~little_set(Z)) | member(Z, universal_set)) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(141,plain,
% 88.38/88.60 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[140])).
% 88.38/88.60 tff(142,plain,
% 88.38/88.60 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set)) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(143,plain,
% 88.38/88.60 (^[Z: $i] : rewrite((member(Z, universal_set) | (~little_set(Z))) <=> ((~little_set(Z)) | member(Z, universal_set)))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(144,plain,
% 88.38/88.60 (![Z: $i] : (member(Z, universal_set) | (~little_set(Z))) <=> ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[143])).
% 88.38/88.60 tff(145,axiom,(![Z: $i] : (member(Z, universal_set) | (~little_set(Z)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','universal_set')).
% 88.38/88.60 tff(146,plain,
% 88.38/88.60 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[145, 144])).
% 88.38/88.60 tff(147,plain,
% 88.38/88.60 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[146, 142])).
% 88.38/88.60 tff(148,plain,(
% 88.38/88.60 ![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(skolemize,[status(sab)],[147])).
% 88.38/88.60 tff(149,plain,
% 88.38/88.60 (![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[148, 141])).
% 88.38/88.60 tff(150,plain,
% 88.38/88.60 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(151,plain,
% 88.38/88.60 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(152,plain,
% 88.38/88.60 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[151, 150])).
% 88.38/88.60 tff(153,plain,
% 88.38/88.60 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[152, 149, 121])).
% 88.38/88.60 tff(154,plain,
% 88.38/88.60 (^[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))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(155,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[154])).
% 88.38/88.60 tff(156,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(157,plain,
% 88.38/88.60 (^[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))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(158,plain,
% 88.38/88.60 (![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)))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[157])).
% 88.38/88.60 tff(159,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')).
% 88.38/88.60 tff(160,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[159, 158])).
% 88.38/88.60 tff(161,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[160, 156])).
% 88.38/88.60 tff(162,plain,(
% 88.38/88.60 ![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 88.38/88.60 inference(skolemize,[status(sab)],[161])).
% 88.38/88.60 tff(163,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[162, 155])).
% 88.38/88.60 tff(164,plain,
% 88.38/88.60 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(165,plain,
% 88.38/88.60 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(166,plain,
% 88.38/88.60 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[165, 164])).
% 88.38/88.60 tff(167,plain,
% 88.38/88.60 (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[166, 163, 153, 139])).
% 88.38/88.60 tff(168,plain,
% 88.38/88.60 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), Y)) <=> (disjoint(X, Y) | member(f23(X, Y), Y)))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(169,plain,
% 88.38/88.60 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[168])).
% 88.38/88.60 tff(170,plain,
% 88.38/88.60 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(171,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','disjoint3')).
% 88.38/88.60 tff(172,plain,
% 88.38/88.60 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[171, 170])).
% 88.38/88.60 tff(173,plain,(
% 88.38/88.60 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 88.38/88.60 inference(skolemize,[status(sab)],[172])).
% 88.38/88.60 tff(174,plain,
% 88.38/88.60 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[173, 169])).
% 88.38/88.60 tff(175,plain,
% 88.38/88.60 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(176,plain,
% 88.38/88.60 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.60 inference(quant_inst,[status(thm)],[])).
% 88.38/88.60 tff(177,plain,
% 88.38/88.60 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[176, 175])).
% 88.38/88.60 tff(178,plain,
% 88.38/88.60 (member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.60 inference(unit_resolution,[status(thm)],[177, 174, 167])).
% 88.38/88.60 tff(179,plain,
% 88.38/88.60 (^[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)))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(180,plain,
% 88.38/88.60 (![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))))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[179])).
% 88.38/88.60 tff(181,plain,
% 88.38/88.60 (![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))))),
% 88.38/88.60 inference(rewrite,[status(thm)],[])).
% 88.38/88.60 tff(182,plain,
% 88.38/88.60 (^[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)))))),
% 88.38/88.60 inference(bind,[status(th)],[])).
% 88.38/88.60 tff(183,plain,
% 88.38/88.60 (![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))))),
% 88.38/88.60 inference(quant_intro,[status(thm)],[182])).
% 88.38/88.60 tff(184,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')).
% 88.38/88.60 tff(185,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[184, 183])).
% 88.38/88.60 tff(186,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[185, 181])).
% 88.38/88.60 tff(187,plain,(
% 88.38/88.60 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 88.38/88.60 inference(skolemize,[status(sab)],[186])).
% 88.38/88.60 tff(188,plain,
% 88.38/88.60 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))),
% 88.38/88.60 inference(modus_ponens,[status(thm)],[187, 180])).
% 88.38/88.60 tff(189,plain,
% 88.38/88.60 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(190,plain,
% 88.38/88.61 (((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(191,plain,
% 88.38/88.61 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.61 inference(monotonicity,[status(thm)],[190])).
% 88.38/88.61 tff(192,plain,
% 88.38/88.61 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(transitivity,[status(thm)],[191, 189])).
% 88.38/88.61 tff(193,plain,
% 88.38/88.61 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.61 inference(quant_inst,[status(thm)],[])).
% 88.38/88.61 tff(194,plain,
% 88.38/88.61 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[193, 192])).
% 88.38/88.61 tff(195,plain,
% 88.38/88.61 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.38/88.61 inference(unit_resolution,[status(thm)],[194, 188, 178])).
% 88.38/88.61 tff(196,plain,
% 88.38/88.61 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.61 inference(commutativity,[status(thm)],[])).
% 88.38/88.61 tff(197,plain,
% 88.38/88.61 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(symmetry,[status(thm)],[196])).
% 88.38/88.61 tff(198,assumption,(~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), introduced(assumption)).
% 88.38/88.61 tff(199,plain,
% 88.38/88.61 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(200,plain,
% 88.38/88.61 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.61 inference(quant_inst,[status(thm)],[])).
% 88.38/88.61 tff(201,plain,
% 88.38/88.61 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[200, 199])).
% 88.38/88.61 tff(202,plain,
% 88.38/88.61 (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.38/88.61 inference(unit_resolution,[status(thm)],[201, 20, 117])).
% 88.38/88.61 tff(203,plain,
% 88.38/88.61 (^[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))))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(204,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[203])).
% 88.38/88.61 tff(205,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(206,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')).
% 88.38/88.61 tff(207,plain,
% 88.38/88.61 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[206, 205])).
% 88.38/88.61 tff(208,plain,(
% 88.38/88.61 ![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(skolemize,[status(sab)],[207])).
% 88.38/88.61 tff(209,plain,
% 88.38/88.61 (![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[208, 204])).
% 88.38/88.61 tff(210,plain,
% 88.38/88.61 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.61 inference(quant_inst,[status(thm)],[])).
% 88.38/88.61 tff(211,plain,
% 88.38/88.61 (ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.61 inference(unit_resolution,[status(thm)],[210, 209])).
% 88.38/88.61 tff(212,plain,
% 88.38/88.61 (non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.38/88.61 inference(symmetry,[status(thm)],[211])).
% 88.38/88.61 tff(213,plain,
% 88.38/88.61 (^[X: $i] : refl((singleton_set(X) = non_ordered_pair(X, X)) <=> (singleton_set(X) = non_ordered_pair(X, X)))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(214,plain,
% 88.38/88.61 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[213])).
% 88.38/88.61 tff(215,plain,
% 88.38/88.61 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X)) <=> ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(216,axiom,(![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','singleton_set')).
% 88.38/88.61 tff(217,plain,
% 88.38/88.61 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[216, 215])).
% 88.38/88.61 tff(218,plain,(
% 88.38/88.61 ![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 88.38/88.61 inference(skolemize,[status(sab)],[217])).
% 88.38/88.61 tff(219,plain,
% 88.38/88.61 (![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[218, 214])).
% 88.38/88.61 tff(220,plain,
% 88.38/88.61 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.61 inference(quant_inst,[status(thm)],[])).
% 88.38/88.61 tff(221,plain,
% 88.38/88.61 (singleton_set(f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.38/88.61 inference(unit_resolution,[status(thm)],[220, 219])).
% 88.38/88.61 tff(222,plain,
% 88.38/88.61 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = singleton_set(f19(compose(b, a)))),
% 88.38/88.61 inference(symmetry,[status(thm)],[221])).
% 88.38/88.61 tff(223,plain,
% 88.38/88.61 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.61 inference(monotonicity,[status(thm)],[222])).
% 88.38/88.61 tff(224,plain,
% 88.38/88.61 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.38/88.61 inference(transitivity,[status(thm)],[223, 212, 202])).
% 88.38/88.61 tff(225,plain,
% 88.38/88.61 (member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(monotonicity,[status(thm)],[224])).
% 88.38/88.61 tff(226,plain,
% 88.38/88.61 (member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.61 inference(symmetry,[status(thm)],[225])).
% 88.38/88.61 tff(227,plain,
% 88.38/88.61 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.38/88.61 inference(symmetry,[status(thm)],[202])).
% 88.38/88.61 tff(228,plain,
% 88.38/88.61 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.61 inference(transitivity,[status(thm)],[227, 211])).
% 88.38/88.61 tff(229,plain,
% 88.38/88.61 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.61 inference(monotonicity,[status(thm)],[228])).
% 88.38/88.61 tff(230,plain,
% 88.38/88.61 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.61 inference(symmetry,[status(thm)],[229])).
% 88.38/88.61 tff(231,plain,
% 88.38/88.61 (^[Y: $i, X: $i] : refl(little_set(non_ordered_pair(X, Y)) <=> little_set(non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(232,plain,
% 88.38/88.61 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[231])).
% 88.38/88.61 tff(233,plain,
% 88.38/88.61 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(234,axiom,(![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','non_ordered_pair4')).
% 88.38/88.61 tff(235,plain,
% 88.38/88.61 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[234, 233])).
% 88.38/88.61 tff(236,plain,(
% 88.38/88.61 ![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 88.38/88.61 inference(skolemize,[status(sab)],[235])).
% 88.38/88.61 tff(237,plain,
% 88.38/88.61 (![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[236, 232])).
% 88.38/88.61 tff(238,plain,
% 88.38/88.61 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.61 inference(quant_inst,[status(thm)],[])).
% 88.38/88.61 tff(239,plain,
% 88.38/88.61 (little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.61 inference(unit_resolution,[status(thm)],[238, 237])).
% 88.38/88.61 tff(240,plain,
% 88.38/88.61 (^[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))))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(241,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[240])).
% 88.38/88.61 tff(242,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(rewrite,[status(thm)],[])).
% 88.38/88.61 tff(243,plain,
% 88.38/88.61 (^[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))))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(244,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[243])).
% 88.38/88.61 tff(245,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(elim_unused_vars,[status(thm)],[])).
% 88.38/88.61 tff(246,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(destructive_equality_resolution,[status(thm)],[])).
% 88.38/88.61 tff(247,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(transitivity,[status(thm)],[246, 245])).
% 88.38/88.61 tff(248,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(transitivity,[status(thm)],[247, 244])).
% 88.38/88.61 tff(249,plain,
% 88.38/88.61 (^[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)))))),
% 88.38/88.61 inference(bind,[status(th)],[])).
% 88.38/88.61 tff(250,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(quant_intro,[status(thm)],[249])).
% 88.38/88.61 tff(251,plain,
% 88.38/88.61 (![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)))),
% 88.38/88.61 inference(transitivity,[status(thm)],[250, 248])).
% 88.38/88.61 tff(252,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')).
% 88.38/88.61 tff(253,plain,
% 88.38/88.61 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[252, 251])).
% 88.38/88.61 tff(254,plain,
% 88.38/88.61 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[253, 242])).
% 88.38/88.61 tff(255,plain,(
% 88.38/88.61 ![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(skolemize,[status(sab)],[254])).
% 88.38/88.61 tff(256,plain,
% 88.38/88.61 (![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))),
% 88.38/88.61 inference(modus_ponens,[status(thm)],[255, 241])).
% 88.38/88.61 tff(257,plain,
% 88.38/88.61 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(258,plain,
% 88.38/88.62 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(259,plain,
% 88.38/88.62 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[258, 257])).
% 88.38/88.62 tff(260,plain,
% 88.38/88.62 ((~little_set(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[259, 256])).
% 88.38/88.62 tff(261,plain,
% 88.38/88.62 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[260, 239])).
% 88.38/88.62 tff(262,plain,
% 88.38/88.62 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[261, 230])).
% 88.38/88.62 tff(263,plain,
% 88.38/88.62 (^[X: $i] : refl((single_valued_set(X) | little_set(f19(X))) <=> (single_valued_set(X) | little_set(f19(X))))),
% 88.38/88.62 inference(bind,[status(th)],[])).
% 88.38/88.62 tff(264,plain,
% 88.38/88.62 (![X: $i] : (single_valued_set(X) | little_set(f19(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f19(X)))),
% 88.38/88.62 inference(quant_intro,[status(thm)],[263])).
% 88.38/88.62 tff(265,plain,
% 88.38/88.62 (![X: $i] : (single_valued_set(X) | little_set(f19(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f19(X)))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(266,axiom,(![X: $i] : (single_valued_set(X) | little_set(f19(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set2')).
% 88.38/88.62 tff(267,plain,
% 88.38/88.62 (![X: $i] : (single_valued_set(X) | little_set(f19(X)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[266, 265])).
% 88.38/88.62 tff(268,plain,(
% 88.38/88.62 ![X: $i] : (single_valued_set(X) | little_set(f19(X)))),
% 88.38/88.62 inference(skolemize,[status(sab)],[267])).
% 88.38/88.62 tff(269,plain,
% 88.38/88.62 (![X: $i] : (single_valued_set(X) | little_set(f19(X)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[268, 264])).
% 88.38/88.62 tff(270,plain,
% 88.38/88.62 (((~![X: $i] : (single_valued_set(X) | little_set(f19(X)))) | (single_valued_set(compose(b, a)) | little_set(f19(compose(b, a))))) <=> ((~![X: $i] : (single_valued_set(X) | little_set(f19(X)))) | single_valued_set(compose(b, a)) | little_set(f19(compose(b, a))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(271,plain,
% 88.38/88.62 ((~![X: $i] : (single_valued_set(X) | little_set(f19(X)))) | (single_valued_set(compose(b, a)) | little_set(f19(compose(b, a))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(272,plain,
% 88.38/88.62 ((~![X: $i] : (single_valued_set(X) | little_set(f19(X)))) | single_valued_set(compose(b, a)) | little_set(f19(compose(b, a)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[271, 270])).
% 88.38/88.62 tff(273,plain,
% 88.38/88.62 (little_set(f19(compose(b, a)))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[272, 269, 106])).
% 88.38/88.62 tff(274,plain,
% 88.38/88.62 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(275,plain,
% 88.38/88.62 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(276,plain,
% 88.38/88.62 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[275, 274])).
% 88.38/88.62 tff(277,plain,
% 88.38/88.62 (member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[276, 135, 273])).
% 88.38/88.62 tff(278,plain,
% 88.38/88.62 (^[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))))),
% 88.38/88.62 inference(bind,[status(th)],[])).
% 88.38/88.62 tff(279,plain,
% 88.38/88.62 (![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)))),
% 88.38/88.62 inference(quant_intro,[status(thm)],[278])).
% 88.38/88.62 tff(280,plain,
% 88.38/88.62 (![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)))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(281,plain,
% 88.38/88.62 (^[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)))))),
% 88.38/88.62 inference(bind,[status(th)],[])).
% 88.38/88.62 tff(282,plain,
% 88.38/88.62 (![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)))),
% 88.38/88.62 inference(quant_intro,[status(thm)],[281])).
% 88.38/88.62 tff(283,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')).
% 88.38/88.62 tff(284,plain,
% 88.38/88.62 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[283, 282])).
% 88.38/88.62 tff(285,plain,
% 88.38/88.62 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[284, 280])).
% 88.38/88.62 tff(286,plain,(
% 88.38/88.62 ![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 88.38/88.62 inference(skolemize,[status(sab)],[285])).
% 88.38/88.62 tff(287,plain,
% 88.38/88.62 (![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[286, 279])).
% 88.38/88.62 tff(288,plain,
% 88.38/88.62 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(289,plain,
% 88.38/88.62 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(290,plain,
% 88.38/88.62 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[289, 288])).
% 88.38/88.62 tff(291,plain,
% 88.38/88.62 ((~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[290, 287, 277])).
% 88.38/88.62 tff(292,plain,
% 88.38/88.62 (member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[291, 262])).
% 88.38/88.62 tff(293,plain,
% 88.38/88.62 (^[Z: $i, X: $i] : refl(((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ((~member(Z, sigma(X))) | member(f16(Z, X), X)))),
% 88.38/88.62 inference(bind,[status(th)],[])).
% 88.38/88.62 tff(294,plain,
% 88.38/88.62 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 88.38/88.62 inference(quant_intro,[status(thm)],[293])).
% 88.38/88.62 tff(295,plain,
% 88.38/88.62 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X)) <=> ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(296,axiom,(![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','sigma1')).
% 88.38/88.62 tff(297,plain,
% 88.38/88.62 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[296, 295])).
% 88.38/88.62 tff(298,plain,(
% 88.38/88.62 ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 88.38/88.62 inference(skolemize,[status(sab)],[297])).
% 88.38/88.62 tff(299,plain,
% 88.38/88.62 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[298, 294])).
% 88.38/88.62 tff(300,plain,
% 88.38/88.62 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(301,plain,
% 88.38/88.62 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(302,plain,
% 88.38/88.62 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[301, 300])).
% 88.38/88.62 tff(303,plain,
% 88.38/88.62 (member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.62 inference(unit_resolution,[status(thm)],[302, 299, 292])).
% 88.38/88.62 tff(304,plain,
% 88.38/88.62 (member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[303, 226])).
% 88.38/88.62 tff(305,plain,
% 88.38/88.62 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(306,plain,
% 88.38/88.62 (((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.62 inference(rewrite,[status(thm)],[])).
% 88.38/88.62 tff(307,plain,
% 88.38/88.62 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))))),
% 88.38/88.62 inference(monotonicity,[status(thm)],[306])).
% 88.38/88.62 tff(308,plain,
% 88.38/88.62 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.62 inference(transitivity,[status(thm)],[307, 305])).
% 88.38/88.62 tff(309,plain,
% 88.38/88.62 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.62 inference(quant_inst,[status(thm)],[])).
% 88.38/88.62 tff(310,plain,
% 88.38/88.62 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.62 inference(modus_ponens,[status(thm)],[309, 308])).
% 88.38/88.62 tff(311,plain,
% 88.38/88.62 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.63 inference(unit_resolution,[status(thm)],[310, 188])).
% 88.38/88.63 tff(312,plain,
% 88.38/88.63 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.63 inference(unit_resolution,[status(thm)],[311, 304])).
% 88.38/88.63 tff(313,plain,
% 88.38/88.63 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.38/88.63 inference(unit_resolution,[status(thm)],[312, 198])).
% 88.38/88.63 tff(314,plain,
% 88.38/88.63 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.63 inference(symmetry,[status(thm)],[313])).
% 88.38/88.63 tff(315,assumption,(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), introduced(assumption)).
% 88.38/88.63 tff(316,assumption,(~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), introduced(assumption)).
% 88.38/88.63 tff(317,plain,
% 88.38/88.63 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.63 inference(monotonicity,[status(thm)],[224])).
% 88.38/88.63 tff(318,plain,
% 88.38/88.63 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.63 inference(symmetry,[status(thm)],[317])).
% 88.38/88.63 tff(319,plain,
% 88.38/88.63 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.63 inference(rewrite,[status(thm)],[])).
% 88.38/88.63 tff(320,plain,
% 88.38/88.63 (((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.63 inference(rewrite,[status(thm)],[])).
% 88.38/88.63 tff(321,plain,
% 88.38/88.63 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.63 inference(monotonicity,[status(thm)],[320])).
% 88.38/88.63 tff(322,plain,
% 88.38/88.63 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.63 inference(transitivity,[status(thm)],[321, 319])).
% 88.38/88.63 tff(323,plain,
% 88.38/88.63 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.63 inference(quant_inst,[status(thm)],[])).
% 88.38/88.63 tff(324,plain,
% 88.38/88.63 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.63 inference(modus_ponens,[status(thm)],[323, 322])).
% 88.38/88.63 tff(325,plain,
% 88.38/88.63 (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.63 inference(unit_resolution,[status(thm)],[324, 163, 277, 292])).
% 88.38/88.63 tff(326,plain,
% 88.38/88.63 (^[Y: $i, X: $i] : refl((disjoint(X, Y) | member(f23(X, Y), X)) <=> (disjoint(X, Y) | member(f23(X, Y), X)))),
% 88.38/88.63 inference(bind,[status(th)],[])).
% 88.38/88.63 tff(327,plain,
% 88.38/88.63 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 88.38/88.63 inference(quant_intro,[status(thm)],[326])).
% 88.38/88.63 tff(328,plain,
% 88.38/88.63 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X)) <=> ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 88.38/88.63 inference(rewrite,[status(thm)],[])).
% 88.38/88.63 tff(329,axiom,(![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','disjoint2')).
% 88.38/88.63 tff(330,plain,
% 88.38/88.63 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 88.38/88.63 inference(modus_ponens,[status(thm)],[329, 328])).
% 88.38/88.63 tff(331,plain,(
% 88.38/88.63 ![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 88.38/88.63 inference(skolemize,[status(sab)],[330])).
% 88.38/88.63 tff(332,plain,
% 88.38/88.63 (![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))),
% 88.38/88.63 inference(modus_ponens,[status(thm)],[331, 327])).
% 88.38/88.63 tff(333,plain,
% 88.38/88.63 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.63 inference(rewrite,[status(thm)],[])).
% 88.38/88.63 tff(334,plain,
% 88.38/88.63 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.63 inference(quant_inst,[status(thm)],[])).
% 88.38/88.63 tff(335,plain,
% 88.38/88.63 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.63 inference(modus_ponens,[status(thm)],[334, 333])).
% 88.38/88.63 tff(336,plain,
% 88.38/88.63 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.63 inference(unit_resolution,[status(thm)],[335, 332, 325])).
% 88.38/88.63 tff(337,plain,
% 88.38/88.63 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.64 inference(rewrite,[status(thm)],[])).
% 88.38/88.64 tff(338,plain,
% 88.38/88.64 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.64 inference(quant_inst,[status(thm)],[])).
% 88.38/88.64 tff(339,plain,
% 88.38/88.64 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.64 inference(modus_ponens,[status(thm)],[338, 337])).
% 88.38/88.64 tff(340,plain,
% 88.38/88.64 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.64 inference(unit_resolution,[status(thm)],[339, 299, 336])).
% 88.38/88.64 tff(341,plain,
% 88.38/88.64 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.38/88.64 inference(modus_ponens,[status(thm)],[340, 318])).
% 88.38/88.64 tff(342,plain,
% 88.38/88.64 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.64 inference(rewrite,[status(thm)],[])).
% 88.38/88.64 tff(343,plain,
% 88.38/88.64 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.38/88.64 inference(quant_inst,[status(thm)],[])).
% 88.38/88.64 tff(344,plain,
% 88.38/88.64 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.64 inference(modus_ponens,[status(thm)],[343, 342])).
% 88.38/88.64 tff(345,plain,
% 88.38/88.64 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.38/88.64 inference(unit_resolution,[status(thm)],[344, 188])).
% 88.38/88.64 tff(346,plain,
% 88.38/88.64 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.64 inference(unit_resolution,[status(thm)],[345, 341])).
% 88.38/88.64 tff(347,plain,
% 88.38/88.64 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.38/88.64 inference(unit_resolution,[status(thm)],[346, 316])).
% 88.38/88.64 tff(348,plain,
% 88.38/88.64 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.64 inference(symmetry,[status(thm)],[347])).
% 88.38/88.64 tff(349,plain,
% 88.38/88.64 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.64 inference(monotonicity,[status(thm)],[348])).
% 88.38/88.64 tff(350,plain,
% 88.38/88.64 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.64 inference(symmetry,[status(thm)],[349])).
% 88.38/88.64 tff(351,plain,
% 88.38/88.64 (^[Z: $i, X: $i] : refl(((~member(Z, sigma(X))) | member(Z, f16(Z, X))) <=> ((~member(Z, sigma(X))) | member(Z, f16(Z, X))))),
% 88.38/88.64 inference(bind,[status(th)],[])).
% 88.38/88.64 tff(352,plain,
% 88.38/88.64 (![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)))),
% 88.38/88.64 inference(quant_intro,[status(thm)],[351])).
% 88.38/88.64 tff(353,plain,
% 88.38/88.64 (![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)))),
% 88.38/88.64 inference(rewrite,[status(thm)],[])).
% 88.38/88.64 tff(354,axiom,(![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','sigma2')).
% 88.38/88.64 tff(355,plain,
% 88.38/88.64 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 88.38/88.64 inference(modus_ponens,[status(thm)],[354, 353])).
% 88.38/88.64 tff(356,plain,(
% 88.38/88.64 ![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 88.38/88.64 inference(skolemize,[status(sab)],[355])).
% 88.38/88.64 tff(357,plain,
% 88.38/88.64 (![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))),
% 88.38/88.64 inference(modus_ponens,[status(thm)],[356, 352])).
% 88.38/88.64 tff(358,plain,
% 88.38/88.64 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.64 inference(rewrite,[status(thm)],[])).
% 88.38/88.64 tff(359,plain,
% 88.38/88.64 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.38/88.64 inference(quant_inst,[status(thm)],[])).
% 88.38/88.64 tff(360,plain,
% 88.38/88.64 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[359, 358])).
% 88.38/88.65 tff(361,plain,
% 88.38/88.65 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[360, 357, 336])).
% 88.38/88.65 tff(362,plain,
% 88.38/88.65 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[361, 350])).
% 88.38/88.65 tff(363,plain,
% 88.38/88.65 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(364,plain,
% 88.38/88.65 (((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(365,plain,
% 88.38/88.65 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.38/88.65 inference(monotonicity,[status(thm)],[364])).
% 88.38/88.65 tff(366,plain,
% 88.38/88.65 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(transitivity,[status(thm)],[365, 363])).
% 88.38/88.65 tff(367,plain,
% 88.38/88.65 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(quant_inst,[status(thm)],[])).
% 88.38/88.65 tff(368,plain,
% 88.38/88.65 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[367, 366])).
% 88.38/88.65 tff(369,plain,
% 88.38/88.65 ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[368, 188])).
% 88.38/88.65 tff(370,plain,
% 88.38/88.65 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[369, 362])).
% 88.38/88.65 tff(371,plain,
% 88.38/88.65 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.65 inference(monotonicity,[status(thm)],[370])).
% 88.38/88.65 tff(372,plain,
% 88.38/88.65 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.38/88.65 inference(transitivity,[status(thm)],[371, 315])).
% 88.38/88.65 tff(373,plain,
% 88.38/88.65 ($false),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[316, 372])).
% 88.38/88.65 tff(374,plain,((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.38/88.65 tff(375,plain,
% 88.38/88.65 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[374, 313])).
% 88.38/88.65 tff(376,plain,
% 88.38/88.65 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.38/88.65 inference(monotonicity,[status(thm)],[314])).
% 88.38/88.65 tff(377,plain,
% 88.38/88.65 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.38/88.65 inference(symmetry,[status(thm)],[376])).
% 88.38/88.65 tff(378,plain,
% 88.38/88.65 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.38/88.65 inference(monotonicity,[status(thm)],[377])).
% 88.38/88.65 tff(379,plain,
% 88.38/88.65 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(380,plain,
% 88.38/88.65 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(quant_inst,[status(thm)],[])).
% 88.38/88.65 tff(381,plain,
% 88.38/88.65 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[380, 379])).
% 88.38/88.65 tff(382,plain,
% 88.38/88.65 (member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[381, 135, 273])).
% 88.38/88.65 tff(383,plain,
% 88.38/88.65 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(384,plain,
% 88.38/88.65 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(quant_inst,[status(thm)],[])).
% 88.38/88.65 tff(385,plain,
% 88.38/88.65 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[384, 383])).
% 88.38/88.65 tff(386,plain,
% 88.38/88.65 (~disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[385, 163, 277, 382])).
% 88.38/88.65 tff(387,plain,
% 88.38/88.65 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(388,plain,
% 88.38/88.65 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.38/88.65 inference(quant_inst,[status(thm)],[])).
% 88.38/88.65 tff(389,plain,
% 88.38/88.65 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(modus_ponens,[status(thm)],[388, 387])).
% 88.38/88.65 tff(390,plain,
% 88.38/88.65 (member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.38/88.65 inference(unit_resolution,[status(thm)],[389, 174, 386])).
% 88.38/88.65 tff(391,plain,
% 88.38/88.65 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.38/88.65 inference(rewrite,[status(thm)],[])).
% 88.38/88.65 tff(392,plain,
% 88.38/88.65 (((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(393,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.49/88.66 inference(monotonicity,[status(thm)],[392])).
% 88.49/88.66 tff(394,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(transitivity,[status(thm)],[393, 391])).
% 88.49/88.66 tff(395,plain,
% 88.49/88.66 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(quant_inst,[status(thm)],[])).
% 88.49/88.66 tff(396,plain,
% 88.49/88.66 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.66 inference(modus_ponens,[status(thm)],[395, 394])).
% 88.49/88.66 tff(397,plain,
% 88.49/88.66 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))),
% 88.49/88.66 inference(unit_resolution,[status(thm)],[396, 188, 390])).
% 88.49/88.66 tff(398,plain,
% 88.49/88.66 (f19(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.66 inference(symmetry,[status(thm)],[397])).
% 88.49/88.66 tff(399,plain,
% 88.49/88.66 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(400,plain,
% 88.49/88.66 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.66 inference(quant_inst,[status(thm)],[])).
% 88.49/88.66 tff(401,plain,
% 88.49/88.66 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.66 inference(modus_ponens,[status(thm)],[400, 399])).
% 88.49/88.66 tff(402,plain,
% 88.49/88.66 (member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.66 inference(unit_resolution,[status(thm)],[401, 357, 292])).
% 88.49/88.66 tff(403,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(404,plain,
% 88.49/88.66 (((~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(405,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.49/88.66 inference(monotonicity,[status(thm)],[404])).
% 88.49/88.66 tff(406,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(transitivity,[status(thm)],[405, 403])).
% 88.49/88.66 tff(407,plain,
% 88.49/88.66 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.66 inference(quant_inst,[status(thm)],[])).
% 88.49/88.66 tff(408,plain,
% 88.49/88.66 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.66 inference(modus_ponens,[status(thm)],[407, 406])).
% 88.49/88.66 tff(409,plain,
% 88.49/88.66 (~disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.66 inference(unit_resolution,[status(thm)],[408, 163, 382, 402])).
% 88.49/88.66 tff(410,plain,
% 88.49/88.66 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(411,plain,
% 88.49/88.66 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.66 inference(quant_inst,[status(thm)],[])).
% 88.49/88.66 tff(412,plain,
% 88.49/88.66 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.66 inference(modus_ponens,[status(thm)],[411, 410])).
% 88.49/88.66 tff(413,plain,
% 88.49/88.66 (member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.66 inference(unit_resolution,[status(thm)],[412, 174, 409])).
% 88.49/88.66 tff(414,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(415,plain,
% 88.49/88.66 (((f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.49/88.66 inference(rewrite,[status(thm)],[])).
% 88.49/88.66 tff(416,plain,
% 88.49/88.66 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[415])).
% 88.49/88.67 tff(417,plain,
% 88.49/88.67 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.49/88.67 inference(transitivity,[status(thm)],[416, 414])).
% 88.49/88.67 tff(418,plain,
% 88.49/88.67 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(419,plain,
% 88.49/88.67 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[418, 417])).
% 88.49/88.67 tff(420,plain,
% 88.49/88.67 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[419, 188, 413])).
% 88.49/88.67 tff(421,assumption,(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.49/88.67 tff(422,plain,
% 88.49/88.67 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[314, 421])).
% 88.49/88.67 tff(423,plain,
% 88.49/88.67 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.67 inference(transitivity,[status(thm)],[422, 420, 398])).
% 88.49/88.67 tff(424,plain,
% 88.49/88.67 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[423])).
% 88.49/88.67 tff(425,plain,
% 88.49/88.67 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a)))),
% 88.49/88.67 inference(symmetry,[status(thm)],[424])).
% 88.49/88.67 tff(426,plain,
% 88.49/88.67 ((f20(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 88.49/88.67 inference(commutativity,[status(thm)],[])).
% 88.49/88.67 tff(427,plain,
% 88.49/88.67 ((f20(compose(b, a)) = f19(compose(b, a))) <=> (f20(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[398])).
% 88.49/88.67 tff(428,plain,
% 88.49/88.67 ((f20(compose(b, a)) = f19(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 88.49/88.67 inference(transitivity,[status(thm)],[427, 426])).
% 88.49/88.67 tff(429,plain,
% 88.49/88.67 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f20(compose(b, a)) = f19(compose(b, a)))),
% 88.49/88.67 inference(symmetry,[status(thm)],[428])).
% 88.49/88.67 tff(430,plain,
% 88.49/88.67 ((~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))) <=> (~(f20(compose(b, a)) = f19(compose(b, a))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[429])).
% 88.49/88.67 tff(431,assumption,(~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))), introduced(assumption)).
% 88.49/88.67 tff(432,plain,
% 88.49/88.67 (~(f20(compose(b, a)) = f19(compose(b, a)))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[431, 430])).
% 88.49/88.67 tff(433,plain,
% 88.49/88.67 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.67 inference(symmetry,[status(thm)],[421])).
% 88.49/88.67 tff(434,plain,
% 88.49/88.67 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[433])).
% 88.49/88.67 tff(435,plain,
% 88.49/88.67 (member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.67 inference(symmetry,[status(thm)],[434])).
% 88.49/88.67 tff(436,plain,
% 88.49/88.67 (^[X: $i] : refl((single_valued_set(X) | little_set(f20(X))) <=> (single_valued_set(X) | little_set(f20(X))))),
% 88.49/88.67 inference(bind,[status(th)],[])).
% 88.49/88.67 tff(437,plain,
% 88.49/88.67 (![X: $i] : (single_valued_set(X) | little_set(f20(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f20(X)))),
% 88.49/88.67 inference(quant_intro,[status(thm)],[436])).
% 88.49/88.67 tff(438,plain,
% 88.49/88.67 (![X: $i] : (single_valued_set(X) | little_set(f20(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f20(X)))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(439,axiom,(![X: $i] : (single_valued_set(X) | little_set(f20(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set3')).
% 88.49/88.67 tff(440,plain,
% 88.49/88.67 (![X: $i] : (single_valued_set(X) | little_set(f20(X)))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[439, 438])).
% 88.49/88.67 tff(441,plain,(
% 88.49/88.67 ![X: $i] : (single_valued_set(X) | little_set(f20(X)))),
% 88.49/88.67 inference(skolemize,[status(sab)],[440])).
% 88.49/88.67 tff(442,plain,
% 88.49/88.67 (![X: $i] : (single_valued_set(X) | little_set(f20(X)))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[441, 437])).
% 88.49/88.67 tff(443,plain,
% 88.49/88.67 (((~![X: $i] : (single_valued_set(X) | little_set(f20(X)))) | (single_valued_set(compose(b, a)) | little_set(f20(compose(b, a))))) <=> ((~![X: $i] : (single_valued_set(X) | little_set(f20(X)))) | single_valued_set(compose(b, a)) | little_set(f20(compose(b, a))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(444,plain,
% 88.49/88.67 ((~![X: $i] : (single_valued_set(X) | little_set(f20(X)))) | (single_valued_set(compose(b, a)) | little_set(f20(compose(b, a))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(445,plain,
% 88.49/88.67 ((~![X: $i] : (single_valued_set(X) | little_set(f20(X)))) | single_valued_set(compose(b, a)) | little_set(f20(compose(b, a)))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[444, 443])).
% 88.49/88.67 tff(446,plain,
% 88.49/88.67 (little_set(f20(compose(b, a)))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[445, 442, 106])).
% 88.49/88.67 tff(447,plain,
% 88.49/88.67 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f20(compose(b, a)))) | member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f20(compose(b, a)))) | member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(448,plain,
% 88.49/88.67 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f20(compose(b, a)))) | member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(449,plain,
% 88.49/88.67 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f20(compose(b, a)))) | member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[448, 447])).
% 88.49/88.67 tff(450,plain,
% 88.49/88.67 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[449, 256, 446])).
% 88.49/88.67 tff(451,plain,
% 88.49/88.67 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(452,plain,
% 88.49/88.67 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(453,plain,
% 88.49/88.67 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[452, 451])).
% 88.49/88.67 tff(454,plain,
% 88.49/88.67 ((~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[453, 287, 450])).
% 88.49/88.67 tff(455,plain,
% 88.49/88.67 (member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[454, 262])).
% 88.49/88.67 tff(456,plain,
% 88.49/88.67 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(457,plain,
% 88.49/88.67 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(458,plain,
% 88.49/88.67 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[457, 456])).
% 88.49/88.67 tff(459,plain,
% 88.49/88.67 (member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.67 inference(unit_resolution,[status(thm)],[458, 357, 455])).
% 88.49/88.67 tff(460,plain,
% 88.49/88.67 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[459, 435])).
% 88.49/88.67 tff(461,plain,
% 88.49/88.67 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(462,plain,
% 88.49/88.67 (((f20(compose(b, a)) = f19(compose(b, a))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.67 inference(rewrite,[status(thm)],[])).
% 88.49/88.67 tff(463,plain,
% 88.49/88.67 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f19(compose(b, a))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.49/88.67 inference(monotonicity,[status(thm)],[462])).
% 88.49/88.67 tff(464,plain,
% 88.49/88.67 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f19(compose(b, a))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.67 inference(transitivity,[status(thm)],[463, 461])).
% 88.49/88.67 tff(465,plain,
% 88.49/88.67 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f19(compose(b, a))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.67 inference(quant_inst,[status(thm)],[])).
% 88.49/88.67 tff(466,plain,
% 88.49/88.67 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.67 inference(modus_ponens,[status(thm)],[465, 464])).
% 88.49/88.68 tff(467,plain,
% 88.49/88.68 ((f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[466, 188])).
% 88.49/88.68 tff(468,plain,
% 88.49/88.68 ($false),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[467, 460, 432])).
% 88.49/88.68 tff(469,plain,((~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.49/88.68 tff(470,plain,
% 88.49/88.68 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[469, 421])).
% 88.49/88.68 tff(471,plain,
% 88.49/88.68 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a))),
% 88.49/88.68 inference(modus_ponens,[status(thm)],[470, 425])).
% 88.49/88.68 tff(472,plain,
% 88.49/88.68 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.68 inference(symmetry,[status(thm)],[422])).
% 88.49/88.68 tff(473,plain,
% 88.49/88.68 (f19(compose(b, a)) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.68 inference(symmetry,[status(thm)],[420])).
% 88.49/88.68 tff(474,plain,
% 88.49/88.68 (f19(compose(b, a)) = f20(compose(b, a))),
% 88.49/88.68 inference(transitivity,[status(thm)],[473, 472, 471])).
% 88.49/88.68 tff(475,plain,
% 88.49/88.68 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.49/88.68 inference(monotonicity,[status(thm)],[474])).
% 88.49/88.68 tff(476,plain,
% 88.49/88.68 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.49/88.68 inference(symmetry,[status(thm)],[475])).
% 88.49/88.68 tff(477,plain,
% 88.49/88.68 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.49/88.68 inference(transitivity,[status(thm)],[313, 476])).
% 88.49/88.68 tff(478,plain,
% 88.49/88.68 ($false),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[198, 477])).
% 88.49/88.68 tff(479,plain,((~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.49/88.68 tff(480,plain,
% 88.49/88.68 (~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[479, 198])).
% 88.49/88.68 tff(481,plain,
% 88.49/88.68 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.68 inference(monotonicity,[status(thm)],[224])).
% 88.49/88.68 tff(482,plain,
% 88.49/88.68 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.49/88.68 inference(symmetry,[status(thm)],[481])).
% 88.49/88.68 tff(483,plain,
% 88.49/88.68 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.68 inference(rewrite,[status(thm)],[])).
% 88.49/88.68 tff(484,plain,
% 88.49/88.68 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.68 inference(quant_inst,[status(thm)],[])).
% 88.49/88.68 tff(485,plain,
% 88.49/88.68 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.68 inference(modus_ponens,[status(thm)],[484, 483])).
% 88.49/88.68 tff(486,plain,
% 88.49/88.68 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.68 inference(unit_resolution,[status(thm)],[485, 299, 455])).
% 88.49/88.68 tff(487,plain,
% 88.49/88.68 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.49/88.68 inference(modus_ponens,[status(thm)],[486, 482])).
% 88.49/88.68 tff(488,plain,
% 88.49/88.68 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.68 inference(rewrite,[status(thm)],[])).
% 88.49/88.68 tff(489,plain,
% 88.49/88.68 (((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.68 inference(rewrite,[status(thm)],[])).
% 88.49/88.68 tff(490,plain,
% 88.49/88.68 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.49/88.68 inference(monotonicity,[status(thm)],[489])).
% 88.49/88.68 tff(491,plain,
% 88.49/88.68 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.49/88.68 inference(transitivity,[status(thm)],[490, 488])).
% 88.49/88.68 tff(492,plain,
% 88.49/88.68 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.49/88.69 inference(quant_inst,[status(thm)],[])).
% 88.49/88.69 tff(493,plain,
% 88.49/88.69 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.69 inference(modus_ponens,[status(thm)],[492, 491])).
% 88.49/88.69 tff(494,plain,
% 88.49/88.69 ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[493, 188])).
% 88.49/88.69 tff(495,plain,
% 88.49/88.69 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[494, 487])).
% 88.49/88.69 tff(496,plain,
% 88.49/88.69 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[495, 480])).
% 88.49/88.69 tff(497,plain,
% 88.49/88.69 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(transitivity,[status(thm)],[496, 314])).
% 88.49/88.69 tff(498,plain,
% 88.49/88.69 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(monotonicity,[status(thm)],[497])).
% 88.49/88.69 tff(499,plain,
% 88.49/88.69 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(monotonicity,[status(thm)],[498])).
% 88.49/88.69 tff(500,plain,
% 88.49/88.69 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(rewrite,[status(thm)],[])).
% 88.49/88.69 tff(501,plain,
% 88.49/88.69 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(quant_inst,[status(thm)],[])).
% 88.49/88.69 tff(502,plain,
% 88.49/88.69 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(modus_ponens,[status(thm)],[501, 500])).
% 88.49/88.69 tff(503,plain,
% 88.49/88.69 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[502, 135, 121])).
% 88.49/88.69 tff(504,plain,
% 88.49/88.69 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.69 inference(rewrite,[status(thm)],[])).
% 88.49/88.69 tff(505,plain,
% 88.49/88.69 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.69 inference(quant_inst,[status(thm)],[])).
% 88.49/88.69 tff(506,plain,
% 88.49/88.69 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(modus_ponens,[status(thm)],[505, 504])).
% 88.49/88.69 tff(507,plain,
% 88.49/88.69 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[506, 163, 503, 139])).
% 88.49/88.69 tff(508,plain,
% 88.49/88.69 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(rewrite,[status(thm)],[])).
% 88.49/88.69 tff(509,plain,
% 88.49/88.69 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.69 inference(quant_inst,[status(thm)],[])).
% 88.49/88.69 tff(510,plain,
% 88.49/88.69 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(modus_ponens,[status(thm)],[509, 508])).
% 88.49/88.69 tff(511,plain,
% 88.49/88.69 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.69 inference(unit_resolution,[status(thm)],[510, 174, 507])).
% 88.49/88.69 tff(512,plain,
% 88.49/88.69 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.69 inference(rewrite,[status(thm)],[])).
% 88.49/88.69 tff(513,plain,
% 88.49/88.69 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.69 inference(rewrite,[status(thm)],[])).
% 88.49/88.69 tff(514,plain,
% 88.49/88.69 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.49/88.70 inference(monotonicity,[status(thm)],[513])).
% 88.49/88.70 tff(515,plain,
% 88.49/88.70 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.70 inference(transitivity,[status(thm)],[514, 512])).
% 88.49/88.70 tff(516,plain,
% 88.49/88.70 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.70 inference(quant_inst,[status(thm)],[])).
% 88.49/88.70 tff(517,plain,
% 88.49/88.70 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.70 inference(modus_ponens,[status(thm)],[516, 515])).
% 88.49/88.70 tff(518,plain,
% 88.49/88.70 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.49/88.70 inference(unit_resolution,[status(thm)],[517, 188, 511])).
% 88.49/88.70 tff(519,assumption,(~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), introduced(assumption)).
% 88.49/88.70 tff(520,plain,
% 88.49/88.70 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.70 inference(quant_inst,[status(thm)],[])).
% 88.49/88.70 tff(521,plain,
% 88.49/88.70 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.70 inference(unit_resolution,[status(thm)],[520, 209])).
% 88.49/88.70 tff(522,plain,
% 88.49/88.70 (non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.49/88.70 inference(symmetry,[status(thm)],[521])).
% 88.49/88.70 tff(523,plain,
% 88.49/88.70 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.70 inference(quant_inst,[status(thm)],[])).
% 88.49/88.70 tff(524,plain,
% 88.49/88.70 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.49/88.70 inference(unit_resolution,[status(thm)],[523, 219])).
% 88.49/88.70 tff(525,plain,
% 88.49/88.70 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.49/88.70 inference(symmetry,[status(thm)],[524])).
% 88.49/88.70 tff(526,plain,
% 88.49/88.70 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.70 inference(monotonicity,[status(thm)],[525])).
% 88.49/88.70 tff(527,plain,
% 88.49/88.70 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.49/88.70 inference(transitivity,[status(thm)],[526, 522])).
% 88.49/88.70 tff(528,plain,
% 88.49/88.70 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.49/88.70 inference(monotonicity,[status(thm)],[527])).
% 88.49/88.70 tff(529,plain,
% 88.49/88.70 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.70 inference(symmetry,[status(thm)],[528])).
% 88.49/88.70 tff(530,plain,
% 88.49/88.70 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.49/88.70 inference(rewrite,[status(thm)],[])).
% 88.49/88.70 tff(531,plain,
% 88.49/88.70 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.49/88.70 inference(quant_inst,[status(thm)],[])).
% 88.49/88.70 tff(532,plain,
% 88.49/88.70 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.71 inference(modus_ponens,[status(thm)],[531, 530])).
% 88.49/88.71 tff(533,plain,
% 88.49/88.71 (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.71 inference(unit_resolution,[status(thm)],[532, 163, 455, 459])).
% 88.49/88.71 tff(534,plain,
% 88.49/88.71 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.71 inference(rewrite,[status(thm)],[])).
% 88.49/88.71 tff(535,plain,
% 88.49/88.71 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.49/88.71 inference(quant_inst,[status(thm)],[])).
% 88.49/88.71 tff(536,plain,
% 88.49/88.71 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.71 inference(modus_ponens,[status(thm)],[535, 534])).
% 88.49/88.71 tff(537,plain,
% 88.49/88.71 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.71 inference(unit_resolution,[status(thm)],[536, 332, 533])).
% 88.49/88.71 tff(538,plain,
% 88.49/88.71 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.49/88.71 inference(rewrite,[status(thm)],[])).
% 88.49/88.71 tff(539,plain,
% 88.49/88.71 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.71 inference(quant_inst,[status(thm)],[])).
% 88.54/88.71 tff(540,plain,
% 88.54/88.71 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.71 inference(modus_ponens,[status(thm)],[539, 538])).
% 88.54/88.71 tff(541,plain,
% 88.54/88.71 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.71 inference(unit_resolution,[status(thm)],[540, 299, 537])).
% 88.54/88.71 tff(542,plain,
% 88.54/88.71 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.71 inference(modus_ponens,[status(thm)],[541, 529])).
% 88.54/88.71 tff(543,plain,
% 88.54/88.71 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.71 inference(rewrite,[status(thm)],[])).
% 88.54/88.71 tff(544,plain,
% 88.54/88.71 (((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.72 inference(rewrite,[status(thm)],[])).
% 88.54/88.72 tff(545,plain,
% 88.54/88.72 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.72 inference(monotonicity,[status(thm)],[544])).
% 88.54/88.72 tff(546,plain,
% 88.54/88.72 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.72 inference(transitivity,[status(thm)],[545, 543])).
% 88.54/88.72 tff(547,plain,
% 88.54/88.72 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.54/88.72 inference(quant_inst,[status(thm)],[])).
% 88.54/88.72 tff(548,plain,
% 88.54/88.72 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(modus_ponens,[status(thm)],[547, 546])).
% 88.54/88.73 tff(549,plain,
% 88.54/88.73 ((~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(unit_resolution,[status(thm)],[548, 188])).
% 88.54/88.73 tff(550,plain,
% 88.54/88.73 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(unit_resolution,[status(thm)],[549, 542])).
% 88.54/88.73 tff(551,plain,
% 88.54/88.73 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.54/88.73 inference(unit_resolution,[status(thm)],[550, 519])).
% 88.54/88.73 tff(552,plain,
% 88.54/88.73 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(symmetry,[status(thm)],[499])).
% 88.54/88.73 tff(553,plain,
% 88.54/88.73 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(symmetry,[status(thm)],[378])).
% 88.54/88.73 tff(554,plain,
% 88.54/88.73 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(symmetry,[status(thm)],[375])).
% 88.54/88.73 tff(555,assumption,(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.54/88.73 tff(556,plain,
% 88.54/88.73 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.54/88.73 inference(symmetry,[status(thm)],[555])).
% 88.54/88.73 tff(557,plain,
% 88.54/88.73 (member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.73 inference(monotonicity,[status(thm)],[556])).
% 88.54/88.73 tff(558,plain,
% 88.54/88.73 (member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.54/88.73 inference(symmetry,[status(thm)],[557])).
% 88.54/88.73 tff(559,plain,
% 88.54/88.73 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.54/88.73 inference(rewrite,[status(thm)],[])).
% 88.54/88.73 tff(560,plain,
% 88.54/88.73 (((~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.54/88.73 inference(rewrite,[status(thm)],[])).
% 88.54/88.73 tff(561,plain,
% 88.54/88.73 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.54/88.73 inference(monotonicity,[status(thm)],[560])).
% 88.54/88.73 tff(562,plain,
% 88.54/88.73 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.54/88.74 inference(transitivity,[status(thm)],[561, 559])).
% 88.54/88.74 tff(563,plain,
% 88.54/88.74 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.54/88.74 inference(quant_inst,[status(thm)],[])).
% 88.54/88.74 tff(564,plain,
% 88.54/88.74 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f20(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f20(compose(b, a)), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.74 inference(modus_ponens,[status(thm)],[563, 562])).
% 88.54/88.74 tff(565,plain,
% 88.54/88.74 (~disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.74 inference(unit_resolution,[status(thm)],[564, 163, 455, 459])).
% 88.54/88.74 tff(566,plain,
% 88.54/88.74 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.74 inference(rewrite,[status(thm)],[])).
% 88.54/88.74 tff(567,plain,
% 88.54/88.74 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.74 inference(quant_inst,[status(thm)],[])).
% 88.54/88.74 tff(568,plain,
% 88.54/88.74 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.74 inference(modus_ponens,[status(thm)],[567, 566])).
% 88.54/88.74 tff(569,plain,
% 88.54/88.74 (member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.74 inference(unit_resolution,[status(thm)],[568, 174, 565])).
% 88.54/88.74 tff(570,plain,
% 88.54/88.74 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.74 inference(rewrite,[status(thm)],[])).
% 88.54/88.74 tff(571,plain,
% 88.54/88.74 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.54/88.74 inference(quant_inst,[status(thm)],[])).
% 88.54/88.74 tff(572,plain,
% 88.54/88.74 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.74 inference(modus_ponens,[status(thm)],[571, 570])).
% 88.54/88.74 tff(573,plain,
% 88.54/88.74 (member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.54/88.74 inference(unit_resolution,[status(thm)],[572, 357, 569])).
% 88.54/88.74 tff(574,plain,
% 88.54/88.74 (member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.54/88.74 inference(modus_ponens,[status(thm)],[573, 558])).
% 88.54/88.74 tff(575,plain,
% 88.54/88.74 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.54/88.74 inference(rewrite,[status(thm)],[])).
% 88.54/88.74 tff(576,plain,
% 88.54/88.74 (((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.54/88.74 inference(rewrite,[status(thm)],[])).
% 88.54/88.74 tff(577,plain,
% 88.54/88.74 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.54/88.74 inference(monotonicity,[status(thm)],[576])).
% 88.54/88.74 tff(578,plain,
% 88.54/88.74 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.54/88.75 inference(transitivity,[status(thm)],[577, 575])).
% 88.54/88.75 tff(579,plain,
% 88.54/88.75 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.54/88.75 inference(quant_inst,[status(thm)],[])).
% 88.54/88.75 tff(580,plain,
% 88.54/88.75 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.54/88.75 inference(modus_ponens,[status(thm)],[579, 578])).
% 88.54/88.75 tff(581,plain,
% 88.54/88.75 ((f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.59/88.75 inference(unit_resolution,[status(thm)],[580, 188])).
% 88.59/88.75 tff(582,plain,
% 88.59/88.75 (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))),
% 88.59/88.75 inference(unit_resolution,[status(thm)],[581, 574])).
% 88.59/88.75 tff(583,plain,
% 88.59/88.75 (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.75 inference(monotonicity,[status(thm)],[582])).
% 88.59/88.75 tff(584,plain,
% 88.59/88.75 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.75 inference(symmetry,[status(thm)],[583])).
% 88.59/88.75 tff(585,plain,
% 88.59/88.75 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.59/88.75 inference(transitivity,[status(thm)],[584, 555])).
% 88.59/88.75 tff(586,plain,
% 88.59/88.75 ($false),
% 88.59/88.75 inference(unit_resolution,[status(thm)],[198, 585])).
% 88.59/88.75 tff(587,plain,((~(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.59/88.75 tff(588,plain,
% 88.59/88.75 (~(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.59/88.75 inference(unit_resolution,[status(thm)],[587, 198])).
% 88.59/88.75 tff(589,plain,
% 88.59/88.75 (member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.75 inference(monotonicity,[status(thm)],[224])).
% 88.59/88.75 tff(590,plain,
% 88.59/88.75 (member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.59/88.75 inference(symmetry,[status(thm)],[589])).
% 88.59/88.75 tff(591,plain,
% 88.59/88.75 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.75 inference(rewrite,[status(thm)],[])).
% 88.59/88.75 tff(592,plain,
% 88.59/88.75 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.75 inference(quant_inst,[status(thm)],[])).
% 88.59/88.75 tff(593,plain,
% 88.59/88.75 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.75 inference(modus_ponens,[status(thm)],[592, 591])).
% 88.59/88.75 tff(594,plain,
% 88.59/88.75 (member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.76 inference(unit_resolution,[status(thm)],[593, 299, 569])).
% 88.59/88.76 tff(595,plain,
% 88.59/88.76 (member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.59/88.76 inference(modus_ponens,[status(thm)],[594, 590])).
% 88.59/88.76 tff(596,plain,
% 88.59/88.76 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.59/88.76 inference(rewrite,[status(thm)],[])).
% 88.59/88.76 tff(597,plain,
% 88.59/88.76 (((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.59/88.76 inference(rewrite,[status(thm)],[])).
% 88.59/88.76 tff(598,plain,
% 88.59/88.76 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))))),
% 88.59/88.76 inference(monotonicity,[status(thm)],[597])).
% 88.59/88.76 tff(599,plain,
% 88.59/88.76 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.59/88.76 inference(transitivity,[status(thm)],[598, 596])).
% 88.59/88.76 tff(600,plain,
% 88.59/88.76 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.59/88.77 inference(quant_inst,[status(thm)],[])).
% 88.59/88.77 tff(601,plain,
% 88.59/88.77 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.59/88.77 inference(modus_ponens,[status(thm)],[600, 599])).
% 88.59/88.77 tff(602,plain,
% 88.59/88.77 ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~member(f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[601, 188])).
% 88.59/88.77 tff(603,plain,
% 88.59/88.77 ((f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[602, 595])).
% 88.59/88.77 tff(604,plain,
% 88.59/88.77 (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[603, 588])).
% 88.59/88.77 tff(605,plain,
% 88.59/88.77 (f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.77 inference(monotonicity,[status(thm)],[497])).
% 88.59/88.77 tff(606,plain,
% 88.59/88.77 (f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(monotonicity,[status(thm)],[605])).
% 88.59/88.77 tff(607,plain,
% 88.59/88.77 (f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(symmetry,[status(thm)],[606])).
% 88.59/88.77 tff(608,plain,
% 88.59/88.77 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.77 inference(monotonicity,[status(thm)],[521])).
% 88.59/88.77 tff(609,plain,
% 88.59/88.77 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(symmetry,[status(thm)],[608])).
% 88.59/88.77 tff(610,plain,
% 88.59/88.77 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(quant_inst,[status(thm)],[])).
% 88.59/88.77 tff(611,plain,
% 88.59/88.77 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[610, 237])).
% 88.59/88.77 tff(612,plain,
% 88.59/88.77 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.77 inference(rewrite,[status(thm)],[])).
% 88.59/88.77 tff(613,plain,
% 88.59/88.77 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.77 inference(quant_inst,[status(thm)],[])).
% 88.59/88.77 tff(614,plain,
% 88.59/88.77 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.77 inference(modus_ponens,[status(thm)],[613, 612])).
% 88.59/88.77 tff(615,plain,
% 88.59/88.77 ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[614, 256])).
% 88.59/88.77 tff(616,plain,
% 88.59/88.77 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.77 inference(unit_resolution,[status(thm)],[615, 611])).
% 88.59/88.77 tff(617,plain,
% 88.59/88.77 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.77 inference(modus_ponens,[status(thm)],[616, 609])).
% 88.59/88.77 tff(618,plain,
% 88.59/88.77 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.77 inference(rewrite,[status(thm)],[])).
% 88.59/88.77 tff(619,plain,
% 88.59/88.77 (((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.78 inference(rewrite,[status(thm)],[])).
% 88.59/88.78 tff(620,plain,
% 88.59/88.78 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.59/88.78 inference(monotonicity,[status(thm)],[619])).
% 88.59/88.78 tff(621,plain,
% 88.59/88.78 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.78 inference(transitivity,[status(thm)],[620, 618])).
% 88.59/88.78 tff(622,plain,
% 88.59/88.78 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.78 inference(quant_inst,[status(thm)],[])).
% 88.59/88.78 tff(623,plain,
% 88.59/88.78 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(modus_ponens,[status(thm)],[622, 621])).
% 88.59/88.78 tff(624,plain,
% 88.59/88.78 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(unit_resolution,[status(thm)],[623, 287, 503])).
% 88.59/88.78 tff(625,plain,
% 88.59/88.78 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(unit_resolution,[status(thm)],[624, 617])).
% 88.59/88.78 tff(626,plain,
% 88.59/88.78 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.59/88.78 inference(rewrite,[status(thm)],[])).
% 88.59/88.78 tff(627,plain,
% 88.59/88.78 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.59/88.78 inference(quant_inst,[status(thm)],[])).
% 88.59/88.78 tff(628,plain,
% 88.59/88.78 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.78 inference(modus_ponens,[status(thm)],[627, 626])).
% 88.59/88.78 tff(629,plain,
% 88.59/88.78 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(unit_resolution,[status(thm)],[628, 163, 625, 139])).
% 88.59/88.78 tff(630,plain,
% 88.59/88.78 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(rewrite,[status(thm)],[])).
% 88.59/88.78 tff(631,plain,
% 88.59/88.78 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.78 inference(quant_inst,[status(thm)],[])).
% 88.59/88.78 tff(632,plain,
% 88.59/88.78 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.78 inference(modus_ponens,[status(thm)],[631, 630])).
% 88.59/88.78 tff(633,plain,
% 88.59/88.78 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.78 inference(unit_resolution,[status(thm)],[632, 332, 629])).
% 88.59/88.78 tff(634,plain,
% 88.59/88.78 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.78 inference(rewrite,[status(thm)],[])).
% 88.59/88.78 tff(635,plain,
% 88.59/88.78 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(rewrite,[status(thm)],[])).
% 88.59/88.79 tff(636,plain,
% 88.59/88.79 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.79 inference(monotonicity,[status(thm)],[635])).
% 88.59/88.79 tff(637,plain,
% 88.59/88.79 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(transitivity,[status(thm)],[636, 634])).
% 88.59/88.79 tff(638,plain,
% 88.59/88.79 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.59/88.79 inference(quant_inst,[status(thm)],[])).
% 88.59/88.79 tff(639,plain,
% 88.59/88.79 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.59/88.79 inference(modus_ponens,[status(thm)],[638, 637])).
% 88.59/88.79 tff(640,plain,
% 88.59/88.79 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.59/88.79 inference(unit_resolution,[status(thm)],[639, 188, 633])).
% 88.59/88.79 tff(641,plain,
% 88.59/88.79 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.59/88.79 inference(transitivity,[status(thm)],[313, 554, 553, 552, 551])).
% 88.59/88.79 tff(642,plain,
% 88.59/88.79 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.79 inference(monotonicity,[status(thm)],[641])).
% 88.59/88.79 tff(643,plain,
% 88.59/88.79 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.59/88.79 inference(transitivity,[status(thm)],[642, 640])).
% 88.59/88.79 tff(644,plain,
% 88.59/88.79 (f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(monotonicity,[status(thm)],[643])).
% 88.59/88.79 tff(645,plain,
% 88.59/88.79 (f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(symmetry,[status(thm)],[644])).
% 88.59/88.79 tff(646,plain,
% 88.59/88.79 (f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.59/88.79 inference(transitivity,[status(thm)],[645, 607, 604, 554, 553, 552, 551])).
% 88.59/88.79 tff(647,plain,
% 88.59/88.79 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(monotonicity,[status(thm)],[646])).
% 88.59/88.79 tff(648,plain,
% 88.59/88.79 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f23(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(symmetry,[status(thm)],[604])).
% 88.59/88.79 tff(649,plain,
% 88.59/88.79 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(transitivity,[status(thm)],[313, 648, 606, 644])).
% 88.59/88.79 tff(650,plain,
% 88.59/88.79 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(commutativity,[status(thm)],[])).
% 88.59/88.79 tff(651,plain,
% 88.59/88.79 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.59/88.79 inference(symmetry,[status(thm)],[650])).
% 88.59/88.79 tff(652,plain,
% 88.59/88.79 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(monotonicity,[status(thm)],[314])).
% 88.59/88.79 tff(653,plain,
% 88.59/88.79 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(symmetry,[status(thm)],[652])).
% 88.59/88.79 tff(654,plain,
% 88.59/88.79 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.79 inference(transitivity,[status(thm)],[499, 378, 375, 314])).
% 88.59/88.79 tff(655,plain,
% 88.59/88.79 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.80 inference(monotonicity,[status(thm)],[654])).
% 88.59/88.80 tff(656,plain,
% 88.59/88.80 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.59/88.80 inference(transitivity,[status(thm)],[655, 653, 651])).
% 88.59/88.80 tff(657,plain,
% 88.59/88.80 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.59/88.80 inference(monotonicity,[status(thm)],[656])).
% 88.59/88.80 tff(658,plain,
% 88.59/88.80 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.59/88.80 inference(modus_ponens,[status(thm)],[519, 657])).
% 88.59/88.80 tff(659,plain,
% 88.59/88.80 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.59/88.80 inference(transitivity,[status(thm)],[223, 212, 202, 521])).
% 88.59/88.80 tff(660,plain,
% 88.59/88.80 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.59/88.80 inference(monotonicity,[status(thm)],[659])).
% 88.59/88.80 tff(661,plain,
% 88.59/88.80 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.80 inference(symmetry,[status(thm)],[660])).
% 88.63/88.80 tff(662,plain,
% 88.63/88.80 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.80 inference(modus_ponens,[status(thm)],[616, 661])).
% 88.63/88.80 tff(663,plain,
% 88.63/88.80 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.80 inference(rewrite,[status(thm)],[])).
% 88.63/88.80 tff(664,plain,
% 88.63/88.80 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.80 inference(rewrite,[status(thm)],[])).
% 88.63/88.80 tff(665,plain,
% 88.63/88.80 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.63/88.80 inference(monotonicity,[status(thm)],[664])).
% 88.63/88.80 tff(666,plain,
% 88.63/88.80 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.80 inference(transitivity,[status(thm)],[665, 663])).
% 88.63/88.80 tff(667,plain,
% 88.63/88.80 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.63/88.80 inference(quant_inst,[status(thm)],[])).
% 88.63/88.80 tff(668,plain,
% 88.63/88.80 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.63/88.80 inference(modus_ponens,[status(thm)],[667, 666])).
% 88.63/88.80 tff(669,plain,
% 88.63/88.80 ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.63/88.80 inference(unit_resolution,[status(thm)],[668, 188])).
% 88.63/88.80 tff(670,plain,
% 88.63/88.80 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.63/88.80 inference(unit_resolution,[status(thm)],[669, 662])).
% 88.63/88.80 tff(671,plain,
% 88.63/88.80 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.63/88.80 inference(unit_resolution,[status(thm)],[670, 658])).
% 88.63/88.80 tff(672,plain,
% 88.63/88.80 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.63/88.80 inference(symmetry,[status(thm)],[671])).
% 88.63/88.80 tff(673,plain,
% 88.63/88.80 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.80 inference(monotonicity,[status(thm)],[672, 649])).
% 88.63/88.80 tff(674,plain,
% 88.63/88.80 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.63/88.80 inference(rewrite,[status(thm)],[])).
% 88.63/88.80 tff(675,plain,
% 88.63/88.80 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.63/88.80 inference(quant_inst,[status(thm)],[])).
% 88.63/88.80 tff(676,plain,
% 88.63/88.80 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.80 inference(modus_ponens,[status(thm)],[675, 674])).
% 88.63/88.80 tff(677,plain,
% 88.63/88.80 (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.80 inference(unit_resolution,[status(thm)],[676, 163, 382, 402])).
% 88.63/88.80 tff(678,plain,
% 88.63/88.80 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.80 inference(rewrite,[status(thm)],[])).
% 88.63/88.80 tff(679,plain,
% 88.63/88.80 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.81 inference(quant_inst,[status(thm)],[])).
% 88.63/88.81 tff(680,plain,
% 88.63/88.81 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.81 inference(modus_ponens,[status(thm)],[679, 678])).
% 88.63/88.81 tff(681,plain,
% 88.63/88.81 (member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.81 inference(unit_resolution,[status(thm)],[680, 332, 677])).
% 88.63/88.81 tff(682,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))))),
% 88.63/88.81 inference(rewrite,[status(thm)],[])).
% 88.63/88.81 tff(683,plain,
% 88.63/88.81 (((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))))),
% 88.63/88.81 inference(rewrite,[status(thm)],[])).
% 88.63/88.81 tff(684,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a)))))),
% 88.63/88.81 inference(monotonicity,[status(thm)],[683])).
% 88.63/88.81 tff(685,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))))),
% 88.63/88.81 inference(transitivity,[status(thm)],[684, 682])).
% 88.63/88.81 tff(686,plain,
% 88.63/88.81 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.63/88.81 inference(quant_inst,[status(thm)],[])).
% 88.63/88.81 tff(687,plain,
% 88.63/88.81 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a)))),
% 88.63/88.81 inference(modus_ponens,[status(thm)],[686, 685])).
% 88.63/88.81 tff(688,plain,
% 88.63/88.81 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))),
% 88.63/88.81 inference(unit_resolution,[status(thm)],[687, 188, 681])).
% 88.63/88.81 tff(689,plain,
% 88.63/88.81 (f19(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.81 inference(symmetry,[status(thm)],[688])).
% 88.63/88.81 tff(690,plain,
% 88.63/88.81 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.63/88.81 inference(transitivity,[status(thm)],[689, 673, 647, 518])).
% 88.63/88.81 tff(691,plain,
% 88.63/88.81 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.63/88.81 inference(monotonicity,[status(thm)],[690])).
% 88.63/88.81 tff(692,plain,
% 88.63/88.81 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.63/88.81 inference(symmetry,[status(thm)],[691])).
% 88.63/88.81 tff(693,plain,
% 88.63/88.81 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.81 inference(monotonicity,[status(thm)],[641, 641])).
% 88.63/88.81 tff(694,plain,
% 88.63/88.81 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.81 inference(symmetry,[status(thm)],[693])).
% 88.63/88.81 tff(695,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.81 inference(rewrite,[status(thm)],[])).
% 88.63/88.81 tff(696,plain,
% 88.63/88.81 (((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.81 inference(rewrite,[status(thm)],[])).
% 88.63/88.81 tff(697,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.63/88.81 inference(monotonicity,[status(thm)],[696])).
% 88.63/88.81 tff(698,plain,
% 88.63/88.81 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.82 inference(transitivity,[status(thm)],[697, 695])).
% 88.63/88.82 tff(699,plain,
% 88.63/88.82 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.82 inference(quant_inst,[status(thm)],[])).
% 88.63/88.82 tff(700,plain,
% 88.63/88.82 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.82 inference(modus_ponens,[status(thm)],[699, 698])).
% 88.63/88.82 tff(701,plain,
% 88.63/88.82 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(unit_resolution,[status(thm)],[700, 163, 139])).
% 88.63/88.82 tff(702,plain,
% 88.63/88.82 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.82 inference(rewrite,[status(thm)],[])).
% 88.63/88.82 tff(703,plain,
% 88.63/88.82 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.82 inference(quant_inst,[status(thm)],[])).
% 88.63/88.82 tff(704,plain,
% 88.63/88.82 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(modus_ponens,[status(thm)],[703, 702])).
% 88.63/88.82 tff(705,plain,
% 88.63/88.82 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(unit_resolution,[status(thm)],[704, 332, 701])).
% 88.63/88.82 tff(706,plain,
% 88.63/88.82 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(rewrite,[status(thm)],[])).
% 88.63/88.82 tff(707,plain,
% 88.63/88.82 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(rewrite,[status(thm)],[])).
% 88.63/88.82 tff(708,plain,
% 88.63/88.82 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.82 inference(monotonicity,[status(thm)],[707])).
% 88.63/88.82 tff(709,plain,
% 88.63/88.82 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(transitivity,[status(thm)],[708, 706])).
% 88.63/88.82 tff(710,plain,
% 88.63/88.82 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.82 inference(quant_inst,[status(thm)],[])).
% 88.63/88.82 tff(711,plain,
% 88.63/88.82 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.63/88.82 inference(modus_ponens,[status(thm)],[710, 709])).
% 88.63/88.82 tff(712,plain,
% 88.63/88.82 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.63/88.82 inference(unit_resolution,[status(thm)],[711, 188, 705])).
% 88.63/88.82 tff(713,plain,
% 88.63/88.82 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(symmetry,[status(thm)],[712])).
% 88.63/88.82 tff(714,plain,
% 88.63/88.82 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.82 inference(transitivity,[status(thm)],[713, 694])).
% 88.63/88.82 tff(715,plain,
% 88.63/88.82 (f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.82 inference(monotonicity,[status(thm)],[714])).
% 88.63/88.82 tff(716,plain,
% 88.63/88.82 (f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(symmetry,[status(thm)],[715])).
% 88.63/88.83 tff(717,plain,
% 88.63/88.83 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[314, 314])).
% 88.63/88.83 tff(718,plain,
% 88.63/88.83 (f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[717])).
% 88.63/88.83 tff(719,plain,
% 88.63/88.83 (f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.63/88.83 inference(transitivity,[status(thm)],[718, 716, 645, 607, 604, 554, 553, 552, 551, 525, 692, 221])).
% 88.63/88.83 tff(720,plain,
% 88.63/88.83 (f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(transitivity,[status(thm)],[718, 716, 645, 607, 604, 314])).
% 88.63/88.83 tff(721,plain,
% 88.63/88.83 ((f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[720])).
% 88.63/88.83 tff(722,plain,
% 88.63/88.83 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(symmetry,[status(thm)],[721])).
% 88.63/88.83 tff(723,plain,
% 88.63/88.83 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[722])).
% 88.63/88.83 tff(724,plain,
% 88.63/88.83 (~(f16(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(modus_ponens,[status(thm)],[198, 723])).
% 88.63/88.83 tff(725,plain,
% 88.63/88.83 ($false),
% 88.63/88.83 inference(unit_resolution,[status(thm)],[724, 719])).
% 88.63/88.83 tff(726,plain,((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.63/88.83 tff(727,plain,
% 88.63/88.83 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.63/88.83 inference(unit_resolution,[status(thm)],[726, 198])).
% 88.63/88.83 tff(728,plain,
% 88.63/88.83 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(symmetry,[status(thm)],[727])).
% 88.63/88.83 tff(729,plain,
% 88.63/88.83 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(transitivity,[status(thm)],[728, 499, 378, 375, 314])).
% 88.63/88.83 tff(730,plain,
% 88.63/88.83 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[729])).
% 88.63/88.83 tff(731,plain,
% 88.63/88.83 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(symmetry,[status(thm)],[730])).
% 88.63/88.83 tff(732,plain,
% 88.63/88.83 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(transitivity,[status(thm)],[731, 197])).
% 88.63/88.83 tff(733,plain,
% 88.63/88.83 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[732])).
% 88.63/88.83 tff(734,plain,
% 88.63/88.83 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.83 inference(modus_ponens,[status(thm)],[198, 733])).
% 88.63/88.83 tff(735,plain,
% 88.63/88.83 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.63/88.83 inference(transitivity,[status(thm)],[526, 522, 227, 211])).
% 88.63/88.83 tff(736,plain,
% 88.63/88.83 (member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[222, 735])).
% 88.63/88.83 tff(737,plain,
% 88.63/88.83 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.83 inference(symmetry,[status(thm)],[736])).
% 88.63/88.83 tff(738,plain,
% 88.63/88.83 (little_set(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> little_set(singleton_set(f19(compose(b, a))))),
% 88.63/88.83 inference(monotonicity,[status(thm)],[222])).
% 88.63/88.83 tff(739,plain,
% 88.63/88.83 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(quant_inst,[status(thm)],[])).
% 88.63/88.83 tff(740,plain,
% 88.63/88.83 (little_set(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.83 inference(unit_resolution,[status(thm)],[739, 237])).
% 88.63/88.83 tff(741,plain,
% 88.63/88.83 (little_set(singleton_set(f19(compose(b, a))))),
% 88.63/88.83 inference(modus_ponens,[status(thm)],[740, 738])).
% 88.63/88.83 tff(742,plain,
% 88.63/88.83 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.63/88.83 inference(rewrite,[status(thm)],[])).
% 88.63/88.83 tff(743,plain,
% 88.63/88.83 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.63/88.83 inference(quant_inst,[status(thm)],[])).
% 88.63/88.83 tff(744,plain,
% 88.63/88.83 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.83 inference(modus_ponens,[status(thm)],[743, 742])).
% 88.63/88.83 tff(745,plain,
% 88.63/88.83 ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.83 inference(unit_resolution,[status(thm)],[744, 135])).
% 88.63/88.83 tff(746,plain,
% 88.63/88.83 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.63/88.83 inference(unit_resolution,[status(thm)],[745, 741])).
% 88.63/88.83 tff(747,plain,
% 88.63/88.83 (member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.83 inference(modus_ponens,[status(thm)],[746, 737])).
% 88.63/88.83 tff(748,plain,
% 88.63/88.83 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(749,plain,
% 88.63/88.84 (((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(750,plain,
% 88.63/88.84 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.63/88.84 inference(monotonicity,[status(thm)],[749])).
% 88.63/88.84 tff(751,plain,
% 88.63/88.84 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.63/88.84 inference(transitivity,[status(thm)],[750, 748])).
% 88.63/88.84 tff(752,plain,
% 88.63/88.84 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.63/88.84 inference(quant_inst,[status(thm)],[])).
% 88.63/88.84 tff(753,plain,
% 88.63/88.84 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.84 inference(modus_ponens,[status(thm)],[752, 751])).
% 88.63/88.84 tff(754,plain,
% 88.63/88.84 ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[753, 188])).
% 88.63/88.84 tff(755,plain,
% 88.63/88.84 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[754, 747])).
% 88.63/88.84 tff(756,plain,
% 88.63/88.84 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[755, 734])).
% 88.63/88.84 tff(757,plain,
% 88.63/88.84 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.63/88.84 inference(symmetry,[status(thm)],[756])).
% 88.63/88.84 tff(758,plain,
% 88.63/88.84 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.84 inference(monotonicity,[status(thm)],[757])).
% 88.63/88.84 tff(759,plain,
% 88.63/88.84 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.63/88.84 inference(symmetry,[status(thm)],[758])).
% 88.63/88.84 tff(760,plain,
% 88.63/88.84 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), universal_set))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(761,plain,
% 88.63/88.84 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), universal_set))),
% 88.63/88.84 inference(quant_inst,[status(thm)],[])).
% 88.63/88.84 tff(762,plain,
% 88.63/88.84 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), universal_set)),
% 88.63/88.84 inference(modus_ponens,[status(thm)],[761, 760])).
% 88.63/88.84 tff(763,plain,
% 88.63/88.84 (member(f19(compose(b, a)), universal_set)),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[762, 149, 273])).
% 88.63/88.84 tff(764,plain,
% 88.63/88.84 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), universal_set)) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), universal_set)) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(765,plain,
% 88.63/88.84 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), universal_set)) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.63/88.84 inference(quant_inst,[status(thm)],[])).
% 88.63/88.84 tff(766,plain,
% 88.63/88.84 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), universal_set)) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.84 inference(modus_ponens,[status(thm)],[765, 764])).
% 88.63/88.84 tff(767,plain,
% 88.63/88.84 (~disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[766, 163, 763, 382])).
% 88.63/88.84 tff(768,plain,
% 88.63/88.84 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(769,plain,
% 88.63/88.84 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.63/88.84 inference(quant_inst,[status(thm)],[])).
% 88.63/88.84 tff(770,plain,
% 88.63/88.84 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.84 inference(modus_ponens,[status(thm)],[769, 768])).
% 88.63/88.84 tff(771,plain,
% 88.63/88.84 (member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.63/88.84 inference(unit_resolution,[status(thm)],[770, 174, 767])).
% 88.63/88.84 tff(772,plain,
% 88.63/88.84 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, 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(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(773,plain,
% 88.63/88.84 (((f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.63/88.84 inference(rewrite,[status(thm)],[])).
% 88.63/88.84 tff(774,plain,
% 88.63/88.84 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, 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(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))))),
% 88.68/88.84 inference(monotonicity,[status(thm)],[773])).
% 88.68/88.84 tff(775,plain,
% 88.68/88.84 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, 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(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.68/88.84 inference(transitivity,[status(thm)],[774, 772])).
% 88.68/88.84 tff(776,plain,
% 88.68/88.84 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.84 inference(quant_inst,[status(thm)],[])).
% 88.68/88.84 tff(777,plain,
% 88.68/88.84 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))),
% 88.68/88.84 inference(modus_ponens,[status(thm)],[776, 775])).
% 88.68/88.84 tff(778,plain,
% 88.68/88.84 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))),
% 88.68/88.84 inference(unit_resolution,[status(thm)],[777, 188, 771])).
% 88.68/88.84 tff(779,plain,
% 88.68/88.84 (f19(compose(b, a)) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.84 inference(symmetry,[status(thm)],[778])).
% 88.68/88.84 tff(780,plain,
% 88.68/88.84 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.68/88.84 inference(transitivity,[status(thm)],[779, 759, 195])).
% 88.68/88.84 tff(781,plain,
% 88.68/88.84 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.68/88.84 inference(monotonicity,[status(thm)],[780])).
% 88.68/88.84 tff(782,plain,
% 88.68/88.84 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.68/88.84 inference(monotonicity,[status(thm)],[781])).
% 88.68/88.84 tff(783,plain,
% 88.68/88.84 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.68/88.84 inference(symmetry,[status(thm)],[782])).
% 88.68/88.84 tff(784,plain,
% 88.68/88.84 (^[Xg: $i, Z: $i, Xf: $i] : refl(((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf)) <=> ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf)))),
% 88.68/88.84 inference(bind,[status(th)],[])).
% 88.68/88.84 tff(785,plain,
% 88.68/88.84 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf)) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))),
% 88.68/88.84 inference(quant_intro,[status(thm)],[784])).
% 88.68/88.84 tff(786,plain,
% 88.68/88.84 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf)) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))),
% 88.68/88.84 inference(rewrite,[status(thm)],[])).
% 88.68/88.84 tff(787,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose5')).
% 88.68/88.84 tff(788,plain,
% 88.68/88.84 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))),
% 88.68/88.84 inference(modus_ponens,[status(thm)],[787, 786])).
% 88.68/88.84 tff(789,plain,(
% 88.68/88.84 ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))),
% 88.68/88.84 inference(skolemize,[status(sab)],[788])).
% 88.68/88.84 tff(790,plain,
% 88.68/88.84 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))),
% 88.68/88.84 inference(modus_ponens,[status(thm)],[789, 785])).
% 88.68/88.84 tff(791,plain,
% 88.68/88.84 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b))),
% 88.68/88.84 inference(rewrite,[status(thm)],[])).
% 88.68/88.84 tff(792,plain,
% 88.68/88.84 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b))),
% 88.68/88.84 inference(quant_inst,[status(thm)],[])).
% 88.68/88.84 tff(793,plain,
% 88.68/88.84 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.68/88.84 inference(modus_ponens,[status(thm)],[792, 791])).
% 88.68/88.84 tff(794,plain,
% 88.68/88.84 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.68/88.84 inference(unit_resolution,[status(thm)],[793, 790, 117])).
% 88.68/88.84 tff(795,plain,
% 88.68/88.84 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.68/88.84 inference(modus_ponens,[status(thm)],[794, 783])).
% 88.68/88.84 tff(796,plain,
% 88.68/88.84 (^[X: $i] : refl((single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X)) <=> (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X)))),
% 88.68/88.84 inference(bind,[status(th)],[])).
% 88.68/88.84 tff(797,plain,
% 88.68/88.84 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X)) <=> ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))),
% 88.68/88.84 inference(quant_intro,[status(thm)],[796])).
% 88.68/88.84 tff(798,plain,
% 88.68/88.84 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X)) <=> ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(799,axiom,(![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set6')).
% 88.68/88.85 tff(800,plain,
% 88.68/88.85 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[799, 798])).
% 88.68/88.85 tff(801,plain,(
% 88.68/88.85 ![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))),
% 88.68/88.85 inference(skolemize,[status(sab)],[800])).
% 88.68/88.85 tff(802,plain,
% 88.68/88.85 (![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[801, 797])).
% 88.68/88.85 tff(803,plain,
% 88.68/88.85 (((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))) | (single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a)))) <=> ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))) | single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a)))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(804,plain,
% 88.68/88.85 ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))) | (single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a)))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(805,plain,
% 88.68/88.85 ((~![X: $i] : (single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X))) | single_valued_set(compose(b, a)) | member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[804, 803])).
% 88.68/88.85 tff(806,plain,
% 88.68/88.85 (member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[805, 802, 106])).
% 88.68/88.85 tff(807,plain,
% 88.68/88.85 (((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(808,plain,
% 88.68/88.85 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | (little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(809,plain,
% 88.68/88.85 ((~![Xg: $i, Z: $i, Xf: $i] : (little_set(f29(Z, Xf, Xg)) | (~member(Z, compose(Xf, Xg))))) | little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a)))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[808, 807])).
% 88.68/88.85 tff(810,plain,
% 88.68/88.85 (little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[809, 61, 806])).
% 88.68/88.85 tff(811,plain,
% 88.68/88.85 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(812,plain,
% 88.68/88.85 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(813,plain,
% 88.68/88.85 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[812, 811])).
% 88.68/88.85 tff(814,plain,
% 88.68/88.85 (member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[813, 135, 810])).
% 88.68/88.85 tff(815,plain,
% 88.68/88.85 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(816,plain,
% 88.68/88.85 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(817,plain,
% 88.68/88.85 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[816, 815])).
% 88.68/88.85 tff(818,plain,
% 88.68/88.85 (member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[817, 149, 810])).
% 88.68/88.85 tff(819,plain,
% 88.68/88.85 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(820,plain,
% 88.68/88.85 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(821,plain,
% 88.68/88.85 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), universal_set)) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[820, 819])).
% 88.68/88.85 tff(822,plain,
% 88.68/88.85 (~disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[821, 163, 818, 814])).
% 88.68/88.85 tff(823,plain,
% 88.68/88.85 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(824,plain,
% 88.68/88.85 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(825,plain,
% 88.68/88.85 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[824, 823])).
% 88.68/88.85 tff(826,plain,
% 88.68/88.85 (member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[825, 174, 822])).
% 88.68/88.85 tff(827,plain,
% 88.68/88.85 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(828,plain,
% 88.68/88.85 (((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(rewrite,[status(thm)],[])).
% 88.68/88.85 tff(829,plain,
% 88.68/88.85 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.85 inference(monotonicity,[status(thm)],[828])).
% 88.68/88.85 tff(830,plain,
% 88.68/88.85 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, 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(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.85 inference(transitivity,[status(thm)],[829, 827])).
% 88.68/88.85 tff(831,plain,
% 88.68/88.85 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.85 inference(quant_inst,[status(thm)],[])).
% 88.68/88.85 tff(832,plain,
% 88.68/88.85 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.85 inference(modus_ponens,[status(thm)],[831, 830])).
% 88.68/88.85 tff(833,plain,
% 88.68/88.85 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.68/88.85 inference(unit_resolution,[status(thm)],[832, 188, 826])).
% 88.68/88.85 tff(834,plain,
% 88.68/88.85 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(835,plain,
% 88.68/88.86 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[834, 209])).
% 88.68/88.86 tff(836,plain,
% 88.68/88.86 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(837,plain,
% 88.68/88.86 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(838,plain,
% 88.68/88.86 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | (Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.86 inference(modus_ponens,[status(thm)],[837, 836])).
% 88.68/88.86 tff(839,plain,
% 88.68/88.86 (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[838, 20, 806])).
% 88.68/88.86 tff(840,plain,
% 88.68/88.86 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)))) | (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(841,plain,
% 88.68/88.86 (ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[840, 209])).
% 88.68/88.86 tff(842,plain,
% 88.68/88.86 (non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.68/88.86 inference(symmetry,[status(thm)],[841])).
% 88.68/88.86 tff(843,plain,
% 88.68/88.86 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(844,plain,
% 88.68/88.86 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(845,plain,
% 88.68/88.86 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f19(compose(b, a)))) | member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.86 inference(modus_ponens,[status(thm)],[844, 843])).
% 88.68/88.86 tff(846,plain,
% 88.68/88.86 (member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[845, 135, 273])).
% 88.68/88.86 tff(847,plain,
% 88.68/88.86 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(848,plain,
% 88.68/88.86 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(849,plain,
% 88.68/88.86 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.86 inference(modus_ponens,[status(thm)],[848, 847])).
% 88.68/88.86 tff(850,plain,
% 88.68/88.86 (~disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[849, 163, 846, 382])).
% 88.68/88.86 tff(851,plain,
% 88.68/88.86 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(852,plain,
% 88.68/88.86 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(853,plain,
% 88.68/88.86 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.86 inference(modus_ponens,[status(thm)],[852, 851])).
% 88.68/88.86 tff(854,plain,
% 88.68/88.86 (member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[853, 174, 850])).
% 88.68/88.86 tff(855,plain,
% 88.68/88.86 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(856,plain,
% 88.68/88.86 (((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(rewrite,[status(thm)],[])).
% 88.68/88.86 tff(857,plain,
% 88.68/88.86 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.68/88.86 inference(monotonicity,[status(thm)],[856])).
% 88.68/88.86 tff(858,plain,
% 88.68/88.86 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(transitivity,[status(thm)],[857, 855])).
% 88.68/88.86 tff(859,plain,
% 88.68/88.86 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(860,plain,
% 88.68/88.86 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.86 inference(modus_ponens,[status(thm)],[859, 858])).
% 88.68/88.86 tff(861,plain,
% 88.68/88.86 (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[860, 188, 854])).
% 88.68/88.86 tff(862,assumption,(~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))), introduced(assumption)).
% 88.68/88.86 tff(863,assumption,(~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))), introduced(assumption)).
% 88.68/88.86 tff(864,plain,
% 88.68/88.86 (non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.86 inference(symmetry,[status(thm)],[835])).
% 88.68/88.86 tff(865,plain,
% 88.68/88.86 ((~![X: $i] : (singleton_set(X) = non_ordered_pair(X, X))) | (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.86 inference(quant_inst,[status(thm)],[])).
% 88.68/88.86 tff(866,plain,
% 88.68/88.86 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.86 inference(unit_resolution,[status(thm)],[865, 219])).
% 88.68/88.86 tff(867,plain,
% 88.68/88.86 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.86 inference(symmetry,[status(thm)],[866])).
% 88.68/88.86 tff(868,plain,
% 88.68/88.86 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.86 inference(monotonicity,[status(thm)],[867])).
% 88.68/88.86 tff(869,plain,
% 88.68/88.86 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.86 inference(transitivity,[status(thm)],[868, 864])).
% 88.68/88.86 tff(870,plain,
% 88.68/88.86 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.86 inference(monotonicity,[status(thm)],[869])).
% 88.68/88.86 tff(871,plain,
% 88.68/88.86 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.86 inference(symmetry,[status(thm)],[870])).
% 88.68/88.86 tff(872,plain,
% 88.68/88.86 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.87 inference(monotonicity,[status(thm)],[867, 835])).
% 88.68/88.87 tff(873,plain,
% 88.68/88.87 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(symmetry,[status(thm)],[872])).
% 88.68/88.87 tff(874,plain,
% 88.68/88.87 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(monotonicity,[status(thm)],[867])).
% 88.68/88.87 tff(875,plain,
% 88.68/88.87 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(876,plain,
% 88.68/88.87 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[875, 237])).
% 88.68/88.87 tff(877,plain,
% 88.68/88.87 (little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[876, 874])).
% 88.68/88.87 tff(878,plain,
% 88.68/88.87 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(879,plain,
% 88.68/88.87 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(880,plain,
% 88.68/88.87 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[879, 878])).
% 88.68/88.87 tff(881,plain,
% 88.68/88.87 ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[880, 135])).
% 88.68/88.87 tff(882,plain,
% 88.68/88.87 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[881, 877])).
% 88.68/88.87 tff(883,plain,
% 88.68/88.87 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[882, 873])).
% 88.68/88.87 tff(884,plain,
% 88.68/88.87 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.68/88.87 inference(symmetry,[status(thm)],[839])).
% 88.68/88.87 tff(885,plain,
% 88.68/88.87 (little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.87 inference(monotonicity,[status(thm)],[884])).
% 88.68/88.87 tff(886,plain,
% 88.68/88.87 (little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(symmetry,[status(thm)],[885])).
% 88.68/88.87 tff(887,plain,
% 88.68/88.87 (^[Y: $i, X: $i] : refl((little_set(X) | (~member(X, Y))) <=> (little_set(X) | (~member(X, Y))))),
% 88.68/88.87 inference(bind,[status(th)],[])).
% 88.68/88.87 tff(888,plain,
% 88.68/88.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(quant_intro,[status(thm)],[887])).
% 88.68/88.87 tff(889,plain,
% 88.68/88.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(890,plain,
% 88.68/88.87 (^[Y: $i, X: $i] : rewrite(((~member(X, Y)) | little_set(X)) <=> (little_set(X) | (~member(X, Y))))),
% 88.68/88.87 inference(bind,[status(th)],[])).
% 88.68/88.87 tff(891,plain,
% 88.68/88.87 (![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X)) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(quant_intro,[status(thm)],[890])).
% 88.68/88.87 tff(892,axiom,(![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','a2')).
% 88.68/88.87 tff(893,plain,
% 88.68/88.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[892, 891])).
% 88.68/88.87 tff(894,plain,
% 88.68/88.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[893, 889])).
% 88.68/88.87 tff(895,plain,(
% 88.68/88.87 ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(skolemize,[status(sab)],[894])).
% 88.68/88.87 tff(896,plain,
% 88.68/88.87 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[895, 888])).
% 88.68/88.87 tff(897,plain,
% 88.68/88.87 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(898,plain,
% 88.68/88.87 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(899,plain,
% 88.68/88.87 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[898, 897])).
% 88.68/88.87 tff(900,plain,
% 88.68/88.87 (little_set(ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[899, 896, 806])).
% 88.68/88.87 tff(901,plain,
% 88.68/88.87 (little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[900, 886])).
% 88.68/88.87 tff(902,plain,
% 88.68/88.87 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(903,plain,
% 88.68/88.87 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(904,plain,
% 88.68/88.87 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[903, 902])).
% 88.68/88.87 tff(905,plain,
% 88.68/88.87 ((~little_set(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[904, 149])).
% 88.68/88.87 tff(906,plain,
% 88.68/88.87 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[905, 901])).
% 88.68/88.87 tff(907,plain,
% 88.68/88.87 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set)))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(908,plain,
% 88.68/88.87 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set)))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(909,plain,
% 88.68/88.87 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, Y)) | (~member(Y, X)) | member(Z, sigma(X)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[908, 907])).
% 88.68/88.87 tff(910,plain,
% 88.68/88.87 ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[909, 287, 906])).
% 88.68/88.87 tff(911,plain,
% 88.68/88.87 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[910, 883])).
% 88.68/88.87 tff(912,plain,
% 88.68/88.87 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)))),
% 88.68/88.87 inference(rewrite,[status(thm)],[])).
% 88.68/88.87 tff(913,plain,
% 88.68/88.87 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set)))),
% 88.68/88.87 inference(quant_inst,[status(thm)],[])).
% 88.68/88.87 tff(914,plain,
% 88.68/88.87 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(Z, f16(Z, X)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), sigma(universal_set))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))),
% 88.68/88.87 inference(modus_ponens,[status(thm)],[913, 912])).
% 88.68/88.87 tff(915,plain,
% 88.68/88.87 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))),
% 88.68/88.87 inference(unit_resolution,[status(thm)],[914, 357, 911])).
% 88.68/88.87 tff(916,plain,
% 88.68/88.87 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.88 inference(rewrite,[status(thm)],[])).
% 88.68/88.88 tff(917,plain,
% 88.68/88.88 (((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.88 inference(rewrite,[status(thm)],[])).
% 88.68/88.88 tff(918,plain,
% 88.68/88.88 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.68/88.88 inference(monotonicity,[status(thm)],[917])).
% 88.68/88.88 tff(919,plain,
% 88.68/88.88 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.88 inference(transitivity,[status(thm)],[918, 916])).
% 88.68/88.88 tff(920,plain,
% 88.68/88.88 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.88 inference(quant_inst,[status(thm)],[])).
% 88.68/88.88 tff(921,plain,
% 88.68/88.88 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set))) | (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.88 inference(modus_ponens,[status(thm)],[920, 919])).
% 88.68/88.88 tff(922,plain,
% 88.68/88.88 (~disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.88 inference(unit_resolution,[status(thm)],[921, 163, 883, 915])).
% 88.68/88.88 tff(923,plain,
% 88.68/88.88 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.88 inference(rewrite,[status(thm)],[])).
% 88.68/88.88 tff(924,plain,
% 88.68/88.88 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.88 inference(quant_inst,[status(thm)],[])).
% 88.68/88.88 tff(925,plain,
% 88.68/88.88 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.88 inference(modus_ponens,[status(thm)],[924, 923])).
% 88.68/88.88 tff(926,plain,
% 88.68/88.88 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.88 inference(unit_resolution,[status(thm)],[925, 174, 922])).
% 88.68/88.88 tff(927,plain,
% 88.68/88.88 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.88 inference(modus_ponens,[status(thm)],[926, 871])).
% 88.68/88.88 tff(928,plain,
% 88.68/88.88 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(929,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.68/88.89 inference(quant_inst,[status(thm)],[])).
% 88.68/88.89 tff(930,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.89 inference(modus_ponens,[status(thm)],[929, 928])).
% 88.68/88.89 tff(931,plain,
% 88.68/88.89 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[930, 188])).
% 88.68/88.89 tff(932,plain,
% 88.68/88.89 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[931, 927])).
% 88.68/88.89 tff(933,plain,
% 88.68/88.89 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[932, 863])).
% 88.68/88.89 tff(934,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(935,plain,
% 88.68/88.89 (((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) <=> ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(936,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.68/88.89 inference(monotonicity,[status(thm)],[935])).
% 88.68/88.89 tff(937,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.89 inference(transitivity,[status(thm)],[936, 934])).
% 88.68/88.89 tff(938,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.89 inference(quant_inst,[status(thm)],[])).
% 88.68/88.89 tff(939,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.89 inference(modus_ponens,[status(thm)],[938, 937])).
% 88.68/88.89 tff(940,plain,
% 88.68/88.89 (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[939, 163, 846, 382])).
% 88.68/88.89 tff(941,plain,
% 88.68/88.89 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(942,plain,
% 88.68/88.89 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.89 inference(quant_inst,[status(thm)],[])).
% 88.68/88.89 tff(943,plain,
% 88.68/88.89 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.89 inference(modus_ponens,[status(thm)],[942, 941])).
% 88.68/88.89 tff(944,plain,
% 88.68/88.89 (member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[943, 332, 940])).
% 88.68/88.89 tff(945,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(946,plain,
% 88.68/88.89 (((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))))),
% 88.68/88.89 inference(rewrite,[status(thm)],[])).
% 88.68/88.89 tff(947,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a)))))),
% 88.68/88.89 inference(monotonicity,[status(thm)],[946])).
% 88.68/88.89 tff(948,plain,
% 88.68/88.89 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))))),
% 88.68/88.89 inference(transitivity,[status(thm)],[947, 945])).
% 88.68/88.89 tff(949,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.89 inference(quant_inst,[status(thm)],[])).
% 88.68/88.89 tff(950,plain,
% 88.68/88.89 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a)))),
% 88.68/88.89 inference(modus_ponens,[status(thm)],[949, 948])).
% 88.68/88.89 tff(951,plain,
% 88.68/88.89 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f19(compose(b, a))),
% 88.68/88.89 inference(unit_resolution,[status(thm)],[950, 188, 944])).
% 88.68/88.89 tff(952,assumption,(~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), introduced(assumption)).
% 88.68/88.89 tff(953,plain,
% 88.68/88.89 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.89 inference(monotonicity,[status(thm)],[222])).
% 88.68/88.89 tff(954,plain,
% 88.68/88.89 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.90 inference(transitivity,[status(thm)],[953, 842, 839])).
% 88.68/88.90 tff(955,plain,
% 88.68/88.90 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.90 inference(monotonicity,[status(thm)],[954])).
% 88.68/88.90 tff(956,plain,
% 88.68/88.90 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.90 inference(symmetry,[status(thm)],[955])).
% 88.68/88.90 tff(957,plain,
% 88.68/88.90 (member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.90 inference(modus_ponens,[status(thm)],[926, 956])).
% 88.68/88.90 tff(958,plain,
% 88.68/88.90 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.90 inference(rewrite,[status(thm)],[])).
% 88.68/88.90 tff(959,plain,
% 88.68/88.90 (((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.90 inference(rewrite,[status(thm)],[])).
% 88.68/88.90 tff(960,plain,
% 88.68/88.90 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.68/88.90 inference(monotonicity,[status(thm)],[959])).
% 88.68/88.90 tff(961,plain,
% 88.68/88.90 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.68/88.90 inference(transitivity,[status(thm)],[960, 958])).
% 88.68/88.90 tff(962,plain,
% 88.68/88.90 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.68/88.90 inference(quant_inst,[status(thm)],[])).
% 88.68/88.90 tff(963,plain,
% 88.68/88.90 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.90 inference(modus_ponens,[status(thm)],[962, 961])).
% 88.68/88.90 tff(964,plain,
% 88.68/88.90 ((~member(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[963, 188])).
% 88.68/88.91 tff(965,plain,
% 88.68/88.91 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[964, 957])).
% 88.68/88.91 tff(966,plain,
% 88.68/88.91 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[965, 952])).
% 88.68/88.91 tff(967,assumption,(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), introduced(assumption)).
% 88.68/88.91 tff(968,plain,
% 88.68/88.91 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(symmetry,[status(thm)],[967])).
% 88.68/88.91 tff(969,plain,
% 88.68/88.91 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.68/88.91 inference(transitivity,[status(thm)],[968, 966])).
% 88.68/88.91 tff(970,plain,
% 88.68/88.91 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) <=> (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.68/88.91 inference(commutativity,[status(thm)],[])).
% 88.68/88.91 tff(971,assumption,(~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), introduced(assumption)).
% 88.68/88.91 tff(972,plain,
% 88.68/88.91 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.91 inference(commutativity,[status(thm)],[])).
% 88.68/88.91 tff(973,plain,
% 88.68/88.91 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.68/88.91 inference(transitivity,[status(thm)],[554, 553, 552, 727])).
% 88.68/88.91 tff(974,plain,
% 88.68/88.91 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.68/88.91 inference(monotonicity,[status(thm)],[973])).
% 88.68/88.91 tff(975,plain,
% 88.68/88.91 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.68/88.91 inference(symmetry,[status(thm)],[974])).
% 88.68/88.91 tff(976,plain,
% 88.68/88.91 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.68/88.91 inference(rewrite,[status(thm)],[])).
% 88.68/88.91 tff(977,plain,
% 88.68/88.91 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.68/88.91 inference(quant_inst,[status(thm)],[])).
% 88.68/88.91 tff(978,plain,
% 88.68/88.91 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[977, 976])).
% 88.68/88.91 tff(979,plain,
% 88.68/88.91 (little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[978, 47, 117])).
% 88.68/88.91 tff(980,plain,
% 88.68/88.91 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.68/88.91 inference(rewrite,[status(thm)],[])).
% 88.68/88.91 tff(981,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.68/88.91 inference(quant_inst,[status(thm)],[])).
% 88.68/88.91 tff(982,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[981, 980])).
% 88.68/88.91 tff(983,plain,
% 88.68/88.91 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[982, 256, 979])).
% 88.68/88.91 tff(984,plain,
% 88.68/88.91 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[983, 975])).
% 88.68/88.91 tff(985,plain,
% 88.68/88.91 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.91 inference(rewrite,[status(thm)],[])).
% 88.68/88.91 tff(986,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.91 inference(quant_inst,[status(thm)],[])).
% 88.68/88.91 tff(987,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[986, 985])).
% 88.68/88.91 tff(988,plain,
% 88.68/88.91 (member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[987, 135, 810])).
% 88.68/88.91 tff(989,plain,
% 88.68/88.91 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.91 inference(rewrite,[status(thm)],[])).
% 88.68/88.91 tff(990,plain,
% 88.68/88.91 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.91 inference(quant_inst,[status(thm)],[])).
% 88.68/88.91 tff(991,plain,
% 88.68/88.91 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[990, 989])).
% 88.68/88.91 tff(992,plain,
% 88.68/88.91 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[991, 163, 988, 814])).
% 88.68/88.91 tff(993,plain,
% 88.68/88.91 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.91 inference(rewrite,[status(thm)],[])).
% 88.68/88.91 tff(994,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.91 inference(quant_inst,[status(thm)],[])).
% 88.68/88.91 tff(995,plain,
% 88.68/88.91 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(modus_ponens,[status(thm)],[994, 993])).
% 88.68/88.91 tff(996,plain,
% 88.68/88.91 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.91 inference(unit_resolution,[status(thm)],[995, 174, 992])).
% 88.68/88.91 tff(997,plain,
% 88.68/88.91 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.92 inference(rewrite,[status(thm)],[])).
% 88.68/88.92 tff(998,plain,
% 88.68/88.92 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.92 inference(rewrite,[status(thm)],[])).
% 88.68/88.92 tff(999,plain,
% 88.68/88.92 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.68/88.92 inference(monotonicity,[status(thm)],[998])).
% 88.68/88.92 tff(1000,plain,
% 88.68/88.92 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.92 inference(transitivity,[status(thm)],[999, 997])).
% 88.68/88.92 tff(1001,plain,
% 88.68/88.92 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.92 inference(quant_inst,[status(thm)],[])).
% 88.68/88.92 tff(1002,plain,
% 88.68/88.92 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 88.68/88.92 tff(1003,plain,
% 88.68/88.92 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.68/88.92 inference(unit_resolution,[status(thm)],[1002, 188, 996])).
% 88.68/88.92 tff(1004,assumption,(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))), introduced(assumption)).
% 88.68/88.92 tff(1005,assumption,(member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), introduced(assumption)).
% 88.68/88.92 tff(1006,assumption,(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), introduced(assumption)).
% 88.68/88.92 tff(1007,plain,
% 88.68/88.92 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.68/88.92 inference(symmetry,[status(thm)],[970])).
% 88.68/88.92 tff(1008,assumption,(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), introduced(assumption)).
% 88.68/88.92 tff(1009,plain,
% 88.68/88.92 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.92 inference(symmetry,[status(thm)],[1008])).
% 88.68/88.92 tff(1010,plain,
% 88.68/88.92 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.68/88.92 inference(transitivity,[status(thm)],[1009, 1004])).
% 88.68/88.92 tff(1011,plain,
% 88.68/88.92 (member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.92 inference(monotonicity,[status(thm)],[1010])).
% 88.68/88.92 tff(1012,plain,
% 88.68/88.92 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.92 inference(symmetry,[status(thm)],[1011])).
% 88.68/88.92 tff(1013,plain,
% 88.68/88.92 (^[X: $i] : refl((single_valued_set(X) | little_set(f21(X))) <=> (single_valued_set(X) | little_set(f21(X))))),
% 88.68/88.92 inference(bind,[status(th)],[])).
% 88.68/88.92 tff(1014,plain,
% 88.68/88.92 (![X: $i] : (single_valued_set(X) | little_set(f21(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f21(X)))),
% 88.68/88.92 inference(quant_intro,[status(thm)],[1013])).
% 88.68/88.92 tff(1015,plain,
% 88.68/88.92 (![X: $i] : (single_valued_set(X) | little_set(f21(X))) <=> ![X: $i] : (single_valued_set(X) | little_set(f21(X)))),
% 88.68/88.92 inference(rewrite,[status(thm)],[])).
% 88.68/88.92 tff(1016,axiom,(![X: $i] : (single_valued_set(X) | little_set(f21(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set4')).
% 88.68/88.92 tff(1017,plain,
% 88.68/88.92 (![X: $i] : (single_valued_set(X) | little_set(f21(X)))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 88.68/88.92 tff(1018,plain,(
% 88.68/88.92 ![X: $i] : (single_valued_set(X) | little_set(f21(X)))),
% 88.68/88.92 inference(skolemize,[status(sab)],[1017])).
% 88.68/88.92 tff(1019,plain,
% 88.68/88.92 (![X: $i] : (single_valued_set(X) | little_set(f21(X)))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1018, 1014])).
% 88.68/88.92 tff(1020,plain,
% 88.68/88.92 (((~![X: $i] : (single_valued_set(X) | little_set(f21(X)))) | (single_valued_set(compose(b, a)) | little_set(f21(compose(b, a))))) <=> ((~![X: $i] : (single_valued_set(X) | little_set(f21(X)))) | single_valued_set(compose(b, a)) | little_set(f21(compose(b, a))))),
% 88.68/88.92 inference(rewrite,[status(thm)],[])).
% 88.68/88.92 tff(1021,plain,
% 88.68/88.92 ((~![X: $i] : (single_valued_set(X) | little_set(f21(X)))) | (single_valued_set(compose(b, a)) | little_set(f21(compose(b, a))))),
% 88.68/88.92 inference(quant_inst,[status(thm)],[])).
% 88.68/88.92 tff(1022,plain,
% 88.68/88.92 ((~![X: $i] : (single_valued_set(X) | little_set(f21(X)))) | single_valued_set(compose(b, a)) | little_set(f21(compose(b, a)))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 88.68/88.92 tff(1023,plain,
% 88.68/88.92 (little_set(f21(compose(b, a)))),
% 88.68/88.92 inference(unit_resolution,[status(thm)],[1022, 1019, 106])).
% 88.68/88.92 tff(1024,plain,
% 88.68/88.92 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f21(compose(b, a)))) | member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f21(compose(b, a)))) | member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.92 inference(rewrite,[status(thm)],[])).
% 88.68/88.92 tff(1025,plain,
% 88.68/88.92 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f21(compose(b, a)))) | member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.92 inference(quant_inst,[status(thm)],[])).
% 88.68/88.92 tff(1026,plain,
% 88.68/88.92 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f21(compose(b, a)))) | member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 88.68/88.92 tff(1027,plain,
% 88.68/88.92 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.92 inference(unit_resolution,[status(thm)],[1026, 256, 1023])).
% 88.68/88.92 tff(1028,plain,
% 88.68/88.92 (member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.92 inference(modus_ponens,[status(thm)],[1027, 1012])).
% 88.68/88.92 tff(1029,plain,
% 88.68/88.92 ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a)))),
% 88.68/88.92 inference(commutativity,[status(thm)],[])).
% 88.68/88.92 tff(1030,plain,
% 88.68/88.92 ((f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.68/88.92 inference(symmetry,[status(thm)],[1029])).
% 88.68/88.92 tff(1031,plain,
% 88.68/88.92 (f19(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.92 inference(symmetry,[status(thm)],[861])).
% 88.68/88.92 tff(1032,plain,
% 88.68/88.92 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.68/88.92 inference(symmetry,[status(thm)],[1006])).
% 88.68/88.92 tff(1033,plain,
% 88.68/88.92 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.92 inference(monotonicity,[status(thm)],[1032])).
% 88.68/88.92 tff(1034,plain,
% 88.68/88.92 (non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.92 inference(transitivity,[status(thm)],[868, 864, 884, 841])).
% 88.68/88.92 tff(1035,plain,
% 88.68/88.92 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.68/88.92 inference(transitivity,[status(thm)],[1032, 222])).
% 88.68/88.92 tff(1036,plain,
% 88.68/88.92 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.92 inference(monotonicity,[status(thm)],[1035, 1034])).
% 88.68/88.92 tff(1037,plain,
% 88.68/88.92 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.93 inference(symmetry,[status(thm)],[1036])).
% 88.68/88.93 tff(1038,plain,
% 88.68/88.93 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1039,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1040,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 88.68/88.93 tff(1041,plain,
% 88.68/88.93 ((~little_set(singleton_set(f19(compose(b, a))))) | member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1040, 135])).
% 88.68/88.93 tff(1042,plain,
% 88.68/88.93 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1041, 741])).
% 88.68/88.93 tff(1043,plain,
% 88.68/88.93 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1042, 1037])).
% 88.68/88.93 tff(1044,plain,
% 88.68/88.93 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(monotonicity,[status(thm)],[1032])).
% 88.68/88.93 tff(1045,plain,
% 88.68/88.93 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.68/88.93 inference(transitivity,[status(thm)],[1044, 972])).
% 88.68/88.93 tff(1046,plain,
% 88.68/88.93 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(symmetry,[status(thm)],[1045])).
% 88.68/88.93 tff(1047,plain,
% 88.68/88.93 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(monotonicity,[status(thm)],[954])).
% 88.68/88.93 tff(1048,plain,
% 88.68/88.93 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(symmetry,[status(thm)],[1047])).
% 88.68/88.93 tff(1049,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1050,plain,
% 88.68/88.93 (little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1049, 237])).
% 88.68/88.93 tff(1051,plain,
% 88.68/88.93 (((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set))) <=> ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1052,plain,
% 88.68/88.93 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1053,plain,
% 88.68/88.93 ((~![Z: $i] : ((~little_set(Z)) | member(Z, universal_set))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 88.68/88.93 tff(1054,plain,
% 88.68/88.93 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1053, 149, 1050])).
% 88.68/88.93 tff(1055,plain,
% 88.68/88.93 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.93 inference(transitivity,[status(thm)],[884, 841])).
% 88.68/88.93 tff(1056,plain,
% 88.68/88.93 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(monotonicity,[status(thm)],[1055])).
% 88.68/88.93 tff(1057,plain,
% 88.68/88.93 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(symmetry,[status(thm)],[1056])).
% 88.68/88.93 tff(1058,plain,
% 88.68/88.93 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1059,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1060,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 88.68/88.93 tff(1061,plain,
% 88.68/88.93 ((~little_set(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1060, 256])).
% 88.68/88.93 tff(1062,plain,
% 88.68/88.93 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1061, 1050])).
% 88.68/88.93 tff(1063,plain,
% 88.68/88.93 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1062, 1057])).
% 88.68/88.93 tff(1064,plain,
% 88.68/88.93 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1065,plain,
% 88.68/88.93 (((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1066,plain,
% 88.68/88.93 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.68/88.93 inference(monotonicity,[status(thm)],[1065])).
% 88.68/88.93 tff(1067,plain,
% 88.68/88.93 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.93 inference(transitivity,[status(thm)],[1066, 1064])).
% 88.68/88.93 tff(1068,plain,
% 88.68/88.93 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1069,plain,
% 88.68/88.93 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), universal_set)) | (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 88.68/88.93 tff(1070,plain,
% 88.68/88.93 (~disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1069, 163, 1063, 1054])).
% 88.68/88.93 tff(1071,plain,
% 88.68/88.93 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.93 inference(rewrite,[status(thm)],[])).
% 88.68/88.93 tff(1072,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.68/88.93 inference(quant_inst,[status(thm)],[])).
% 88.68/88.93 tff(1073,plain,
% 88.68/88.93 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 88.68/88.93 tff(1074,plain,
% 88.68/88.93 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.68/88.93 inference(unit_resolution,[status(thm)],[1073, 174, 1070])).
% 88.68/88.93 tff(1075,plain,
% 88.68/88.93 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.93 inference(modus_ponens,[status(thm)],[1074, 1048])).
% 88.68/88.93 tff(1076,plain,
% 88.68/88.93 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.94 inference(rewrite,[status(thm)],[])).
% 88.68/88.94 tff(1077,plain,
% 88.68/88.94 (((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.94 inference(rewrite,[status(thm)],[])).
% 88.68/88.94 tff(1078,plain,
% 88.68/88.94 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.68/88.94 inference(monotonicity,[status(thm)],[1077])).
% 88.68/88.94 tff(1079,plain,
% 88.68/88.94 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.68/88.94 inference(transitivity,[status(thm)],[1078, 1076])).
% 88.68/88.94 tff(1080,plain,
% 88.68/88.94 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.68/88.94 inference(quant_inst,[status(thm)],[])).
% 88.68/88.94 tff(1081,plain,
% 88.68/88.94 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.68/88.94 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 88.68/88.94 tff(1082,plain,
% 88.68/88.94 ((~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.94 inference(unit_resolution,[status(thm)],[1081, 188])).
% 88.78/88.94 tff(1083,plain,
% 88.78/88.94 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.94 inference(unit_resolution,[status(thm)],[1082, 1075])).
% 88.78/88.94 tff(1084,plain,
% 88.78/88.94 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.78/88.94 inference(unit_resolution,[status(thm)],[1083, 971])).
% 88.78/88.94 tff(1085,plain,
% 88.78/88.94 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.94 inference(symmetry,[status(thm)],[1084])).
% 88.78/88.94 tff(1086,plain,
% 88.78/88.94 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.94 inference(transitivity,[status(thm)],[1009, 1004, 1085])).
% 88.78/88.94 tff(1087,plain,
% 88.78/88.94 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.78/88.94 inference(monotonicity,[status(thm)],[1086])).
% 88.78/88.94 tff(1088,plain,
% 88.78/88.94 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.78/88.94 inference(symmetry,[status(thm)],[1087])).
% 88.78/88.94 tff(1089,plain,
% 88.78/88.94 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.94 inference(transitivity,[status(thm)],[1088, 1046])).
% 88.78/88.94 tff(1090,plain,
% 88.78/88.94 ((~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.94 inference(monotonicity,[status(thm)],[1089])).
% 88.78/88.94 tff(1091,plain,
% 88.78/88.94 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.94 inference(modus_ponens,[status(thm)],[971, 1090])).
% 88.78/88.94 tff(1092,plain,
% 88.78/88.94 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.94 inference(rewrite,[status(thm)],[])).
% 88.78/88.94 tff(1093,plain,
% 88.78/88.94 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.95 inference(rewrite,[status(thm)],[])).
% 88.78/88.95 tff(1094,plain,
% 88.78/88.95 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1093])).
% 88.78/88.95 tff(1095,plain,
% 88.78/88.95 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1094, 1092])).
% 88.78/88.95 tff(1096,plain,
% 88.78/88.95 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.78/88.95 inference(quant_inst,[status(thm)],[])).
% 88.78/88.95 tff(1097,plain,
% 88.78/88.95 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.95 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 88.78/88.95 tff(1098,plain,
% 88.78/88.95 ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.95 inference(unit_resolution,[status(thm)],[1097, 188])).
% 88.78/88.95 tff(1099,plain,
% 88.78/88.95 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.95 inference(unit_resolution,[status(thm)],[1098, 1091, 1043])).
% 88.78/88.95 tff(1100,plain,
% 88.78/88.95 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.95 inference(symmetry,[status(thm)],[1099])).
% 88.78/88.95 tff(1101,plain,
% 88.78/88.95 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1100])).
% 88.78/88.95 tff(1102,plain,
% 88.78/88.95 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.95 inference(symmetry,[status(thm)],[833])).
% 88.78/88.95 tff(1103,plain,
% 88.78/88.95 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1102, 1101, 1033, 778, 1031])).
% 88.78/88.95 tff(1104,plain,
% 88.78/88.95 ((f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1103])).
% 88.78/88.95 tff(1105,plain,
% 88.78/88.95 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a)))),
% 88.78/88.95 inference(symmetry,[status(thm)],[1104])).
% 88.78/88.95 tff(1106,plain,
% 88.78/88.95 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1105, 1030])).
% 88.78/88.95 tff(1107,plain,
% 88.78/88.95 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1106])).
% 88.78/88.95 tff(1108,plain,
% 88.78/88.95 ((f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.78/88.95 inference(commutativity,[status(thm)],[])).
% 88.78/88.95 tff(1109,plain,
% 88.78/88.95 ((f21(compose(b, a)) = f19(compose(b, a))) <=> (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1031])).
% 88.78/88.95 tff(1110,plain,
% 88.78/88.95 ((f21(compose(b, a)) = f19(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1109, 1108])).
% 88.78/88.95 tff(1111,plain,
% 88.78/88.95 ((~(f21(compose(b, a)) = f19(compose(b, a)))) <=> (~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1110])).
% 88.78/88.95 tff(1112,assumption,(f21(compose(b, a)) = f19(compose(b, a))), introduced(assumption)).
% 88.78/88.95 tff(1113,plain,
% 88.78/88.95 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1112])).
% 88.78/88.95 tff(1114,plain,
% 88.78/88.95 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1084, 1113])).
% 88.78/88.95 tff(1115,plain,
% 88.78/88.95 ($false),
% 88.78/88.95 inference(unit_resolution,[status(thm)],[971, 1114])).
% 88.78/88.95 tff(1116,plain,((~(f21(compose(b, a)) = f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.78/88.95 tff(1117,plain,
% 88.78/88.95 (~(f21(compose(b, a)) = f19(compose(b, a)))),
% 88.78/88.95 inference(unit_resolution,[status(thm)],[1116, 971])).
% 88.78/88.95 tff(1118,plain,
% 88.78/88.95 (~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.78/88.95 inference(modus_ponens,[status(thm)],[1117, 1111])).
% 88.78/88.95 tff(1119,plain,
% 88.78/88.95 (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.95 inference(modus_ponens,[status(thm)],[1118, 1107])).
% 88.78/88.95 tff(1120,plain,
% 88.78/88.95 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.95 inference(rewrite,[status(thm)],[])).
% 88.78/88.95 tff(1121,plain,
% 88.78/88.95 (((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.95 inference(rewrite,[status(thm)],[])).
% 88.78/88.95 tff(1122,plain,
% 88.78/88.95 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.78/88.95 inference(monotonicity,[status(thm)],[1121])).
% 88.78/88.95 tff(1123,plain,
% 88.78/88.95 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.95 inference(transitivity,[status(thm)],[1122, 1120])).
% 88.78/88.95 tff(1124,plain,
% 88.78/88.95 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.95 inference(quant_inst,[status(thm)],[])).
% 88.78/88.95 tff(1125,plain,
% 88.78/88.95 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 88.78/88.96 tff(1126,plain,
% 88.78/88.96 ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1125, 188])).
% 88.78/88.96 tff(1127,plain,
% 88.78/88.96 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1126, 1119, 1028])).
% 88.78/88.96 tff(1128,plain,
% 88.78/88.96 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.78/88.96 inference(symmetry,[status(thm)],[1127])).
% 88.78/88.96 tff(1129,plain,
% 88.78/88.96 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.78/88.96 inference(symmetry,[status(thm)],[1033])).
% 88.78/88.96 tff(1130,plain,
% 88.78/88.96 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.78/88.96 inference(transitivity,[status(thm)],[779, 1129, 195])).
% 88.78/88.96 tff(1131,plain,
% 88.78/88.96 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1130])).
% 88.78/88.96 tff(1132,plain,
% 88.78/88.96 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1131])).
% 88.78/88.96 tff(1133,plain,
% 88.78/88.96 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(symmetry,[status(thm)],[1132])).
% 88.78/88.96 tff(1134,plain,
% 88.78/88.96 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[794, 1133])).
% 88.78/88.96 tff(1135,plain,
% 88.78/88.96 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.96 inference(symmetry,[status(thm)],[1101])).
% 88.78/88.96 tff(1136,plain,
% 88.78/88.96 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.78/88.96 inference(transitivity,[status(thm)],[779, 1129, 1135, 833])).
% 88.78/88.96 tff(1137,plain,
% 88.78/88.96 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1136])).
% 88.78/88.96 tff(1138,plain,
% 88.78/88.96 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1137])).
% 88.78/88.96 tff(1139,plain,
% 88.78/88.96 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(symmetry,[status(thm)],[1138])).
% 88.78/88.96 tff(1140,plain,
% 88.78/88.96 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1141,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b))),
% 88.78/88.96 inference(quant_inst,[status(thm)],[])).
% 88.78/88.96 tff(1142,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 88.78/88.96 tff(1143,plain,
% 88.78/88.96 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1142, 790, 806])).
% 88.78/88.96 tff(1144,plain,
% 88.78/88.96 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 88.78/88.96 tff(1145,plain,
% 88.78/88.96 (^[Xg: $i, Z: $i, Xf: $i] : refl(((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg))) <=> ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg))))),
% 88.78/88.96 inference(bind,[status(th)],[])).
% 88.78/88.96 tff(1146,plain,
% 88.78/88.96 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))),
% 88.78/88.96 inference(quant_intro,[status(thm)],[1145])).
% 88.78/88.96 tff(1147,plain,
% 88.78/88.96 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg))) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1148,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose3')).
% 88.78/88.96 tff(1149,plain,
% 88.78/88.96 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 88.78/88.96 tff(1150,plain,(
% 88.78/88.96 ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))),
% 88.78/88.96 inference(skolemize,[status(sab)],[1149])).
% 88.78/88.96 tff(1151,plain,
% 88.78/88.96 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1150, 1146])).
% 88.78/88.96 tff(1152,plain,
% 88.78/88.96 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1153,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.78/88.96 inference(quant_inst,[status(thm)],[])).
% 88.78/88.96 tff(1154,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 88.78/88.96 tff(1155,plain,
% 88.78/88.96 (little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1154, 1151, 117])).
% 88.78/88.96 tff(1156,plain,
% 88.78/88.96 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1157,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.96 inference(quant_inst,[status(thm)],[])).
% 88.78/88.96 tff(1158,plain,
% 88.78/88.96 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f31(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 88.78/88.96 tff(1159,plain,
% 88.78/88.96 (little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1158, 1151, 806])).
% 88.78/88.96 tff(1160,plain,
% 88.78/88.96 (function(b) <=> function(b)),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1161,axiom,(function(b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_function')).
% 88.78/88.96 tff(1162,plain,
% 88.78/88.96 (function(b)),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 88.78/88.96 tff(1163,plain,
% 88.78/88.96 (^[Xf: $i] : refl(((~function(Xf)) | single_valued_set(Xf)) <=> ((~function(Xf)) | single_valued_set(Xf)))),
% 88.78/88.96 inference(bind,[status(th)],[])).
% 88.78/88.96 tff(1164,plain,
% 88.78/88.96 (![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf)) <=> ![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))),
% 88.78/88.96 inference(quant_intro,[status(thm)],[1163])).
% 88.78/88.96 tff(1165,plain,
% 88.78/88.96 (![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf)) <=> ![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1166,axiom,(![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','function2')).
% 88.78/88.96 tff(1167,plain,
% 88.78/88.96 (![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 88.78/88.96 tff(1168,plain,(
% 88.78/88.96 ![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))),
% 88.78/88.96 inference(skolemize,[status(sab)],[1167])).
% 88.78/88.96 tff(1169,plain,
% 88.78/88.96 (![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1168, 1164])).
% 88.78/88.96 tff(1170,plain,
% 88.78/88.96 (((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | ((~function(b)) | single_valued_set(b))) <=> ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | (~function(b)) | single_valued_set(b))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1171,plain,
% 88.78/88.96 ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | ((~function(b)) | single_valued_set(b))),
% 88.78/88.96 inference(quant_inst,[status(thm)],[])).
% 88.78/88.96 tff(1172,plain,
% 88.78/88.96 ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | (~function(b)) | single_valued_set(b)),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 88.78/88.96 tff(1173,plain,
% 88.78/88.96 (single_valued_set(b)),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1172, 1169, 1162])).
% 88.78/88.96 tff(1174,plain,
% 88.78/88.96 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))))),
% 88.78/88.96 inference(bind,[status(th)],[])).
% 88.78/88.96 tff(1175,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(quant_intro,[status(thm)],[1174])).
% 88.78/88.96 tff(1176,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1177,plain,
% 88.78/88.96 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~single_valued_set(X)) | (~little_set(U))) <=> ((~little_set(U)) | (~single_valued_set(X)))), ((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) <=> (((~little_set(U)) | (~single_valued_set(X))) | (~little_set(V))))), rewrite((((~little_set(U)) | (~single_valued_set(X))) | (~little_set(V))) <=> ((~little_set(U)) | (~little_set(V)) | (~single_valued_set(X)))), ((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) <=> ((~little_set(U)) | (~little_set(V)) | (~single_valued_set(X))))), (((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) <=> (((~little_set(U)) | (~little_set(V)) | (~single_valued_set(X))) | (~little_set(W))))), rewrite((((~little_set(U)) | (~little_set(V)) | (~single_valued_set(X))) | (~little_set(W))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~single_valued_set(X)))), (((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~single_valued_set(X))))), ((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) <=> (((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~single_valued_set(X))) | (~member(ordered_pair(U, V), X))))), rewrite((((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~single_valued_set(X))) | (~member(ordered_pair(U, V), X))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))), ((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))))), (((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) <=> (((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) | (~member(ordered_pair(U, W), X))))), rewrite((((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) | (~member(ordered_pair(U, W), X))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))), (((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))))), ((((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) | (V = W)) <=> (((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) | (V = W)))), rewrite((((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X))) | (V = W)) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))), ((((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) | (V = W)) <=> ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))))),
% 88.78/88.96 inference(bind,[status(th)],[])).
% 88.78/88.96 tff(1178,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : (((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(quant_intro,[status(thm)],[1177])).
% 88.78/88.96 tff(1179,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~single_valued_set(X)) | (~little_set(U))) | (~little_set(V))) | (~little_set(W))) | (~member(ordered_pair(U, V), X))) | (~member(ordered_pair(U, W), X))) | (V = W))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set1')).
% 88.78/88.96 tff(1180,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 88.78/88.96 tff(1181,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1180, 1176])).
% 88.78/88.96 tff(1182,plain,(
% 88.78/88.96 ![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(skolemize,[status(sab)],[1181])).
% 88.78/88.96 tff(1183,plain,
% 88.78/88.96 (![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1182, 1175])).
% 88.78/88.96 tff(1184,plain,
% 88.78/88.96 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1185,plain,
% 88.78/88.96 (((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b))) <=> ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b)))),
% 88.78/88.96 inference(rewrite,[status(thm)],[])).
% 88.78/88.96 tff(1186,plain,
% 88.78/88.96 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b))))),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1185])).
% 88.78/88.96 tff(1187,plain,
% 88.78/88.96 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b)))),
% 88.78/88.96 inference(transitivity,[status(thm)],[1186, 1184])).
% 88.78/88.96 tff(1188,plain,
% 88.78/88.96 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))),
% 88.78/88.96 inference(quant_inst,[status(thm)],[])).
% 88.78/88.96 tff(1189,plain,
% 88.78/88.96 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~single_valued_set(b))),
% 88.78/88.96 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 88.78/88.96 tff(1190,plain,
% 88.78/88.96 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.78/88.96 inference(unit_resolution,[status(thm)],[1189, 1183, 1173, 273, 1159, 1155, 1144, 1134])).
% 88.78/88.96 tff(1191,plain,
% 88.78/88.96 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.78/88.96 inference(symmetry,[status(thm)],[1190])).
% 88.78/88.96 tff(1192,plain,
% 88.78/88.96 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.96 inference(monotonicity,[status(thm)],[1191])).
% 88.78/88.96 tff(1193,plain,
% 88.78/88.96 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(monotonicity,[status(thm)],[1192])).
% 88.78/88.97 tff(1194,plain,
% 88.78/88.97 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(symmetry,[status(thm)],[1193])).
% 88.78/88.97 tff(1195,plain,
% 88.78/88.97 (^[Xg: $i, Z: $i, Xf: $i] : refl(((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg)) <=> ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg)))),
% 88.78/88.97 inference(bind,[status(th)],[])).
% 88.78/88.97 tff(1196,plain,
% 88.78/88.97 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg)) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))),
% 88.78/88.97 inference(quant_intro,[status(thm)],[1195])).
% 88.78/88.97 tff(1197,plain,
% 88.78/88.97 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg)) <=> ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1198,axiom,(![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','compose6')).
% 88.78/88.97 tff(1199,plain,
% 88.78/88.97 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 88.78/88.97 tff(1200,plain,(
% 88.78/88.97 ![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))),
% 88.78/88.97 inference(skolemize,[status(sab)],[1199])).
% 88.78/88.97 tff(1201,plain,
% 88.78/88.97 (![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1200, 1196])).
% 88.78/88.97 tff(1202,plain,
% 88.78/88.97 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1203,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | ((~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a))),
% 88.78/88.97 inference(quant_inst,[status(thm)],[])).
% 88.78/88.97 tff(1204,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | (~member(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 88.78/88.97 tff(1205,plain,
% 88.78/88.97 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(unit_resolution,[status(thm)],[1204, 1201, 117])).
% 88.78/88.97 tff(1206,plain,
% 88.78/88.97 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1205, 1194])).
% 88.78/88.97 tff(1207,plain,
% 88.78/88.97 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1208,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.97 inference(quant_inst,[status(thm)],[])).
% 88.78/88.97 tff(1209,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | little_set(f30(Z, Xf, Xg)))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 88.78/88.97 tff(1210,plain,
% 88.78/88.97 (little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.97 inference(unit_resolution,[status(thm)],[1209, 47, 806])).
% 88.78/88.97 tff(1211,plain,
% 88.78/88.97 (((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a))) <=> ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1212,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | ((~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a))),
% 88.78/88.97 inference(quant_inst,[status(thm)],[])).
% 88.78/88.97 tff(1213,plain,
% 88.78/88.97 ((~![Xg: $i, Z: $i, Xf: $i] : ((~member(Z, compose(Xf, Xg))) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg))) | (~member(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), compose(b, a))) | member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 88.78/88.97 tff(1214,plain,
% 88.78/88.97 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 88.78/88.97 inference(unit_resolution,[status(thm)],[1213, 1201, 806])).
% 88.78/88.97 tff(1215,plain,
% 88.78/88.97 (function(a) <=> function(a)),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1216,axiom,(function(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_function')).
% 88.78/88.97 tff(1217,plain,
% 88.78/88.97 (function(a)),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 88.78/88.97 tff(1218,plain,
% 88.78/88.97 (((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | ((~function(a)) | single_valued_set(a))) <=> ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | (~function(a)) | single_valued_set(a))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1219,plain,
% 88.78/88.97 ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | ((~function(a)) | single_valued_set(a))),
% 88.78/88.97 inference(quant_inst,[status(thm)],[])).
% 88.78/88.97 tff(1220,plain,
% 88.78/88.97 ((~![Xf: $i] : ((~function(Xf)) | single_valued_set(Xf))) | (~function(a)) | single_valued_set(a)),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 88.78/88.97 tff(1221,plain,
% 88.78/88.97 (single_valued_set(a)),
% 88.78/88.97 inference(unit_resolution,[status(thm)],[1220, 1169, 1217])).
% 88.78/88.97 tff(1222,plain,
% 88.78/88.97 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1223,plain,
% 88.78/88.97 (((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a))) <=> ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1224,plain,
% 88.78/88.97 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.97 inference(monotonicity,[status(thm)],[1223])).
% 88.78/88.97 tff(1225,plain,
% 88.78/88.97 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.97 inference(transitivity,[status(thm)],[1224, 1222])).
% 88.78/88.97 tff(1226,plain,
% 88.78/88.97 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))),
% 88.78/88.97 inference(quant_inst,[status(thm)],[])).
% 88.78/88.97 tff(1227,plain,
% 88.78/88.97 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 88.78/88.97 tff(1228,plain,
% 88.78/88.97 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.78/88.97 inference(unit_resolution,[status(thm)],[1227, 1183, 1221, 1214, 1159, 1210, 979, 1206])).
% 88.78/88.97 tff(1229,plain,
% 88.78/88.97 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.78/88.97 inference(transitivity,[status(thm)],[1228, 1128])).
% 88.78/88.97 tff(1230,plain,
% 88.78/88.97 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f20(compose(b, a)) = f21(compose(b, a)))),
% 88.78/88.97 inference(monotonicity,[status(thm)],[1229])).
% 88.78/88.97 tff(1231,plain,
% 88.78/88.97 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.78/88.97 inference(symmetry,[status(thm)],[1230])).
% 88.78/88.97 tff(1232,plain,
% 88.78/88.97 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.78/88.97 inference(transitivity,[status(thm)],[1231, 1007])).
% 88.78/88.97 tff(1233,plain,
% 88.78/88.97 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))))),
% 88.78/88.97 inference(monotonicity,[status(thm)],[1232])).
% 88.78/88.97 tff(1234,plain,
% 88.78/88.97 (^[X: $i] : refl((single_valued_set(X) | (~(f20(X) = f21(X)))) <=> (single_valued_set(X) | (~(f20(X) = f21(X)))))),
% 88.78/88.97 inference(bind,[status(th)],[])).
% 88.78/88.97 tff(1235,plain,
% 88.78/88.97 (![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X)))) <=> ![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))),
% 88.78/88.97 inference(quant_intro,[status(thm)],[1234])).
% 88.78/88.97 tff(1236,plain,
% 88.78/88.97 (![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X)))) <=> ![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))),
% 88.78/88.97 inference(rewrite,[status(thm)],[])).
% 88.78/88.97 tff(1237,axiom,(![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))), file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax','single_valued_set7')).
% 88.78/88.97 tff(1238,plain,
% 88.78/88.97 (![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 88.78/88.97 tff(1239,plain,(
% 88.78/88.97 ![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))),
% 88.78/88.97 inference(skolemize,[status(sab)],[1238])).
% 88.78/88.97 tff(1240,plain,
% 88.78/88.97 (![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))),
% 88.78/88.97 inference(modus_ponens,[status(thm)],[1239, 1235])).
% 88.78/88.97 tff(1241,plain,
% 88.78/88.97 (((~![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))) | (single_valued_set(compose(b, a)) | (~(f20(compose(b, a)) = f21(compose(b, a)))))) <=> ((~![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))) | single_valued_set(compose(b, a)) | (~(f20(compose(b, a)) = f21(compose(b, a)))))),
% 88.78/88.98 inference(rewrite,[status(thm)],[])).
% 88.78/88.98 tff(1242,plain,
% 88.78/88.98 ((~![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))) | (single_valued_set(compose(b, a)) | (~(f20(compose(b, a)) = f21(compose(b, a)))))),
% 88.78/88.98 inference(quant_inst,[status(thm)],[])).
% 88.78/88.98 tff(1243,plain,
% 88.78/88.98 ((~![X: $i] : (single_valued_set(X) | (~(f20(X) = f21(X))))) | single_valued_set(compose(b, a)) | (~(f20(compose(b, a)) = f21(compose(b, a))))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 88.78/88.98 tff(1244,plain,
% 88.78/88.98 (~(f20(compose(b, a)) = f21(compose(b, a)))),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[1243, 1240, 106])).
% 88.78/88.98 tff(1245,plain,
% 88.78/88.98 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1244, 1233])).
% 88.78/88.98 tff(1246,plain,
% 88.78/88.98 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1228])).
% 88.78/88.98 tff(1247,plain,
% 88.78/88.98 ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.78/88.98 inference(symmetry,[status(thm)],[1246])).
% 88.78/88.98 tff(1248,plain,
% 88.78/88.98 ((~(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1247])).
% 88.78/88.98 tff(1249,plain,
% 88.78/88.98 ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1128, 1031])).
% 88.78/88.98 tff(1250,plain,
% 88.78/88.98 ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.78/88.98 inference(transitivity,[status(thm)],[1249, 1108])).
% 88.78/88.98 tff(1251,plain,
% 88.78/88.98 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.78/88.98 inference(symmetry,[status(thm)],[1250])).
% 88.78/88.98 tff(1252,plain,
% 88.78/88.98 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1251])).
% 88.78/88.98 tff(1253,plain,
% 88.78/88.98 (~(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1118, 1252])).
% 88.78/88.98 tff(1254,plain,
% 88.78/88.98 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1253, 1248])).
% 88.78/88.98 tff(1255,plain,
% 88.78/88.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.78/88.98 inference(rewrite,[status(thm)],[])).
% 88.78/88.98 tff(1256,plain,
% 88.78/88.98 (((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.78/88.98 inference(rewrite,[status(thm)],[])).
% 88.78/88.98 tff(1257,plain,
% 88.78/88.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1256])).
% 88.78/88.98 tff(1258,plain,
% 88.78/88.98 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.78/88.98 inference(transitivity,[status(thm)],[1257, 1255])).
% 88.78/88.98 tff(1259,plain,
% 88.78/88.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.78/88.98 inference(quant_inst,[status(thm)],[])).
% 88.78/88.98 tff(1260,plain,
% 88.78/88.98 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 88.78/88.98 tff(1261,plain,
% 88.78/88.98 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[1260, 188])).
% 88.78/88.98 tff(1262,plain,
% 88.78/88.98 ($false),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[1261, 1254, 1245, 1005])).
% 88.78/88.98 tff(1263,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.78/88.98 tff(1264,plain,
% 88.78/88.98 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[1263, 1004, 1006, 1005, 971])).
% 88.78/88.98 tff(1265,plain,
% 88.78/88.98 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[932, 1264])).
% 88.78/88.98 tff(1266,plain,
% 88.78/88.98 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(symmetry,[status(thm)],[1265])).
% 88.78/88.98 tff(1267,plain,
% 88.78/88.98 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.78/88.98 inference(transitivity,[status(thm)],[1266, 1004])).
% 88.78/88.98 tff(1268,plain,
% 88.78/88.98 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(commutativity,[status(thm)],[])).
% 88.78/88.98 tff(1269,plain,
% 88.78/88.98 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.98 inference(symmetry,[status(thm)],[1268])).
% 88.78/88.98 tff(1270,plain,
% 88.78/88.98 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1004])).
% 88.78/88.98 tff(1271,plain,
% 88.78/88.98 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.98 inference(transitivity,[status(thm)],[1270, 1269])).
% 88.78/88.98 tff(1272,plain,
% 88.78/88.98 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1271])).
% 88.78/88.98 tff(1273,plain,
% 88.78/88.98 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1264, 1272])).
% 88.78/88.98 tff(1274,plain,
% 88.78/88.98 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(transitivity,[status(thm)],[953, 842, 839, 835])).
% 88.78/88.98 tff(1275,plain,
% 88.78/88.98 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.98 inference(monotonicity,[status(thm)],[1274])).
% 88.78/88.98 tff(1276,plain,
% 88.78/88.98 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.78/88.98 inference(symmetry,[status(thm)],[1275])).
% 88.78/88.98 tff(1277,plain,
% 88.78/88.98 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(quant_inst,[status(thm)],[])).
% 88.78/88.98 tff(1278,plain,
% 88.78/88.98 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.98 inference(unit_resolution,[status(thm)],[1277, 237])).
% 88.78/88.98 tff(1279,plain,
% 88.78/88.98 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.98 inference(rewrite,[status(thm)],[])).
% 88.78/88.98 tff(1280,plain,
% 88.78/88.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.78/88.98 inference(quant_inst,[status(thm)],[])).
% 88.78/88.98 tff(1281,plain,
% 88.78/88.98 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.98 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 88.78/88.98 tff(1282,plain,
% 88.78/88.98 ((~little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1281, 256])).
% 88.78/88.99 tff(1283,plain,
% 88.78/88.99 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1282, 1278])).
% 88.78/88.99 tff(1284,plain,
% 88.78/88.99 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.78/88.99 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 88.78/88.99 tff(1285,plain,
% 88.78/88.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.78/88.99 inference(rewrite,[status(thm)],[])).
% 88.78/88.99 tff(1286,plain,
% 88.78/88.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.78/88.99 inference(quant_inst,[status(thm)],[])).
% 88.78/88.99 tff(1287,plain,
% 88.78/88.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.78/88.99 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 88.78/88.99 tff(1288,plain,
% 88.78/88.99 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1287, 188])).
% 88.78/88.99 tff(1289,plain,
% 88.78/88.99 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1288, 1284])).
% 88.78/88.99 tff(1290,plain,
% 88.78/88.99 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1289, 1273])).
% 88.78/88.99 tff(1291,plain,
% 88.78/88.99 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1290, 1267])).
% 88.78/88.99 tff(1292,plain,
% 88.78/88.99 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(symmetry,[status(thm)],[1291])).
% 88.78/88.99 tff(1293,plain,
% 88.78/88.99 (f19(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.99 inference(symmetry,[status(thm)],[951])).
% 88.78/88.99 tff(1294,plain,
% 88.78/88.99 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.78/88.99 inference(transitivity,[status(thm)],[1293, 1292, 1003])).
% 88.78/88.99 tff(1295,plain,
% 88.78/88.99 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1294])).
% 88.78/88.99 tff(1296,plain,
% 88.78/88.99 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.78/88.99 inference(symmetry,[status(thm)],[1295])).
% 88.78/88.99 tff(1297,plain,
% 88.78/88.99 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(symmetry,[status(thm)],[1004])).
% 88.78/88.99 tff(1298,plain,
% 88.78/88.99 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.78/88.99 inference(transitivity,[status(thm)],[1084, 1297, 1265, 867, 1296, 221])).
% 88.78/88.99 tff(1299,plain,
% 88.78/88.99 ($false),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[971, 1298])).
% 88.78/88.99 tff(1300,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.78/88.99 tff(1301,plain,
% 88.78/88.99 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[1300, 756, 971, 984])).
% 88.78/88.99 tff(1302,plain,
% 88.78/88.99 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.78/88.99 inference(unit_resolution,[status(thm)],[965, 1301])).
% 88.78/88.99 tff(1303,plain,
% 88.78/88.99 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1302])).
% 88.78/88.99 tff(1304,plain,
% 88.78/88.99 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.78/88.99 inference(transitivity,[status(thm)],[1303, 972])).
% 88.78/88.99 tff(1305,plain,
% 88.78/88.99 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1304])).
% 88.78/88.99 tff(1306,assumption,(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.78/88.99 tff(1307,plain,
% 88.78/88.99 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(symmetry,[status(thm)],[1306])).
% 88.78/88.99 tff(1308,plain,
% 88.78/88.99 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.78/88.99 inference(transitivity,[status(thm)],[1307, 1008])).
% 88.78/88.99 tff(1309,plain,
% 88.78/88.99 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1084, 1308])).
% 88.78/88.99 tff(1310,plain,
% 88.78/88.99 ((~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.78/88.99 inference(monotonicity,[status(thm)],[1309])).
% 88.78/88.99 tff(1311,plain,
% 88.78/88.99 (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.78/88.99 inference(modus_ponens,[status(thm)],[971, 1310])).
% 88.78/88.99 tff(1312,plain,
% 88.78/88.99 (non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.78/88.99 inference(transitivity,[status(thm)],[864, 884, 841])).
% 88.78/88.99 tff(1313,plain,
% 88.78/88.99 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.83/88.99 inference(monotonicity,[status(thm)],[1312])).
% 88.83/88.99 tff(1314,plain,
% 88.83/88.99 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.83/88.99 inference(symmetry,[status(thm)],[1313])).
% 88.83/88.99 tff(1315,plain,
% 88.83/88.99 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.83/88.99 inference(modus_ponens,[status(thm)],[1062, 1314])).
% 88.83/88.99 tff(1316,plain,
% 88.83/88.99 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.83/88.99 inference(rewrite,[status(thm)],[])).
% 88.83/88.99 tff(1317,plain,
% 88.83/88.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.83/88.99 inference(quant_inst,[status(thm)],[])).
% 88.83/88.99 tff(1318,plain,
% 88.83/88.99 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 88.83/89.00 tff(1319,plain,
% 88.83/89.00 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1318, 188])).
% 88.83/89.00 tff(1320,plain,
% 88.83/89.00 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1319, 1315])).
% 88.83/89.00 tff(1321,plain,
% 88.83/89.00 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1320, 1311])).
% 88.83/89.00 tff(1322,plain,
% 88.83/89.00 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1321])).
% 88.83/89.00 tff(1323,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[867, 1322])).
% 88.83/89.00 tff(1324,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[1009, 1306])).
% 88.83/89.00 tff(1325,plain,
% 88.83/89.00 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1324, 1323])).
% 88.83/89.00 tff(1326,plain,
% 88.83/89.00 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1325])).
% 88.83/89.00 tff(1327,plain,
% 88.83/89.00 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.00 inference(transitivity,[status(thm)],[1293, 1326, 1003])).
% 88.83/89.00 tff(1328,plain,
% 88.83/89.00 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1327])).
% 88.83/89.00 tff(1329,plain,
% 88.83/89.00 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1328])).
% 88.83/89.00 tff(1330,plain,
% 88.83/89.00 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[1084, 1321, 1329, 221])).
% 88.83/89.00 tff(1331,plain,
% 88.83/89.00 ($false),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[971, 1330])).
% 88.83/89.00 tff(1332,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.83/89.00 tff(1333,plain,
% 88.83/89.00 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1332, 1302, 971])).
% 88.83/89.00 tff(1334,plain,
% 88.83/89.00 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[1333, 1305])).
% 88.83/89.00 tff(1335,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1289, 1334])).
% 88.83/89.00 tff(1336,plain,
% 88.83/89.00 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[932, 1333])).
% 88.83/89.00 tff(1337,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1336])).
% 88.83/89.00 tff(1338,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.00 inference(transitivity,[status(thm)],[1337, 1302, 756])).
% 88.83/89.00 tff(1339,plain,
% 88.83/89.00 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1338])).
% 88.83/89.00 tff(1340,plain,
% 88.83/89.00 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1339])).
% 88.83/89.00 tff(1341,plain,
% 88.83/89.00 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.00 inference(transitivity,[status(thm)],[779, 759, 1340, 833])).
% 88.83/89.00 tff(1342,plain,
% 88.83/89.00 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1341])).
% 88.83/89.00 tff(1343,plain,
% 88.83/89.00 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[1342, 1335])).
% 88.83/89.00 tff(1344,plain,
% 88.83/89.00 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1343])).
% 88.83/89.00 tff(1345,plain,
% 88.83/89.00 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1344])).
% 88.83/89.00 tff(1346,plain,
% 88.83/89.00 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[1027, 1345])).
% 88.83/89.00 tff(1347,plain,
% 88.83/89.00 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.83/89.00 inference(rewrite,[status(thm)],[])).
% 88.83/89.00 tff(1348,plain,
% 88.83/89.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.83/89.00 inference(quant_inst,[status(thm)],[])).
% 88.83/89.00 tff(1349,plain,
% 88.83/89.00 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 88.83/89.00 tff(1350,plain,
% 88.83/89.00 ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1349, 188, 1117])).
% 88.83/89.00 tff(1351,plain,
% 88.83/89.00 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.00 inference(unit_resolution,[status(thm)],[1350, 1346])).
% 88.83/89.00 tff(1352,plain,
% 88.83/89.00 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1351])).
% 88.83/89.00 tff(1353,plain,
% 88.83/89.00 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.00 inference(transitivity,[status(thm)],[1003, 1102, 1339, 758, 778, 1031])).
% 88.83/89.00 tff(1354,plain,
% 88.83/89.00 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1353, 1352])).
% 88.83/89.00 tff(1355,plain,
% 88.83/89.00 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1354])).
% 88.83/89.00 tff(1356,plain,
% 88.83/89.00 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1355])).
% 88.83/89.00 tff(1357,plain,
% 88.83/89.00 (~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[1118, 1356])).
% 88.83/89.00 tff(1358,assumption,(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), introduced(assumption)).
% 88.83/89.00 tff(1359,plain,
% 88.83/89.00 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.00 inference(transitivity,[status(thm)],[554, 553, 552, 1358])).
% 88.83/89.00 tff(1360,plain,
% 88.83/89.00 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1359])).
% 88.83/89.00 tff(1361,plain,
% 88.83/89.00 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1360])).
% 88.83/89.00 tff(1362,plain,
% 88.83/89.00 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[983, 1361])).
% 88.83/89.00 tff(1363,assumption,(f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), introduced(assumption)).
% 88.83/89.00 tff(1364,plain,
% 88.83/89.00 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1363])).
% 88.83/89.00 tff(1365,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[968, 1306, 222])).
% 88.83/89.00 tff(1366,plain,
% 88.83/89.00 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.83/89.00 inference(monotonicity,[status(thm)],[1365, 735])).
% 88.83/89.00 tff(1367,plain,
% 88.83/89.00 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.00 inference(symmetry,[status(thm)],[1366])).
% 88.83/89.00 tff(1368,plain,
% 88.83/89.00 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.00 inference(modus_ponens,[status(thm)],[746, 1367])).
% 88.83/89.00 tff(1369,plain,
% 88.83/89.00 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.00 inference(transitivity,[status(thm)],[968, 1306])).
% 88.83/89.00 tff(1370,plain,
% 88.83/89.00 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1369])).
% 88.83/89.01 tff(1371,plain,
% 88.83/89.01 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.01 inference(transitivity,[status(thm)],[1370, 196])).
% 88.83/89.01 tff(1372,plain,
% 88.83/89.01 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1371])).
% 88.83/89.01 tff(1373,plain,
% 88.83/89.01 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1358])).
% 88.83/89.01 tff(1374,plain,
% 88.83/89.01 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(transitivity,[status(thm)],[1373, 499, 378, 375, 314])).
% 88.83/89.01 tff(1375,plain,
% 88.83/89.01 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1374])).
% 88.83/89.01 tff(1376,plain,
% 88.83/89.01 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1375])).
% 88.83/89.01 tff(1377,plain,
% 88.83/89.01 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(transitivity,[status(thm)],[1376, 1372])).
% 88.83/89.01 tff(1378,plain,
% 88.83/89.01 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1377])).
% 88.83/89.01 tff(1379,plain,
% 88.83/89.01 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(modus_ponens,[status(thm)],[198, 1378])).
% 88.83/89.01 tff(1380,plain,
% 88.83/89.01 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.83/89.01 inference(rewrite,[status(thm)],[])).
% 88.83/89.01 tff(1381,plain,
% 88.83/89.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.83/89.01 inference(quant_inst,[status(thm)],[])).
% 88.83/89.01 tff(1382,plain,
% 88.83/89.01 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.83/89.01 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 88.83/89.01 tff(1383,plain,
% 88.83/89.01 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.83/89.01 inference(unit_resolution,[status(thm)],[1382, 188])).
% 88.83/89.01 tff(1384,plain,
% 88.83/89.01 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.01 inference(unit_resolution,[status(thm)],[1383, 1379, 1368])).
% 88.83/89.01 tff(1385,plain,
% 88.83/89.01 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1384])).
% 88.83/89.01 tff(1386,plain,
% 88.83/89.01 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1385])).
% 88.83/89.01 tff(1387,plain,
% 88.83/89.01 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1386])).
% 88.83/89.01 tff(1388,plain,
% 88.83/89.01 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1369])).
% 88.83/89.01 tff(1389,plain,
% 88.83/89.01 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.01 inference(symmetry,[status(thm)],[1388])).
% 88.83/89.01 tff(1390,plain,
% 88.83/89.01 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.83/89.01 inference(transitivity,[status(thm)],[779, 1389, 1387, 195])).
% 88.83/89.01 tff(1391,plain,
% 88.83/89.01 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1390])).
% 88.83/89.01 tff(1392,plain,
% 88.83/89.01 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1391])).
% 88.83/89.01 tff(1393,plain,
% 88.83/89.01 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(symmetry,[status(thm)],[1392])).
% 88.83/89.01 tff(1394,plain,
% 88.83/89.01 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(modus_ponens,[status(thm)],[794, 1393])).
% 88.83/89.01 tff(1395,plain,
% 88.83/89.01 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.01 inference(transitivity,[status(thm)],[779, 1389, 833])).
% 88.83/89.01 tff(1396,plain,
% 88.83/89.01 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1395])).
% 88.83/89.01 tff(1397,plain,
% 88.83/89.01 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(monotonicity,[status(thm)],[1396])).
% 88.83/89.01 tff(1398,plain,
% 88.83/89.01 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(symmetry,[status(thm)],[1397])).
% 88.83/89.01 tff(1399,plain,
% 88.83/89.01 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.83/89.01 inference(modus_ponens,[status(thm)],[1143, 1398])).
% 88.83/89.01 tff(1400,plain,
% 88.83/89.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(rewrite,[status(thm)],[])).
% 88.83/89.02 tff(1401,plain,
% 88.83/89.02 (((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~single_valued_set(b))) <=> ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(rewrite,[status(thm)],[])).
% 88.83/89.02 tff(1402,plain,
% 88.83/89.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1401])).
% 88.83/89.02 tff(1403,plain,
% 88.83/89.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(transitivity,[status(thm)],[1402, 1400])).
% 88.83/89.02 tff(1404,plain,
% 88.83/89.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~single_valued_set(b)))),
% 88.83/89.02 inference(quant_inst,[status(thm)],[])).
% 88.83/89.02 tff(1405,plain,
% 88.83/89.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)) | (~member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)) | (~single_valued_set(b)) | (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.02 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 88.83/89.02 tff(1406,plain,
% 88.83/89.02 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.83/89.02 inference(unit_resolution,[status(thm)],[1405, 1183, 1173, 273, 1159, 1155, 1399, 1394])).
% 88.83/89.02 tff(1407,plain,
% 88.83/89.02 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.02 inference(symmetry,[status(thm)],[1406])).
% 88.83/89.02 tff(1408,plain,
% 88.83/89.02 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1407])).
% 88.83/89.02 tff(1409,plain,
% 88.83/89.02 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1408])).
% 88.83/89.02 tff(1410,plain,
% 88.83/89.02 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 88.83/89.02 inference(symmetry,[status(thm)],[1409])).
% 88.83/89.02 tff(1411,plain,
% 88.83/89.02 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 88.83/89.02 inference(modus_ponens,[status(thm)],[1214, 1410])).
% 88.83/89.02 tff(1412,plain,
% 88.83/89.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(rewrite,[status(thm)],[])).
% 88.83/89.02 tff(1413,plain,
% 88.83/89.02 (((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a))) <=> ((~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(rewrite,[status(thm)],[])).
% 88.83/89.02 tff(1414,plain,
% 88.83/89.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1413])).
% 88.83/89.02 tff(1415,plain,
% 88.83/89.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.02 inference(transitivity,[status(thm)],[1414, 1412])).
% 88.83/89.02 tff(1416,plain,
% 88.83/89.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))),
% 88.83/89.02 inference(quant_inst,[status(thm)],[])).
% 88.83/89.02 tff(1417,plain,
% 88.83/89.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.02 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 88.83/89.02 tff(1418,plain,
% 88.83/89.02 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.83/89.02 inference(unit_resolution,[status(thm)],[1417, 1183, 1221, 1210, 1205, 1155, 979, 1411])).
% 88.83/89.02 tff(1419,plain,
% 88.83/89.02 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.02 inference(symmetry,[status(thm)],[1418])).
% 88.83/89.02 tff(1420,plain,
% 88.83/89.02 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.83/89.02 inference(transitivity,[status(thm)],[1419, 1364])).
% 88.83/89.02 tff(1421,plain,
% 88.83/89.02 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f20(compose(b, a)) = f21(compose(b, a)))),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1420])).
% 88.83/89.02 tff(1422,plain,
% 88.83/89.02 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.02 inference(symmetry,[status(thm)],[1421])).
% 88.83/89.02 tff(1423,plain,
% 88.83/89.02 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.83/89.02 inference(transitivity,[status(thm)],[1422, 1007])).
% 88.83/89.02 tff(1424,plain,
% 88.83/89.02 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))))),
% 88.83/89.02 inference(monotonicity,[status(thm)],[1423])).
% 88.83/89.02 tff(1425,plain,
% 88.83/89.02 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.83/89.03 inference(modus_ponens,[status(thm)],[1244, 1424])).
% 88.83/89.03 tff(1426,plain,
% 88.83/89.03 ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.03 inference(commutativity,[status(thm)],[])).
% 88.83/89.03 tff(1427,plain,
% 88.83/89.03 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1003])).
% 88.83/89.03 tff(1428,plain,
% 88.83/89.03 (f19(compose(b, a)) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.83/89.03 inference(transitivity,[status(thm)],[779, 1389, 833, 1427])).
% 88.83/89.03 tff(1429,plain,
% 88.83/89.03 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1419, 1428])).
% 88.83/89.03 tff(1430,plain,
% 88.83/89.03 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.83/89.03 inference(transitivity,[status(thm)],[1429, 1426])).
% 88.83/89.03 tff(1431,plain,
% 88.83/89.03 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1430])).
% 88.83/89.03 tff(1432,plain,
% 88.83/89.03 ((~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1431])).
% 88.83/89.03 tff(1433,assumption,(~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), introduced(assumption)).
% 88.83/89.03 tff(1434,plain,
% 88.83/89.03 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.83/89.03 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 88.83/89.03 tff(1435,plain,
% 88.83/89.03 ($false),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1261, 1434, 1425, 1362])).
% 88.83/89.03 tff(1436,plain,((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~(f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.83/89.03 tff(1437,plain,
% 88.83/89.03 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1436, 1351, 727, 1302, 1336, 198])).
% 88.83/89.03 tff(1438,plain,
% 88.83/89.03 ($false),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1437, 1357])).
% 88.83/89.03 tff(1439,plain,((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.83/89.03 tff(1440,plain,
% 88.83/89.03 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1439, 971])).
% 88.83/89.03 tff(1441,plain,
% 88.83/89.03 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1440])).
% 88.83/89.03 tff(1442,assumption,(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.83/89.03 tff(1443,plain,
% 88.83/89.03 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1442])).
% 88.83/89.03 tff(1444,plain,
% 88.83/89.03 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1442])).
% 88.83/89.03 tff(1445,assumption,(~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), introduced(assumption)).
% 88.83/89.03 tff(1446,plain,
% 88.83/89.03 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[495, 1445])).
% 88.83/89.03 tff(1447,plain,
% 88.83/89.03 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.03 inference(transitivity,[status(thm)],[1446, 1444])).
% 88.83/89.03 tff(1448,plain,
% 88.83/89.03 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1447])).
% 88.83/89.03 tff(1449,plain,
% 88.83/89.03 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.03 inference(transitivity,[status(thm)],[1448, 1443])).
% 88.83/89.03 tff(1450,plain,
% 88.83/89.03 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1449])).
% 88.83/89.03 tff(1451,plain,
% 88.83/89.03 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1450])).
% 88.83/89.03 tff(1452,plain,
% 88.83/89.03 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[469, 1446])).
% 88.83/89.03 tff(1453,plain,
% 88.83/89.03 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f20(compose(b, a))),
% 88.83/89.03 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 88.83/89.03 tff(1454,plain,
% 88.83/89.03 (f20(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1453])).
% 88.83/89.03 tff(1455,plain,
% 88.83/89.03 (f20(compose(b, a)) = f19(compose(b, a))),
% 88.83/89.03 inference(transitivity,[status(thm)],[1454, 1448, 1443, 397])).
% 88.83/89.03 tff(1456,plain,
% 88.83/89.03 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1455])).
% 88.83/89.03 tff(1457,plain,
% 88.83/89.03 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.83/89.03 inference(symmetry,[status(thm)],[1456])).
% 88.83/89.03 tff(1458,plain,
% 88.83/89.03 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.83/89.03 inference(transitivity,[status(thm)],[1442, 1457])).
% 88.83/89.03 tff(1459,plain,
% 88.83/89.03 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1447])).
% 88.83/89.03 tff(1460,plain,
% 88.83/89.03 ((~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.83/89.03 inference(monotonicity,[status(thm)],[1459])).
% 88.83/89.03 tff(1461,plain,
% 88.83/89.03 (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.03 inference(modus_ponens,[status(thm)],[1445, 1460])).
% 88.83/89.03 tff(1462,plain,
% 88.83/89.03 ($false),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1461, 1458])).
% 88.83/89.03 tff(1463,plain,((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.83/89.03 tff(1464,plain,
% 88.83/89.03 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.83/89.03 inference(unit_resolution,[status(thm)],[1463, 1440])).
% 88.83/89.04 tff(1465,plain,
% 88.83/89.04 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.83/89.04 inference(monotonicity,[status(thm)],[1464, 1441])).
% 88.83/89.04 tff(1466,plain,
% 88.83/89.04 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.04 inference(transitivity,[status(thm)],[1465, 1])).
% 88.83/89.04 tff(1467,plain,
% 88.83/89.04 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.04 inference(symmetry,[status(thm)],[1466])).
% 88.83/89.04 tff(1468,plain,
% 88.83/89.04 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.04 inference(monotonicity,[status(thm)],[1464, 525])).
% 88.83/89.04 tff(1469,plain,
% 88.83/89.04 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.04 inference(symmetry,[status(thm)],[1468])).
% 88.83/89.04 tff(1470,plain,
% 88.83/89.04 ((singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.04 inference(commutativity,[status(thm)],[])).
% 88.83/89.04 tff(1471,assumption,(~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), introduced(assumption)).
% 88.83/89.04 tff(1472,plain,
% 88.83/89.04 (f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.04 inference(monotonicity,[status(thm)],[1440])).
% 88.83/89.04 tff(1473,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.83/89.04 inference(rewrite,[status(thm)],[])).
% 88.83/89.04 tff(1474,plain,
% 88.83/89.04 (((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.83/89.04 inference(rewrite,[status(thm)],[])).
% 88.83/89.04 tff(1475,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.83/89.04 inference(monotonicity,[status(thm)],[1474])).
% 88.83/89.04 tff(1476,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.83/89.04 inference(transitivity,[status(thm)],[1475, 1473])).
% 88.83/89.04 tff(1477,plain,
% 88.83/89.04 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.83/89.04 inference(quant_inst,[status(thm)],[])).
% 88.83/89.04 tff(1478,plain,
% 88.83/89.04 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.83/89.04 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 88.83/89.04 tff(1479,plain,
% 88.83/89.04 (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.04 inference(unit_resolution,[status(thm)],[1478, 163, 292, 382])).
% 88.83/89.04 tff(1480,plain,
% 88.83/89.04 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.83/89.04 inference(rewrite,[status(thm)],[])).
% 88.83/89.04 tff(1481,plain,
% 88.83/89.04 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.83/89.04 inference(quant_inst,[status(thm)],[])).
% 88.83/89.04 tff(1482,plain,
% 88.83/89.04 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.04 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 88.83/89.04 tff(1483,plain,
% 88.83/89.04 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.04 inference(unit_resolution,[status(thm)],[1482, 174, 1479])).
% 88.83/89.04 tff(1484,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.83/89.04 inference(rewrite,[status(thm)],[])).
% 88.83/89.04 tff(1485,plain,
% 88.83/89.04 (((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.83/89.04 inference(rewrite,[status(thm)],[])).
% 88.83/89.04 tff(1486,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))))),
% 88.83/89.04 inference(monotonicity,[status(thm)],[1485])).
% 88.83/89.04 tff(1487,plain,
% 88.83/89.04 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))))),
% 88.83/89.04 inference(transitivity,[status(thm)],[1486, 1484])).
% 88.83/89.04 tff(1488,plain,
% 88.83/89.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.83/89.04 inference(quant_inst,[status(thm)],[])).
% 88.83/89.04 tff(1489,plain,
% 88.83/89.04 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a)))),
% 88.83/89.04 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 88.83/89.04 tff(1490,plain,
% 88.83/89.04 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f19(compose(b, a))),
% 88.83/89.05 inference(unit_resolution,[status(thm)],[1489, 188, 1483])).
% 88.83/89.05 tff(1491,plain,
% 88.83/89.05 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.83/89.05 inference(monotonicity,[status(thm)],[1440])).
% 88.83/89.05 tff(1492,plain,
% 88.83/89.05 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))),
% 88.83/89.05 inference(transitivity,[status(thm)],[1491, 1490])).
% 88.83/89.05 tff(1493,plain,
% 88.83/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(monotonicity,[status(thm)],[1492])).
% 88.83/89.05 tff(1494,plain,
% 88.83/89.05 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(monotonicity,[status(thm)],[1493])).
% 88.83/89.05 tff(1495,plain,
% 88.83/89.05 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(symmetry,[status(thm)],[1494])).
% 88.83/89.05 tff(1496,plain,
% 88.83/89.05 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(commutativity,[status(thm)],[])).
% 88.83/89.05 tff(1497,plain,
% 88.83/89.05 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.83/89.05 inference(monotonicity,[status(thm)],[1464])).
% 88.83/89.05 tff(1498,plain,
% 88.83/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(monotonicity,[status(thm)],[1497])).
% 88.83/89.05 tff(1499,plain,
% 88.83/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.83/89.05 inference(symmetry,[status(thm)],[1498])).
% 88.83/89.05 tff(1500,plain,
% 88.83/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.83/89.05 inference(transitivity,[status(thm)],[1499, 1358])).
% 88.83/89.05 tff(1501,plain,
% 88.83/89.05 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.05 inference(monotonicity,[status(thm)],[1500, 1441])).
% 88.89/89.05 tff(1502,plain,
% 88.89/89.05 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.05 inference(transitivity,[status(thm)],[1501, 1496])).
% 88.89/89.05 tff(1503,plain,
% 88.89/89.05 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.05 inference(transitivity,[status(thm)],[1502, 1495])).
% 88.89/89.05 tff(1504,plain,
% 88.89/89.05 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.05 inference(monotonicity,[status(thm)],[1503])).
% 88.89/89.05 tff(1505,plain,
% 88.89/89.05 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.89/89.05 inference(unit_resolution,[status(thm)],[1463, 1442])).
% 88.89/89.05 tff(1506,plain,
% 88.89/89.05 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.05 inference(monotonicity,[status(thm)],[1505])).
% 88.89/89.05 tff(1507,plain,
% 88.89/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.05 inference(monotonicity,[status(thm)],[1506])).
% 88.89/89.05 tff(1508,plain,
% 88.89/89.05 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.05 inference(symmetry,[status(thm)],[1507])).
% 88.89/89.05 tff(1509,assumption,(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.89/89.05 tff(1510,plain,
% 88.89/89.05 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.05 inference(symmetry,[status(thm)],[1509])).
% 88.89/89.05 tff(1511,plain,
% 88.89/89.05 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.89/89.05 inference(transitivity,[status(thm)],[1510, 1508, 1358])).
% 88.89/89.05 tff(1512,plain,
% 88.89/89.05 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(monotonicity,[status(thm)],[1511])).
% 88.89/89.06 tff(1513,plain,
% 88.89/89.06 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.89/89.06 inference(symmetry,[status(thm)],[1512])).
% 88.89/89.06 tff(1514,plain,
% 88.89/89.06 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.06 inference(rewrite,[status(thm)],[])).
% 88.89/89.06 tff(1515,plain,
% 88.89/89.06 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.06 inference(quant_inst,[status(thm)],[])).
% 88.89/89.06 tff(1516,plain,
% 88.89/89.06 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 88.89/89.06 tff(1517,plain,
% 88.89/89.06 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(unit_resolution,[status(thm)],[1516, 135, 121])).
% 88.89/89.06 tff(1518,plain,
% 88.89/89.06 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.06 inference(rewrite,[status(thm)],[])).
% 88.89/89.06 tff(1519,plain,
% 88.89/89.06 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.06 inference(quant_inst,[status(thm)],[])).
% 88.89/89.06 tff(1520,plain,
% 88.89/89.06 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.06 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 88.89/89.06 tff(1521,plain,
% 88.89/89.06 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(unit_resolution,[status(thm)],[1520, 163, 1517, 503])).
% 88.89/89.06 tff(1522,plain,
% 88.89/89.06 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.06 inference(rewrite,[status(thm)],[])).
% 88.89/89.06 tff(1523,plain,
% 88.89/89.06 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.06 inference(quant_inst,[status(thm)],[])).
% 88.89/89.06 tff(1524,plain,
% 88.89/89.06 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), Y))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 88.89/89.06 tff(1525,plain,
% 88.89/89.06 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.06 inference(unit_resolution,[status(thm)],[1524, 174, 1521])).
% 88.89/89.06 tff(1526,plain,
% 88.89/89.06 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.89/89.06 inference(modus_ponens,[status(thm)],[1525, 1513])).
% 88.89/89.06 tff(1527,plain,
% 88.89/89.06 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.89/89.06 inference(rewrite,[status(thm)],[])).
% 88.89/89.06 tff(1528,plain,
% 88.89/89.06 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.89/89.06 inference(rewrite,[status(thm)],[])).
% 88.89/89.06 tff(1529,plain,
% 88.89/89.06 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.89/89.06 inference(monotonicity,[status(thm)],[1528])).
% 88.89/89.06 tff(1530,plain,
% 88.89/89.06 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.89/89.06 inference(transitivity,[status(thm)],[1529, 1527])).
% 88.89/89.06 tff(1531,plain,
% 88.89/89.06 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.89/89.06 inference(quant_inst,[status(thm)],[])).
% 88.89/89.06 tff(1532,plain,
% 88.89/89.06 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.89/89.07 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 88.89/89.07 tff(1533,plain,
% 88.89/89.07 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.89/89.07 inference(unit_resolution,[status(thm)],[1532, 188])).
% 88.89/89.07 tff(1534,plain,
% 88.89/89.07 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f19(compose(b, a))),
% 88.89/89.07 inference(unit_resolution,[status(thm)],[1533, 1526])).
% 88.89/89.07 tff(1535,plain,
% 88.89/89.07 (f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1534])).
% 88.89/89.07 tff(1536,plain,
% 88.89/89.07 ((f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1535])).
% 88.89/89.07 tff(1537,plain,
% 88.89/89.07 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(symmetry,[status(thm)],[1536])).
% 88.89/89.07 tff(1538,plain,
% 88.89/89.07 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1442, 1510])).
% 88.89/89.07 tff(1539,plain,
% 88.89/89.07 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1538])).
% 88.89/89.07 tff(1540,plain,
% 88.89/89.07 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(symmetry,[status(thm)],[1539])).
% 88.89/89.07 tff(1541,plain,
% 88.89/89.07 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1508, 1358])).
% 88.89/89.07 tff(1542,plain,
% 88.89/89.07 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1541])).
% 88.89/89.07 tff(1543,plain,
% 88.89/89.07 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1542, 650])).
% 88.89/89.07 tff(1544,plain,
% 88.89/89.07 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(symmetry,[status(thm)],[1543])).
% 88.89/89.07 tff(1545,plain,
% 88.89/89.07 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1544, 1540, 1537])).
% 88.89/89.07 tff(1546,plain,
% 88.89/89.07 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1511])).
% 88.89/89.07 tff(1547,plain,
% 88.89/89.07 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.89/89.07 inference(symmetry,[status(thm)],[1546])).
% 88.89/89.07 tff(1548,plain,
% 88.89/89.07 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.89/89.07 inference(modus_ponens,[status(thm)],[503, 1547])).
% 88.89/89.07 tff(1549,plain,
% 88.89/89.07 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.89/89.07 inference(rewrite,[status(thm)],[])).
% 88.89/89.07 tff(1550,plain,
% 88.89/89.07 (((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.89/89.07 inference(rewrite,[status(thm)],[])).
% 88.89/89.07 tff(1551,plain,
% 88.89/89.07 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1550])).
% 88.89/89.07 tff(1552,plain,
% 88.89/89.07 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1551, 1549])).
% 88.89/89.07 tff(1553,plain,
% 88.89/89.07 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.89/89.07 inference(quant_inst,[status(thm)],[])).
% 88.89/89.07 tff(1554,plain,
% 88.89/89.07 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.89/89.07 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 88.89/89.07 tff(1555,plain,
% 88.89/89.07 ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.89/89.07 inference(unit_resolution,[status(thm)],[1554, 188])).
% 88.89/89.07 tff(1556,plain,
% 88.89/89.07 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.89/89.07 inference(unit_resolution,[status(thm)],[1555, 1548])).
% 88.89/89.07 tff(1557,plain,
% 88.89/89.07 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1556])).
% 88.89/89.07 tff(1558,plain,
% 88.89/89.07 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1557, 221, 1444])).
% 88.89/89.07 tff(1559,plain,
% 88.89/89.07 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.07 inference(monotonicity,[status(thm)],[1558])).
% 88.89/89.07 tff(1560,plain,
% 88.89/89.07 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.07 inference(transitivity,[status(thm)],[1559, 1])).
% 88.89/89.07 tff(1561,plain,
% 88.89/89.07 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.08 inference(symmetry,[status(thm)],[1560])).
% 88.89/89.08 tff(1562,plain,
% 88.89/89.08 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.08 inference(monotonicity,[status(thm)],[1561])).
% 88.89/89.08 tff(1563,plain,
% 88.89/89.08 (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[1471, 1562])).
% 88.89/89.08 tff(1564,plain,
% 88.89/89.08 (non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.08 inference(transitivity,[status(thm)],[522, 227, 211])).
% 88.89/89.08 tff(1565,plain,
% 88.89/89.08 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.89/89.08 inference(monotonicity,[status(thm)],[1564])).
% 88.89/89.08 tff(1566,plain,
% 88.89/89.08 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.08 inference(symmetry,[status(thm)],[1565])).
% 88.89/89.08 tff(1567,plain,
% 88.89/89.08 (member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[261, 1566])).
% 88.89/89.08 tff(1568,plain,
% 88.89/89.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.08 inference(rewrite,[status(thm)],[])).
% 88.89/89.08 tff(1569,plain,
% 88.89/89.08 (((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.08 inference(rewrite,[status(thm)],[])).
% 88.89/89.08 tff(1570,plain,
% 88.89/89.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.89/89.08 inference(monotonicity,[status(thm)],[1569])).
% 88.89/89.08 tff(1571,plain,
% 88.89/89.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.08 inference(transitivity,[status(thm)],[1570, 1568])).
% 88.89/89.08 tff(1572,plain,
% 88.89/89.08 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.08 inference(quant_inst,[status(thm)],[])).
% 88.89/89.08 tff(1573,plain,
% 88.89/89.08 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 88.89/89.08 tff(1574,plain,
% 88.89/89.08 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.08 inference(unit_resolution,[status(thm)],[1573, 188])).
% 88.89/89.08 tff(1575,plain,
% 88.89/89.08 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.08 inference(unit_resolution,[status(thm)],[1574, 1567])).
% 88.89/89.08 tff(1576,plain,
% 88.89/89.08 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.89/89.08 inference(unit_resolution,[status(thm)],[1575, 1563])).
% 88.89/89.08 tff(1577,plain,
% 88.89/89.08 (f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[1576, 1545])).
% 88.89/89.08 tff(1578,plain,
% 88.89/89.08 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.89/89.08 inference(monotonicity,[status(thm)],[1537])).
% 88.89/89.08 tff(1579,plain,
% 88.89/89.08 (~(f16(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[1471, 1578])).
% 88.89/89.08 tff(1580,plain,
% 88.89/89.08 ($false),
% 88.89/89.08 inference(unit_resolution,[status(thm)],[1579, 1577])).
% 88.89/89.08 tff(1581,plain,((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.89/89.08 tff(1582,plain,
% 88.89/89.08 (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.89/89.08 inference(unit_resolution,[status(thm)],[1581, 1358, 1440, 1471])).
% 88.89/89.08 tff(1583,plain,
% 88.89/89.08 (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.08 inference(modus_ponens,[status(thm)],[1582, 1504])).
% 88.89/89.08 tff(1584,plain,
% 88.89/89.08 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.08 inference(monotonicity,[status(thm)],[527])).
% 88.89/89.08 tff(1585,plain,
% 88.89/89.08 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.08 inference(symmetry,[status(thm)],[1584])).
% 88.89/89.08 tff(1586,plain,
% 88.89/89.08 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.09 inference(rewrite,[status(thm)],[])).
% 88.89/89.09 tff(1587,plain,
% 88.89/89.09 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.89/89.09 inference(quant_inst,[status(thm)],[])).
% 88.89/89.09 tff(1588,plain,
% 88.89/89.09 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~member(f19(compose(b, a)), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.09 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 88.89/89.09 tff(1589,plain,
% 88.89/89.09 (~disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(unit_resolution,[status(thm)],[1588, 163, 292, 402])).
% 88.89/89.09 tff(1590,plain,
% 88.89/89.09 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.09 inference(rewrite,[status(thm)],[])).
% 88.89/89.09 tff(1591,plain,
% 88.89/89.09 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.89/89.09 inference(quant_inst,[status(thm)],[])).
% 88.89/89.09 tff(1592,plain,
% 88.89/89.09 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 88.89/89.09 tff(1593,plain,
% 88.89/89.09 (member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(unit_resolution,[status(thm)],[1592, 332, 1589])).
% 88.89/89.09 tff(1594,plain,
% 88.89/89.09 (((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(rewrite,[status(thm)],[])).
% 88.89/89.09 tff(1595,plain,
% 88.89/89.09 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | ((~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(quant_inst,[status(thm)],[])).
% 88.89/89.09 tff(1596,plain,
% 88.89/89.09 ((~![Z: $i, X: $i] : ((~member(Z, sigma(X))) | member(f16(Z, X), X))) | (~member(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.09 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 88.89/89.09 tff(1597,plain,
% 88.89/89.09 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.89/89.09 inference(unit_resolution,[status(thm)],[1596, 299, 1593])).
% 88.89/89.09 tff(1598,plain,
% 88.89/89.09 (member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.09 inference(modus_ponens,[status(thm)],[1597, 1585])).
% 88.89/89.09 tff(1599,plain,
% 88.89/89.09 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.89/89.10 inference(rewrite,[status(thm)],[])).
% 88.89/89.10 tff(1600,plain,
% 88.89/89.10 (((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.10 inference(rewrite,[status(thm)],[])).
% 88.93/89.10 tff(1601,plain,
% 88.93/89.10 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.93/89.10 inference(monotonicity,[status(thm)],[1600])).
% 88.93/89.10 tff(1602,plain,
% 88.93/89.10 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.10 inference(transitivity,[status(thm)],[1601, 1599])).
% 88.93/89.10 tff(1603,plain,
% 88.93/89.10 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.93/89.11 inference(quant_inst,[status(thm)],[])).
% 88.93/89.11 tff(1604,plain,
% 88.93/89.11 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 88.93/89.11 tff(1605,plain,
% 88.93/89.11 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(unit_resolution,[status(thm)],[1604, 188])).
% 88.93/89.11 tff(1606,plain,
% 88.93/89.11 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(unit_resolution,[status(thm)],[1605, 1598])).
% 88.93/89.11 tff(1607,plain,
% 88.93/89.11 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.93/89.11 inference(unit_resolution,[status(thm)],[1606, 1583])).
% 88.93/89.11 tff(1608,plain,
% 88.93/89.11 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(symmetry,[status(thm)],[1607])).
% 88.93/89.11 tff(1609,plain,
% 88.93/89.11 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1608, 1493])).
% 88.93/89.11 tff(1610,plain,
% 88.93/89.11 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1609])).
% 88.93/89.11 tff(1611,plain,
% 88.93/89.11 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(symmetry,[status(thm)],[195])).
% 88.93/89.11 tff(1612,plain,
% 88.93/89.11 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.93/89.11 inference(unit_resolution,[status(thm)],[346, 1582])).
% 88.93/89.11 tff(1613,plain,
% 88.93/89.11 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1373, 1498, 1612])).
% 88.93/89.11 tff(1614,plain,
% 88.93/89.11 (member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1613])).
% 88.93/89.11 tff(1615,plain,
% 88.93/89.11 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(symmetry,[status(thm)],[1614])).
% 88.93/89.11 tff(1616,plain,
% 88.93/89.11 (member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(modus_ponens,[status(thm)],[450, 1615])).
% 88.93/89.11 tff(1617,plain,
% 88.93/89.11 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(commutativity,[status(thm)],[])).
% 88.93/89.11 tff(1618,plain,
% 88.93/89.11 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.11 inference(symmetry,[status(thm)],[1617])).
% 88.93/89.11 tff(1619,plain,
% 88.93/89.11 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1440])).
% 88.93/89.11 tff(1620,plain,
% 88.93/89.11 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1619, 196])).
% 88.93/89.11 tff(1621,plain,
% 88.93/89.11 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1502, 1620, 197])).
% 88.93/89.11 tff(1622,plain,
% 88.93/89.11 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1621])).
% 88.93/89.11 tff(1623,plain,
% 88.93/89.11 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.11 inference(modus_ponens,[status(thm)],[1582, 1622])).
% 88.93/89.11 tff(1624,plain,
% 88.93/89.11 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.93/89.11 inference(unit_resolution,[status(thm)],[755, 1623])).
% 88.93/89.11 tff(1625,plain,
% 88.93/89.11 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.93/89.11 inference(modus_ponens,[status(thm)],[1624, 1618])).
% 88.93/89.11 tff(1626,assumption,(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), introduced(assumption)).
% 88.93/89.11 tff(1627,assumption,(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), introduced(assumption)).
% 88.93/89.11 tff(1628,plain,
% 88.93/89.11 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1442])).
% 88.93/89.11 tff(1629,plain,
% 88.93/89.11 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.93/89.11 inference(transitivity,[status(thm)],[968, 1004])).
% 88.93/89.11 tff(1630,plain,
% 88.93/89.11 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.11 inference(commutativity,[status(thm)],[])).
% 88.93/89.11 tff(1631,plain,
% 88.93/89.11 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1084, 1297, 967])).
% 88.93/89.11 tff(1632,plain,
% 88.93/89.11 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1631])).
% 88.93/89.11 tff(1633,plain,
% 88.93/89.11 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.11 inference(transitivity,[status(thm)],[1632, 1630])).
% 88.93/89.11 tff(1634,plain,
% 88.93/89.11 ((~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[1633])).
% 88.93/89.11 tff(1635,plain,
% 88.93/89.11 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.11 inference(modus_ponens,[status(thm)],[971, 1634])).
% 88.93/89.11 tff(1636,plain,
% 88.93/89.11 (member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.93/89.11 inference(monotonicity,[status(thm)],[222, 1034])).
% 88.93/89.11 tff(1637,plain,
% 88.93/89.11 (member(singleton_set(f19(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.12 inference(symmetry,[status(thm)],[1636])).
% 88.93/89.12 tff(1638,plain,
% 88.93/89.12 (member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.12 inference(modus_ponens,[status(thm)],[1042, 1637])).
% 88.93/89.12 tff(1639,plain,
% 88.93/89.12 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.12 inference(rewrite,[status(thm)],[])).
% 88.93/89.12 tff(1640,plain,
% 88.93/89.12 (((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.12 inference(rewrite,[status(thm)],[])).
% 88.93/89.12 tff(1641,plain,
% 88.93/89.12 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.93/89.12 inference(monotonicity,[status(thm)],[1640])).
% 88.93/89.12 tff(1642,plain,
% 88.93/89.12 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.12 inference(transitivity,[status(thm)],[1641, 1639])).
% 88.93/89.12 tff(1643,plain,
% 88.93/89.12 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.93/89.12 inference(quant_inst,[status(thm)],[])).
% 88.93/89.12 tff(1644,plain,
% 88.93/89.12 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.12 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 88.93/89.12 tff(1645,plain,
% 88.93/89.12 ((~member(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[1644, 188])).
% 88.93/89.12 tff(1646,plain,
% 88.93/89.12 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[1645, 1638])).
% 88.93/89.12 tff(1647,plain,
% 88.93/89.12 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[1646, 1635])).
% 88.93/89.12 tff(1648,plain,
% 88.93/89.12 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.93/89.12 inference(symmetry,[status(thm)],[1647])).
% 88.93/89.12 tff(1649,plain,
% 88.93/89.12 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.12 inference(transitivity,[status(thm)],[1648, 1444])).
% 88.93/89.12 tff(1650,plain,
% 88.93/89.12 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.12 inference(monotonicity,[status(thm)],[1649, 1629])).
% 88.93/89.12 tff(1651,plain,
% 88.93/89.12 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.93/89.12 inference(transitivity,[status(thm)],[1427, 1650, 1628, 951])).
% 88.93/89.12 tff(1652,plain,
% 88.93/89.12 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.93/89.12 inference(monotonicity,[status(thm)],[1651])).
% 88.93/89.12 tff(1653,plain,
% 88.93/89.12 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.93/89.12 inference(transitivity,[status(thm)],[1084, 1297, 967, 867, 1652, 221])).
% 88.93/89.12 tff(1654,plain,
% 88.93/89.12 ($false),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[971, 1653])).
% 88.93/89.12 tff(1655,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.93/89.12 tff(1656,plain,
% 88.93/89.12 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[1655, 1004, 971, 1442])).
% 88.93/89.12 tff(1657,plain,
% 88.93/89.12 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.12 inference(unit_resolution,[status(thm)],[932, 1656])).
% 88.93/89.12 tff(1658,plain,
% 88.93/89.12 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1657])).
% 88.93/89.13 tff(1659,plain,
% 88.93/89.13 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1658, 1004])).
% 88.93/89.13 tff(1660,plain,
% 88.93/89.13 (member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1659])).
% 88.93/89.13 tff(1661,plain,
% 88.93/89.13 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1660])).
% 88.93/89.13 tff(1662,plain,
% 88.93/89.13 (member(f21(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(modus_ponens,[status(thm)],[1027, 1661])).
% 88.93/89.13 tff(1663,plain,
% 88.93/89.13 (f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1442])).
% 88.93/89.13 tff(1664,plain,
% 88.93/89.13 ((singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(commutativity,[status(thm)],[])).
% 88.93/89.13 tff(1665,plain,
% 88.93/89.13 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[867])).
% 88.93/89.13 tff(1666,plain,
% 88.93/89.13 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1665, 1664])).
% 88.93/89.13 tff(1667,plain,
% 88.93/89.13 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1666])).
% 88.93/89.13 tff(1668,plain,
% 88.93/89.13 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1004, 867])).
% 88.93/89.13 tff(1669,plain,
% 88.93/89.13 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1668, 1667])).
% 88.93/89.13 tff(1670,plain,
% 88.93/89.13 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1669])).
% 88.93/89.13 tff(1671,plain,
% 88.93/89.13 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.13 inference(modus_ponens,[status(thm)],[1656, 1670])).
% 88.93/89.13 tff(1672,plain,
% 88.93/89.13 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[867, 1274])).
% 88.93/89.13 tff(1673,plain,
% 88.93/89.13 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1672])).
% 88.93/89.13 tff(1674,plain,
% 88.93/89.13 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.93/89.13 inference(modus_ponens,[status(thm)],[882, 1673])).
% 88.93/89.13 tff(1675,plain,
% 88.93/89.13 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.93/89.13 inference(rewrite,[status(thm)],[])).
% 88.93/89.13 tff(1676,plain,
% 88.93/89.13 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))))) <=> ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.93/89.13 inference(rewrite,[status(thm)],[])).
% 88.93/89.13 tff(1677,plain,
% 88.93/89.13 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1676])).
% 88.93/89.13 tff(1678,plain,
% 88.93/89.13 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1677, 1675])).
% 88.93/89.13 tff(1679,plain,
% 88.93/89.13 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))))),
% 88.93/89.13 inference(quant_inst,[status(thm)],[])).
% 88.93/89.13 tff(1680,plain,
% 88.93/89.13 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.13 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 88.93/89.13 tff(1681,plain,
% 88.93/89.13 ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.13 inference(unit_resolution,[status(thm)],[1680, 188])).
% 88.93/89.13 tff(1682,plain,
% 88.93/89.13 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.13 inference(unit_resolution,[status(thm)],[1681, 1674])).
% 88.93/89.13 tff(1683,plain,
% 88.93/89.13 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.93/89.13 inference(unit_resolution,[status(thm)],[1682, 1671])).
% 88.93/89.13 tff(1684,plain,
% 88.93/89.13 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1683, 1444])).
% 88.93/89.13 tff(1685,plain,
% 88.93/89.13 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1684])).
% 88.93/89.13 tff(1686,plain,
% 88.93/89.13 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1102, 1685, 1663, 778, 1031])).
% 88.93/89.13 tff(1687,plain,
% 88.93/89.13 ((f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1686])).
% 88.93/89.13 tff(1688,plain,
% 88.93/89.13 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a)))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1687])).
% 88.93/89.13 tff(1689,plain,
% 88.93/89.13 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.13 inference(transitivity,[status(thm)],[1688, 1030])).
% 88.93/89.13 tff(1690,plain,
% 88.93/89.13 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.13 inference(monotonicity,[status(thm)],[1689])).
% 88.93/89.13 tff(1691,plain,
% 88.93/89.13 (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.13 inference(modus_ponens,[status(thm)],[862, 1690])).
% 88.93/89.13 tff(1692,plain,
% 88.93/89.13 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.93/89.13 inference(unit_resolution,[status(thm)],[1126, 1691, 1662])).
% 88.93/89.13 tff(1693,plain,
% 88.93/89.13 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1692])).
% 88.93/89.13 tff(1694,plain,
% 88.93/89.13 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))),
% 88.93/89.13 inference(symmetry,[status(thm)],[1626])).
% 88.93/89.13 tff(1695,plain,
% 88.93/89.13 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f20(compose(b, a)) = f21(compose(b, a)))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1694, 1693])).
% 88.93/89.14 tff(1696,plain,
% 88.93/89.14 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.14 inference(symmetry,[status(thm)],[1695])).
% 88.93/89.14 tff(1697,plain,
% 88.93/89.14 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1696])).
% 88.93/89.14 tff(1698,plain,
% 88.93/89.14 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.14 inference(modus_ponens,[status(thm)],[1244, 1697])).
% 88.93/89.14 tff(1699,plain,
% 88.93/89.14 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.14 inference(transitivity,[status(thm)],[1627, 1444])).
% 88.93/89.14 tff(1700,plain,
% 88.93/89.14 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1699])).
% 88.93/89.14 tff(1701,plain,
% 88.93/89.14 (f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.93/89.14 inference(symmetry,[status(thm)],[1700])).
% 88.93/89.14 tff(1702,plain,
% 88.93/89.14 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.93/89.14 inference(symmetry,[status(thm)],[1663])).
% 88.93/89.14 tff(1703,plain,
% 88.93/89.14 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.93/89.14 inference(transitivity,[status(thm)],[779, 1702, 1701, 195])).
% 88.93/89.14 tff(1704,plain,
% 88.93/89.14 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1703])).
% 88.93/89.14 tff(1705,plain,
% 88.93/89.14 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1704])).
% 88.93/89.14 tff(1706,plain,
% 88.93/89.14 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(symmetry,[status(thm)],[1705])).
% 88.93/89.14 tff(1707,plain,
% 88.93/89.14 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(modus_ponens,[status(thm)],[794, 1706])).
% 88.93/89.14 tff(1708,plain,
% 88.93/89.14 (f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.14 inference(symmetry,[status(thm)],[1685])).
% 88.93/89.14 tff(1709,plain,
% 88.93/89.14 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.93/89.14 inference(transitivity,[status(thm)],[779, 1702, 1708, 833])).
% 88.93/89.14 tff(1710,plain,
% 88.93/89.14 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1709])).
% 88.93/89.14 tff(1711,plain,
% 88.93/89.14 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1710])).
% 88.93/89.14 tff(1712,plain,
% 88.93/89.14 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(symmetry,[status(thm)],[1711])).
% 88.93/89.14 tff(1713,plain,
% 88.93/89.14 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.93/89.14 inference(modus_ponens,[status(thm)],[1143, 1712])).
% 88.93/89.14 tff(1714,plain,
% 88.93/89.14 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.93/89.14 inference(unit_resolution,[status(thm)],[1189, 1183, 1173, 273, 1159, 1155, 1713, 1707])).
% 88.93/89.14 tff(1715,plain,
% 88.93/89.14 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.93/89.14 inference(symmetry,[status(thm)],[1714])).
% 88.93/89.14 tff(1716,plain,
% 88.93/89.14 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1715])).
% 88.93/89.14 tff(1717,plain,
% 88.93/89.14 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1716])).
% 88.93/89.14 tff(1718,plain,
% 88.93/89.14 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.93/89.14 inference(symmetry,[status(thm)],[1717])).
% 88.93/89.14 tff(1719,plain,
% 88.93/89.14 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.93/89.14 inference(modus_ponens,[status(thm)],[1205, 1718])).
% 88.93/89.14 tff(1720,plain,
% 88.93/89.14 ($false),
% 88.93/89.14 inference(unit_resolution,[status(thm)],[1227, 1183, 1221, 1214, 1159, 1210, 979, 1719, 1698])).
% 88.93/89.14 tff(1721,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.93/89.14 tff(1722,plain,
% 88.93/89.14 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.93/89.14 inference(unit_resolution,[status(thm)],[1721, 862, 1442, 1627, 1626, 971])).
% 88.93/89.14 tff(1723,plain,
% 88.93/89.14 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.93/89.14 inference(unit_resolution,[status(thm)],[965, 1722])).
% 88.93/89.14 tff(1724,plain,
% 88.93/89.14 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1723])).
% 88.93/89.14 tff(1725,plain,
% 88.93/89.14 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.93/89.14 inference(transitivity,[status(thm)],[1724, 972])).
% 88.93/89.14 tff(1726,plain,
% 88.93/89.14 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.93/89.14 inference(monotonicity,[status(thm)],[1725])).
% 88.93/89.14 tff(1727,plain,
% 88.93/89.14 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.14 inference(transitivity,[status(thm)],[1009, 1306, 1444])).
% 88.98/89.14 tff(1728,plain,
% 88.98/89.14 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.14 inference(monotonicity,[status(thm)],[1727, 1323])).
% 88.98/89.14 tff(1729,plain,
% 88.98/89.14 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.98/89.14 inference(transitivity,[status(thm)],[1427, 1728, 1628, 951])).
% 88.98/89.14 tff(1730,plain,
% 88.98/89.14 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.98/89.14 inference(monotonicity,[status(thm)],[1729])).
% 88.98/89.14 tff(1731,plain,
% 88.98/89.14 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.14 inference(transitivity,[status(thm)],[1084, 1321, 1730, 221])).
% 88.98/89.14 tff(1732,plain,
% 88.98/89.14 ($false),
% 88.98/89.14 inference(unit_resolution,[status(thm)],[971, 1731])).
% 88.98/89.14 tff(1733,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.14 tff(1734,plain,
% 88.98/89.14 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.14 inference(unit_resolution,[status(thm)],[1733, 1723, 1442, 971])).
% 88.98/89.14 tff(1735,plain,
% 88.98/89.14 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.14 inference(modus_ponens,[status(thm)],[1734, 1726])).
% 88.98/89.14 tff(1736,plain,
% 88.98/89.14 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.14 inference(unit_resolution,[status(thm)],[1289, 1735])).
% 88.98/89.14 tff(1737,plain,
% 88.98/89.14 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.14 inference(unit_resolution,[status(thm)],[932, 1734])).
% 88.98/89.14 tff(1738,plain,
% 88.98/89.14 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.14 inference(symmetry,[status(thm)],[1737])).
% 88.98/89.14 tff(1739,plain,
% 88.98/89.14 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.14 inference(transitivity,[status(thm)],[1738, 1723, 1444])).
% 88.98/89.14 tff(1740,plain,
% 88.98/89.14 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.14 inference(monotonicity,[status(thm)],[1739])).
% 88.98/89.14 tff(1741,plain,
% 88.98/89.14 (f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.14 inference(symmetry,[status(thm)],[1740])).
% 88.98/89.14 tff(1742,plain,
% 88.98/89.14 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.14 inference(transitivity,[status(thm)],[779, 1702, 1741, 833])).
% 88.98/89.14 tff(1743,plain,
% 88.98/89.14 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.14 inference(monotonicity,[status(thm)],[1742])).
% 88.98/89.14 tff(1744,plain,
% 88.98/89.14 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.14 inference(transitivity,[status(thm)],[1743, 1736])).
% 88.98/89.14 tff(1745,plain,
% 88.98/89.14 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.14 inference(monotonicity,[status(thm)],[1744])).
% 88.98/89.14 tff(1746,plain,
% 88.98/89.14 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.14 inference(symmetry,[status(thm)],[1745])).
% 88.98/89.14 tff(1747,plain,
% 88.98/89.14 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.14 inference(modus_ponens,[status(thm)],[1027, 1746])).
% 88.98/89.14 tff(1748,plain,
% 88.98/89.14 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f19(compose(b, a)))),
% 88.98/89.15 inference(symmetry,[status(thm)],[1110])).
% 88.98/89.15 tff(1749,plain,
% 88.98/89.15 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f21(compose(b, a)) = f19(compose(b, a))))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1748])).
% 88.98/89.15 tff(1750,plain,
% 88.98/89.15 (~(f21(compose(b, a)) = f19(compose(b, a)))),
% 88.98/89.15 inference(modus_ponens,[status(thm)],[862, 1749])).
% 88.98/89.15 tff(1751,plain,
% 88.98/89.15 ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1349, 188])).
% 88.98/89.15 tff(1752,plain,
% 88.98/89.15 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1751, 1750, 1747])).
% 88.98/89.15 tff(1753,plain,
% 88.98/89.15 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1626, 1752])).
% 88.98/89.15 tff(1754,plain,
% 88.98/89.15 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1753])).
% 88.98/89.15 tff(1755,plain,
% 88.98/89.15 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.15 inference(modus_ponens,[status(thm)],[1244, 1754])).
% 88.98/89.15 tff(1756,plain,
% 88.98/89.15 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1742])).
% 88.98/89.15 tff(1757,plain,
% 88.98/89.15 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1756])).
% 88.98/89.15 tff(1758,plain,
% 88.98/89.15 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.15 inference(symmetry,[status(thm)],[1757])).
% 88.98/89.15 tff(1759,plain,
% 88.98/89.15 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.15 inference(modus_ponens,[status(thm)],[1143, 1758])).
% 88.98/89.15 tff(1760,plain,
% 88.98/89.15 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1189, 1183, 1173, 273, 1159, 1155, 1759, 1707])).
% 88.98/89.15 tff(1761,plain,
% 88.98/89.15 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.98/89.15 inference(symmetry,[status(thm)],[1760])).
% 88.98/89.15 tff(1762,plain,
% 88.98/89.15 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1761])).
% 88.98/89.15 tff(1763,plain,
% 88.98/89.15 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1762])).
% 88.98/89.15 tff(1764,plain,
% 88.98/89.15 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.15 inference(symmetry,[status(thm)],[1763])).
% 88.98/89.15 tff(1765,plain,
% 88.98/89.15 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.15 inference(modus_ponens,[status(thm)],[1205, 1764])).
% 88.98/89.15 tff(1766,plain,
% 88.98/89.15 ($false),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1227, 1183, 1221, 1214, 1159, 1210, 979, 1765, 1755])).
% 88.98/89.15 tff(1767,plain,((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.15 tff(1768,plain,
% 88.98/89.15 (~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1767, 1625, 1118, 1440, 971])).
% 88.98/89.15 tff(1769,plain,
% 88.98/89.15 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.15 inference(rewrite,[status(thm)],[])).
% 88.98/89.15 tff(1770,plain,
% 88.98/89.15 (((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.15 inference(rewrite,[status(thm)],[])).
% 88.98/89.15 tff(1771,plain,
% 88.98/89.15 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1770])).
% 88.98/89.15 tff(1772,plain,
% 88.98/89.15 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.15 inference(transitivity,[status(thm)],[1771, 1769])).
% 88.98/89.15 tff(1773,plain,
% 88.98/89.15 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.15 inference(quant_inst,[status(thm)],[])).
% 88.98/89.15 tff(1774,plain,
% 88.98/89.15 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 88.98/89.15 tff(1775,plain,
% 88.98/89.15 ((f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1774, 188])).
% 88.98/89.15 tff(1776,plain,
% 88.98/89.15 (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1775, 1768, 1616])).
% 88.98/89.15 tff(1777,plain,
% 88.98/89.15 (f20(compose(b, a)) = f19(compose(b, a))),
% 88.98/89.15 inference(transitivity,[status(thm)],[1776, 1611, 1610, 1472, 778])).
% 88.98/89.15 tff(1778,plain,
% 88.98/89.15 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1777])).
% 88.98/89.15 tff(1779,plain,
% 88.98/89.15 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.15 inference(transitivity,[status(thm)],[1612, 1778])).
% 88.98/89.15 tff(1780,plain,
% 88.98/89.15 ($false),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1582, 1779])).
% 88.98/89.15 tff(1781,plain,((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.15 tff(1782,plain,
% 88.98/89.15 (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[1781, 1471, 971])).
% 88.98/89.15 tff(1783,plain,
% 88.98/89.15 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(unit_resolution,[status(thm)],[550, 1782])).
% 88.98/89.15 tff(1784,plain,
% 88.98/89.15 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.15 inference(transitivity,[status(thm)],[1499, 1783, 525])).
% 88.98/89.15 tff(1785,plain,
% 88.98/89.15 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.15 inference(monotonicity,[status(thm)],[1784])).
% 88.98/89.15 tff(1786,plain,
% 88.98/89.15 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.16 inference(transitivity,[status(thm)],[1785, 1470])).
% 88.98/89.16 tff(1787,plain,
% 88.98/89.16 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.16 inference(transitivity,[status(thm)],[1786, 1469])).
% 88.98/89.16 tff(1788,plain,
% 88.98/89.16 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1787])).
% 88.98/89.16 tff(1789,plain,
% 88.98/89.16 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1498])).
% 88.98/89.16 tff(1790,plain,
% 88.98/89.16 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1789])).
% 88.98/89.16 tff(1791,plain,
% 88.98/89.16 (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.16 inference(modus_ponens,[status(thm)],[1782, 1790])).
% 88.98/89.16 tff(1792,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.98/89.16 inference(rewrite,[status(thm)],[])).
% 88.98/89.16 tff(1793,plain,
% 88.98/89.16 (((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.98/89.16 inference(rewrite,[status(thm)],[])).
% 88.98/89.16 tff(1794,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1793])).
% 88.98/89.16 tff(1795,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.98/89.16 inference(transitivity,[status(thm)],[1794, 1792])).
% 88.98/89.16 tff(1796,plain,
% 88.98/89.16 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 88.98/89.16 inference(quant_inst,[status(thm)],[])).
% 88.98/89.16 tff(1797,plain,
% 88.98/89.16 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~member(f19(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.98/89.16 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 88.98/89.16 tff(1798,plain,
% 88.98/89.16 (~disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.16 inference(unit_resolution,[status(thm)],[1797, 163, 277, 382])).
% 88.98/89.16 tff(1799,plain,
% 88.98/89.16 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.16 inference(rewrite,[status(thm)],[])).
% 88.98/89.16 tff(1800,plain,
% 88.98/89.16 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.16 inference(quant_inst,[status(thm)],[])).
% 88.98/89.16 tff(1801,plain,
% 88.98/89.16 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.16 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 88.98/89.16 tff(1802,plain,
% 88.98/89.16 (member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.16 inference(unit_resolution,[status(thm)],[1801, 332, 1798])).
% 88.98/89.16 tff(1803,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))))),
% 88.98/89.16 inference(rewrite,[status(thm)],[])).
% 88.98/89.16 tff(1804,plain,
% 88.98/89.16 (((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))))),
% 88.98/89.16 inference(rewrite,[status(thm)],[])).
% 88.98/89.16 tff(1805,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a)))))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1804])).
% 88.98/89.16 tff(1806,plain,
% 88.98/89.16 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))))),
% 88.98/89.16 inference(transitivity,[status(thm)],[1805, 1803])).
% 88.98/89.16 tff(1807,plain,
% 88.98/89.16 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.98/89.16 inference(quant_inst,[status(thm)],[])).
% 88.98/89.16 tff(1808,plain,
% 88.98/89.16 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a)))),
% 88.98/89.16 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 88.98/89.16 tff(1809,plain,
% 88.98/89.16 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f19(compose(b, a))),
% 88.98/89.16 inference(unit_resolution,[status(thm)],[1808, 188, 1802])).
% 88.98/89.16 tff(1810,plain,
% 88.98/89.16 (f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1444])).
% 88.98/89.16 tff(1811,plain,
% 88.98/89.16 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.16 inference(symmetry,[status(thm)],[1810])).
% 88.98/89.16 tff(1812,assumption,(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), introduced(assumption)).
% 88.98/89.16 tff(1813,plain,
% 88.98/89.16 (f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.16 inference(symmetry,[status(thm)],[1506])).
% 88.98/89.16 tff(1814,plain,
% 88.98/89.16 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.16 inference(monotonicity,[status(thm)],[1813])).
% 88.98/89.16 tff(1815,assumption,(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), introduced(assumption)).
% 88.98/89.16 tff(1816,plain,
% 88.98/89.16 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1815])).
% 88.98/89.17 tff(1817,plain,
% 88.98/89.17 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.17 inference(transitivity,[status(thm)],[1816, 1814, 1812])).
% 88.98/89.17 tff(1818,plain,
% 88.98/89.17 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1816])).
% 88.98/89.17 tff(1819,plain,
% 88.98/89.17 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1818])).
% 88.98/89.17 tff(1820,plain,
% 88.98/89.17 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.17 inference(transitivity,[status(thm)],[1819, 651])).
% 88.98/89.17 tff(1821,plain,
% 88.98/89.17 ((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1820])).
% 88.98/89.17 tff(1822,assumption,(~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), introduced(assumption)).
% 88.98/89.17 tff(1823,plain,
% 88.98/89.17 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.17 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 88.98/89.17 tff(1824,plain,
% 88.98/89.17 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.17 inference(unit_resolution,[status(thm)],[670, 1823])).
% 88.98/89.17 tff(1825,plain,
% 88.98/89.17 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1824])).
% 88.98/89.17 tff(1826,plain,
% 88.98/89.17 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.17 inference(transitivity,[status(thm)],[1442, 1825])).
% 88.98/89.17 tff(1827,plain,
% 88.98/89.17 (f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1826, 1817])).
% 88.98/89.17 tff(1828,plain,
% 88.98/89.17 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1827])).
% 88.98/89.17 tff(1829,plain,
% 88.98/89.17 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(symmetry,[status(thm)],[518])).
% 88.98/89.17 tff(1830,plain,
% 88.98/89.17 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.98/89.17 inference(transitivity,[status(thm)],[1829, 1828, 1811, 1809])).
% 88.98/89.17 tff(1831,plain,
% 88.98/89.17 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1830])).
% 88.98/89.17 tff(1832,plain,
% 88.98/89.17 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1831])).
% 88.98/89.17 tff(1833,plain,
% 88.98/89.17 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.17 inference(transitivity,[status(thm)],[1442, 222, 1832, 524])).
% 88.98/89.17 tff(1834,plain,
% 88.98/89.17 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1817])).
% 88.98/89.17 tff(1835,plain,
% 88.98/89.17 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[1834])).
% 88.98/89.17 tff(1836,plain,
% 88.98/89.17 (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(modus_ponens,[status(thm)],[1471, 1835])).
% 88.98/89.17 tff(1837,plain,
% 88.98/89.17 ($false),
% 88.98/89.17 inference(unit_resolution,[status(thm)],[1836, 1833])).
% 88.98/89.17 tff(1838,plain,((~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.17 tff(1839,plain,
% 88.98/89.17 (~(f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.17 inference(unit_resolution,[status(thm)],[1838, 1783, 1440, 1471, 1791])).
% 88.98/89.17 tff(1840,plain,
% 88.98/89.17 (~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(modus_ponens,[status(thm)],[1839, 1788])).
% 88.98/89.17 tff(1841,plain,
% 88.98/89.17 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.17 inference(monotonicity,[status(thm)],[527])).
% 88.98/89.17 tff(1842,plain,
% 88.98/89.17 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.17 inference(symmetry,[status(thm)],[1841])).
% 88.98/89.17 tff(1843,plain,
% 88.98/89.17 (member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.17 inference(modus_ponens,[status(thm)],[486, 1842])).
% 88.98/89.17 tff(1844,plain,
% 88.98/89.17 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.18 inference(rewrite,[status(thm)],[])).
% 88.98/89.18 tff(1845,plain,
% 88.98/89.18 (((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.18 inference(rewrite,[status(thm)],[])).
% 88.98/89.18 tff(1846,plain,
% 88.98/89.18 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.18 inference(monotonicity,[status(thm)],[1845])).
% 88.98/89.18 tff(1847,plain,
% 88.98/89.18 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.18 inference(transitivity,[status(thm)],[1846, 1844])).
% 88.98/89.18 tff(1848,plain,
% 88.98/89.18 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.98/89.18 inference(quant_inst,[status(thm)],[])).
% 88.98/89.18 tff(1849,plain,
% 88.98/89.18 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 88.98/89.18 tff(1850,plain,
% 88.98/89.18 ((~member(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(unit_resolution,[status(thm)],[1849, 188])).
% 88.98/89.18 tff(1851,plain,
% 88.98/89.18 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(unit_resolution,[status(thm)],[1850, 1843])).
% 88.98/89.18 tff(1852,plain,
% 88.98/89.18 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.18 inference(unit_resolution,[status(thm)],[1851, 1840])).
% 88.98/89.18 tff(1853,plain,
% 88.98/89.18 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(symmetry,[status(thm)],[1852])).
% 88.98/89.18 tff(1854,plain,
% 88.98/89.18 ((~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))))),
% 88.98/89.18 inference(monotonicity,[status(thm)],[1007])).
% 88.98/89.18 tff(1855,plain,
% 88.98/89.18 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(monotonicity,[status(thm)],[1440])).
% 88.98/89.18 tff(1856,plain,
% 88.98/89.18 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(commutativity,[status(thm)],[])).
% 88.98/89.18 tff(1857,plain,
% 88.98/89.18 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.18 inference(transitivity,[status(thm)],[1499, 1783])).
% 88.98/89.18 tff(1858,plain,
% 88.98/89.18 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.18 inference(monotonicity,[status(thm)],[1857, 1441])).
% 88.98/89.18 tff(1859,plain,
% 88.98/89.18 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.18 inference(transitivity,[status(thm)],[1858, 1856])).
% 88.98/89.18 tff(1860,plain,
% 88.98/89.18 ((f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.18 inference(transitivity,[status(thm)],[1859, 1855, 1618])).
% 88.98/89.18 tff(1861,plain,
% 88.98/89.18 (f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.18 inference(unit_resolution,[status(thm)],[346, 1839])).
% 88.98/89.18 tff(1862,plain,
% 88.98/89.18 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.18 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 88.98/89.18 tff(1863,plain,
% 88.98/89.18 (~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.18 inference(unit_resolution,[status(thm)],[1767, 1862, 1118, 1440, 971])).
% 88.98/89.18 tff(1864,plain,
% 88.98/89.18 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.18 inference(modus_ponens,[status(thm)],[1863, 1854])).
% 88.98/89.18 tff(1865,plain,
% 88.98/89.18 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.18 inference(transitivity,[status(thm)],[1853, 1464])).
% 88.98/89.18 tff(1866,plain,
% 88.98/89.18 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1865])).
% 88.98/89.19 tff(1867,plain,
% 88.98/89.19 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[983, 1866])).
% 88.98/89.19 tff(1868,plain,
% 88.98/89.19 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1260, 188, 1867])).
% 88.98/89.19 tff(1869,plain,
% 88.98/89.19 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1868, 1864])).
% 88.98/89.19 tff(1870,plain,
% 88.98/89.19 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f23(sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(symmetry,[status(thm)],[1783])).
% 88.98/89.19 tff(1871,plain,
% 88.98/89.19 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1870, 1498, 1861, 1441])).
% 88.98/89.19 tff(1872,plain,
% 88.98/89.19 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1871])).
% 88.98/89.19 tff(1873,plain,
% 88.98/89.19 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1611, 1872, 1472, 778])).
% 88.98/89.19 tff(1874,plain,
% 88.98/89.19 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1873, 1869])).
% 88.98/89.19 tff(1875,plain,
% 88.98/89.19 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.19 inference(symmetry,[status(thm)],[1874])).
% 88.98/89.19 tff(1876,plain,
% 88.98/89.19 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1440, 1875, 1853, 1464])).
% 88.98/89.19 tff(1877,plain,
% 88.98/89.19 ($false),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1471, 1876])).
% 88.98/89.19 tff(1878,plain,((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.19 tff(1879,plain,
% 88.98/89.19 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1878, 971])).
% 88.98/89.19 tff(1880,plain,
% 88.98/89.19 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[1879, 1467])).
% 88.98/89.19 tff(1881,plain,
% 88.98/89.19 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[469, 1880])).
% 88.98/89.19 tff(1882,plain,
% 88.98/89.19 (f20(compose(b, a)) = f19(compose(b, a))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[1881, 429])).
% 88.98/89.19 tff(1883,plain,
% 88.98/89.19 (f19(compose(b, a)) = f20(compose(b, a))),
% 88.98/89.19 inference(symmetry,[status(thm)],[1882])).
% 88.98/89.19 tff(1884,plain,
% 88.98/89.19 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1883])).
% 88.98/89.19 tff(1885,plain,
% 88.98/89.19 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1884, 970])).
% 88.98/89.19 tff(1886,plain,
% 88.98/89.19 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.98/89.19 inference(symmetry,[status(thm)],[1885])).
% 88.98/89.19 tff(1887,plain,
% 88.98/89.19 ((~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1886])).
% 88.98/89.19 tff(1888,plain,
% 88.98/89.19 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1856, 1855, 1618])).
% 88.98/89.19 tff(1889,plain,
% 88.98/89.19 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = singleton_set(f19(compose(b, a)))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1440, 222])).
% 88.98/89.19 tff(1890,plain,
% 88.98/89.19 (non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[1889, 1879])).
% 88.98/89.19 tff(1891,plain,
% 88.98/89.19 (non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(transitivity,[status(thm)],[1890, 212, 202, 521])).
% 88.98/89.19 tff(1892,plain,
% 88.98/89.19 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[525, 1891])).
% 88.98/89.19 tff(1893,plain,
% 88.98/89.19 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.19 inference(symmetry,[status(thm)],[1892])).
% 88.98/89.19 tff(1894,plain,
% 88.98/89.19 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(monotonicity,[status(thm)],[525])).
% 88.98/89.19 tff(1895,plain,
% 88.98/89.19 ((~![Y: $i, X: $i] : little_set(non_ordered_pair(X, Y))) | little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(quant_inst,[status(thm)],[])).
% 88.98/89.19 tff(1896,plain,
% 88.98/89.19 (little_set(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1895, 237])).
% 88.98/89.19 tff(1897,plain,
% 88.98/89.19 (little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[1896, 1894])).
% 88.98/89.19 tff(1898,plain,
% 88.98/89.19 (((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.19 inference(rewrite,[status(thm)],[])).
% 88.98/89.19 tff(1899,plain,
% 88.98/89.19 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.19 inference(quant_inst,[status(thm)],[])).
% 88.98/89.19 tff(1900,plain,
% 88.98/89.19 ((~![Y: $i, X: $i] : ((~little_set(X)) | member(X, non_ordered_pair(X, Y)))) | (~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 88.98/89.19 tff(1901,plain,
% 88.98/89.19 ((~little_set(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1900, 135])).
% 88.98/89.19 tff(1902,plain,
% 88.98/89.19 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.19 inference(unit_resolution,[status(thm)],[1901, 1897])).
% 88.98/89.19 tff(1903,plain,
% 88.98/89.19 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.19 inference(modus_ponens,[status(thm)],[1902, 1893])).
% 88.98/89.19 tff(1904,plain,
% 88.98/89.19 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(rewrite,[status(thm)],[])).
% 88.98/89.20 tff(1905,plain,
% 88.98/89.20 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(rewrite,[status(thm)],[])).
% 88.98/89.20 tff(1906,plain,
% 88.98/89.20 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))))),
% 88.98/89.20 inference(monotonicity,[status(thm)],[1905])).
% 88.98/89.20 tff(1907,plain,
% 88.98/89.20 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(transitivity,[status(thm)],[1906, 1904])).
% 88.98/89.20 tff(1908,plain,
% 88.98/89.20 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(quant_inst,[status(thm)],[])).
% 88.98/89.20 tff(1909,plain,
% 88.98/89.20 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.98/89.20 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 88.98/89.20 tff(1910,plain,
% 88.98/89.20 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.98/89.20 inference(unit_resolution,[status(thm)],[1909, 188])).
% 88.98/89.20 tff(1911,plain,
% 88.98/89.20 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.20 inference(unit_resolution,[status(thm)],[1910, 1903])).
% 88.98/89.20 tff(1912,plain,
% 88.98/89.20 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.20 inference(modus_ponens,[status(thm)],[1911, 1888])).
% 88.98/89.20 tff(1913,plain,
% 88.98/89.20 (~(f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.20 inference(unit_resolution,[status(thm)],[1767, 1912, 1118, 1440, 971])).
% 88.98/89.20 tff(1914,plain,
% 88.98/89.20 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.98/89.20 inference(modus_ponens,[status(thm)],[1913, 1887])).
% 88.98/89.20 tff(1915,plain,
% 88.98/89.20 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.20 inference(transitivity,[status(thm)],[1441, 1879])).
% 88.98/89.20 tff(1916,plain,
% 88.98/89.20 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.20 inference(monotonicity,[status(thm)],[1915])).
% 88.98/89.20 tff(1917,plain,
% 88.98/89.20 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.20 inference(symmetry,[status(thm)],[1916])).
% 88.98/89.20 tff(1918,plain,
% 88.98/89.20 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 88.98/89.20 inference(monotonicity,[status(thm)],[1891])).
% 88.98/89.20 tff(1919,plain,
% 88.98/89.20 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.20 inference(symmetry,[status(thm)],[1918])).
% 88.98/89.20 tff(1920,plain,
% 88.98/89.20 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 88.98/89.20 inference(modus_ponens,[status(thm)],[616, 1919])).
% 88.98/89.20 tff(1921,plain,
% 88.98/89.20 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(rewrite,[status(thm)],[])).
% 88.98/89.20 tff(1922,plain,
% 88.98/89.20 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))) <=> ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.20 inference(rewrite,[status(thm)],[])).
% 88.98/89.20 tff(1923,plain,
% 88.98/89.20 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[1922])).
% 88.98/89.21 tff(1924,plain,
% 88.98/89.21 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.21 inference(transitivity,[status(thm)],[1923, 1921])).
% 88.98/89.21 tff(1925,plain,
% 88.98/89.21 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))))),
% 88.98/89.21 inference(quant_inst,[status(thm)],[])).
% 88.98/89.21 tff(1926,plain,
% 88.98/89.21 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.98/89.21 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 88.98/89.21 tff(1927,plain,
% 88.98/89.21 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 88.98/89.21 inference(unit_resolution,[status(thm)],[1926, 188])).
% 88.98/89.21 tff(1928,plain,
% 88.98/89.21 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 88.98/89.21 inference(unit_resolution,[status(thm)],[1927, 1920])).
% 88.98/89.21 tff(1929,plain,
% 88.98/89.21 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.21 inference(transitivity,[status(thm)],[1928, 1879])).
% 88.98/89.21 tff(1930,plain,
% 88.98/89.21 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[1929])).
% 88.98/89.21 tff(1931,plain,
% 88.98/89.21 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.21 inference(modus_ponens,[status(thm)],[983, 1930])).
% 88.98/89.21 tff(1932,plain,
% 88.98/89.21 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.21 inference(modus_ponens,[status(thm)],[1931, 1917])).
% 88.98/89.21 tff(1933,plain,
% 88.98/89.21 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.98/89.21 inference(rewrite,[status(thm)],[])).
% 88.98/89.21 tff(1934,plain,
% 88.98/89.21 (((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.98/89.21 inference(rewrite,[status(thm)],[])).
% 88.98/89.21 tff(1935,plain,
% 88.98/89.21 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[1934])).
% 88.98/89.21 tff(1936,plain,
% 88.98/89.21 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.98/89.21 inference(transitivity,[status(thm)],[1935, 1933])).
% 88.98/89.21 tff(1937,plain,
% 88.98/89.21 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 88.98/89.21 inference(quant_inst,[status(thm)],[])).
% 88.98/89.21 tff(1938,plain,
% 88.98/89.21 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.21 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 88.98/89.21 tff(1939,plain,
% 88.98/89.21 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.21 inference(unit_resolution,[status(thm)],[1938, 188])).
% 88.98/89.21 tff(1940,plain,
% 88.98/89.21 ($false),
% 88.98/89.21 inference(unit_resolution,[status(thm)],[1939, 1932, 1914])).
% 88.98/89.21 tff(1941,plain,(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.21 tff(1942,plain,
% 88.98/89.21 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[1941])).
% 88.98/89.21 tff(1943,plain,
% 88.98/89.21 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.21 inference(symmetry,[status(thm)],[1942])).
% 88.98/89.21 tff(1944,plain,
% 88.98/89.21 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[967])).
% 88.98/89.21 tff(1945,plain,
% 88.98/89.21 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.21 inference(transitivity,[status(thm)],[1944, 1630])).
% 88.98/89.21 tff(1946,plain,
% 88.98/89.21 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.21 inference(transitivity,[status(thm)],[1945, 1943])).
% 88.98/89.21 tff(1947,plain,
% 88.98/89.21 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.21 inference(monotonicity,[status(thm)],[1946])).
% 88.98/89.21 tff(1948,plain,
% 88.98/89.21 (~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.21 inference(modus_ponens,[status(thm)],[952, 1947])).
% 88.98/89.21 tff(1949,plain,
% 88.98/89.21 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.22 inference(monotonicity,[status(thm)],[869])).
% 88.98/89.22 tff(1950,plain,
% 88.98/89.22 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.22 inference(symmetry,[status(thm)],[1949])).
% 88.98/89.22 tff(1951,plain,
% 88.98/89.22 (member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.22 inference(modus_ponens,[status(thm)],[1074, 1950])).
% 88.98/89.22 tff(1952,plain,
% 88.98/89.22 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.98/89.22 inference(rewrite,[status(thm)],[])).
% 88.98/89.22 tff(1953,plain,
% 88.98/89.22 (((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.98/89.22 inference(rewrite,[status(thm)],[])).
% 88.98/89.22 tff(1954,plain,
% 88.98/89.22 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))))),
% 88.98/89.22 inference(monotonicity,[status(thm)],[1953])).
% 88.98/89.22 tff(1955,plain,
% 88.98/89.22 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.98/89.22 inference(transitivity,[status(thm)],[1954, 1952])).
% 88.98/89.22 tff(1956,plain,
% 88.98/89.22 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.98/89.22 inference(quant_inst,[status(thm)],[])).
% 88.98/89.22 tff(1957,plain,
% 88.98/89.22 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.22 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 88.98/89.22 tff(1958,plain,
% 88.98/89.22 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~member(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.22 inference(unit_resolution,[status(thm)],[1957, 188])).
% 88.98/89.22 tff(1959,plain,
% 88.98/89.22 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.22 inference(unit_resolution,[status(thm)],[1958, 1951])).
% 88.98/89.22 tff(1960,plain,
% 88.98/89.22 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.22 inference(unit_resolution,[status(thm)],[1959, 1948])).
% 88.98/89.22 tff(1961,plain,
% 88.98/89.22 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.22 inference(symmetry,[status(thm)],[1960])).
% 88.98/89.22 tff(1962,plain,
% 88.98/89.22 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.22 inference(transitivity,[status(thm)],[1961, 1941])).
% 88.98/89.22 tff(1963,plain,
% 88.98/89.22 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.22 inference(monotonicity,[status(thm)],[1962, 969])).
% 88.98/89.22 tff(1964,plain,
% 88.98/89.22 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 88.98/89.22 inference(transitivity,[status(thm)],[1427, 1963, 951])).
% 88.98/89.22 tff(1965,plain,
% 88.98/89.22 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 88.98/89.22 inference(monotonicity,[status(thm)],[1964])).
% 88.98/89.22 tff(1966,plain,
% 88.98/89.22 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.22 inference(symmetry,[status(thm)],[1965])).
% 88.98/89.22 tff(1967,plain,
% 88.98/89.22 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.22 inference(transitivity,[status(thm)],[222, 1966, 866])).
% 88.98/89.22 tff(1968,plain,
% 88.98/89.22 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.22 inference(monotonicity,[status(thm)],[1945])).
% 88.98/89.22 tff(1969,plain,
% 88.98/89.22 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.22 inference(modus_ponens,[status(thm)],[952, 1968])).
% 88.98/89.22 tff(1970,plain,
% 88.98/89.22 ($false),
% 88.98/89.22 inference(unit_resolution,[status(thm)],[1969, 1967])).
% 88.98/89.22 tff(1971,plain,((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.23 tff(1972,plain,
% 88.98/89.23 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1971, 933])).
% 88.98/89.23 tff(1973,plain,
% 88.98/89.23 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[933])).
% 88.98/89.23 tff(1974,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1972])).
% 88.98/89.23 tff(1975,plain,
% 88.98/89.23 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(transitivity,[status(thm)],[1941, 1974, 933, 867])).
% 88.98/89.23 tff(1976,plain,
% 88.98/89.23 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1975])).
% 88.98/89.23 tff(1977,plain,
% 88.98/89.23 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(transitivity,[status(thm)],[1976, 1664])).
% 88.98/89.23 tff(1978,plain,
% 88.98/89.23 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.23 inference(commutativity,[status(thm)],[])).
% 88.98/89.23 tff(1979,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1941])).
% 88.98/89.23 tff(1980,plain,
% 88.98/89.23 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(transitivity,[status(thm)],[866, 968, 1306, 1979])).
% 88.98/89.23 tff(1981,plain,
% 88.98/89.23 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1980])).
% 88.98/89.23 tff(1982,plain,
% 88.98/89.23 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.23 inference(transitivity,[status(thm)],[1981, 1978])).
% 88.98/89.23 tff(1983,plain,
% 88.98/89.23 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1982])).
% 88.98/89.23 tff(1984,plain,
% 88.98/89.23 ((~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1983])).
% 88.98/89.23 tff(1985,assumption,(~(f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))), introduced(assumption)).
% 88.98/89.23 tff(1986,plain,
% 88.98/89.23 (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 88.98/89.23 tff(1987,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1320, 1986])).
% 88.98/89.23 tff(1988,plain,
% 88.98/89.23 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1987])).
% 88.98/89.23 tff(1989,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1395])).
% 88.98/89.23 tff(1990,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.23 inference(transitivity,[status(thm)],[1989, 1988])).
% 88.98/89.23 tff(1991,plain,
% 88.98/89.23 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1990])).
% 88.98/89.23 tff(1992,plain,
% 88.98/89.23 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1991])).
% 88.98/89.23 tff(1993,plain,
% 88.98/89.23 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[1027, 1992])).
% 88.98/89.23 tff(1994,plain,
% 88.98/89.23 (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[1112, 1110])).
% 88.98/89.23 tff(1995,plain,
% 88.98/89.23 ($false),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[862, 1994])).
% 88.98/89.23 tff(1996,plain,((~(f21(compose(b, a)) = f19(compose(b, a)))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.23 tff(1997,plain,
% 88.98/89.23 (~(f21(compose(b, a)) = f19(compose(b, a)))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1996, 862])).
% 88.98/89.23 tff(1998,plain,
% 88.98/89.23 ((f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1349, 188, 1997])).
% 88.98/89.23 tff(1999,plain,
% 88.98/89.23 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1998, 1993])).
% 88.98/89.23 tff(2000,plain,
% 88.98/89.23 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.98/89.23 inference(symmetry,[status(thm)],[1999])).
% 88.98/89.23 tff(2001,plain,
% 88.98/89.23 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.23 inference(transitivity,[status(thm)],[1003, 1102, 1388, 778, 1031])).
% 88.98/89.23 tff(2002,plain,
% 88.98/89.23 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[2001, 2000])).
% 88.98/89.23 tff(2003,plain,
% 88.98/89.23 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(symmetry,[status(thm)],[2002])).
% 88.98/89.23 tff(2004,plain,
% 88.98/89.23 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[2003])).
% 88.98/89.23 tff(2005,plain,
% 88.98/89.23 (~(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[862, 2004])).
% 88.98/89.23 tff(2006,plain,
% 88.98/89.23 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1436, 1999, 198, 727, 967, 1306])).
% 88.98/89.23 tff(2007,plain,
% 88.98/89.23 ($false),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[2006, 2005])).
% 88.98/89.23 tff(2008,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.23 tff(2009,plain,
% 88.98/89.23 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[2008, 1972, 933, 198, 862])).
% 88.98/89.23 tff(2010,plain,
% 88.98/89.23 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[2009, 1977])).
% 88.98/89.23 tff(2011,plain,
% 88.98/89.23 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[1972])).
% 88.98/89.23 tff(2012,plain,
% 88.98/89.23 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.23 inference(transitivity,[status(thm)],[2011, 972])).
% 88.98/89.23 tff(2013,plain,
% 88.98/89.23 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.23 inference(monotonicity,[status(thm)],[2012])).
% 88.98/89.23 tff(2014,plain,
% 88.98/89.23 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.23 inference(modus_ponens,[status(thm)],[863, 2013])).
% 88.98/89.23 tff(2015,plain,
% 88.98/89.23 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[1289, 2014])).
% 88.98/89.23 tff(2016,plain,
% 88.98/89.23 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.23 inference(transitivity,[status(thm)],[2015, 2010, 866, 1973, 1972])).
% 88.98/89.23 tff(2017,plain,
% 88.98/89.23 ($false),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[2014, 2016])).
% 88.98/89.23 tff(2018,plain,((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.23 tff(2019,plain,
% 88.98/89.23 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.23 inference(unit_resolution,[status(thm)],[2018, 862, 198])).
% 88.98/89.23 tff(2020,plain,
% 88.98/89.23 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 88.98/89.23 inference(transitivity,[status(thm)],[728, 499, 378, 375])).
% 88.98/89.23 tff(2021,plain,
% 88.98/89.23 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2020])).
% 88.98/89.24 tff(2022,plain,
% 88.98/89.24 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[983, 2021])).
% 88.98/89.24 tff(2023,assumption,(~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))), introduced(assumption)).
% 88.98/89.24 tff(2024,plain,
% 88.98/89.24 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[1297, 866])).
% 88.98/89.24 tff(2025,plain,
% 88.98/89.24 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2024])).
% 88.98/89.24 tff(2026,plain,
% 88.98/89.24 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.24 inference(transitivity,[status(thm)],[2025, 1667])).
% 88.98/89.24 tff(2027,plain,
% 88.98/89.24 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2026])).
% 88.98/89.24 tff(2028,plain,
% 88.98/89.24 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[2023, 2027])).
% 88.98/89.24 tff(2029,plain,
% 88.98/89.24 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[1682, 2028])).
% 88.98/89.24 tff(2030,plain,
% 88.98/89.24 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2029])).
% 88.98/89.24 tff(2031,plain,
% 88.98/89.24 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.24 inference(transitivity,[status(thm)],[1102, 2030, 778, 1031])).
% 88.98/89.24 tff(2032,plain,
% 88.98/89.24 ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2031])).
% 88.98/89.24 tff(2033,plain,
% 88.98/89.24 ((f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.98/89.24 inference(transitivity,[status(thm)],[2032, 1108])).
% 88.98/89.24 tff(2034,plain,
% 88.98/89.24 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2033])).
% 88.98/89.24 tff(2035,plain,
% 88.98/89.24 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2034])).
% 88.98/89.24 tff(2036,plain,
% 88.98/89.24 (~(f21(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[862, 2035])).
% 88.98/89.24 tff(2037,plain,
% 88.98/89.24 (f21(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[1126, 2036, 1028])).
% 88.98/89.24 tff(2038,plain,
% 88.98/89.24 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2037])).
% 88.98/89.24 tff(2039,plain,
% 88.98/89.24 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2030])).
% 88.98/89.24 tff(2040,plain,
% 88.98/89.24 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.24 inference(transitivity,[status(thm)],[779, 2039, 833])).
% 88.98/89.24 tff(2041,plain,
% 88.98/89.24 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2040])).
% 88.98/89.24 tff(2042,plain,
% 88.98/89.24 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2041])).
% 88.98/89.24 tff(2043,plain,
% 88.98/89.24 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.24 inference(symmetry,[status(thm)],[2042])).
% 88.98/89.24 tff(2044,plain,
% 88.98/89.24 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[1143, 2043])).
% 88.98/89.24 tff(2045,plain,
% 88.98/89.24 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[1189, 1183, 1173, 273, 1159, 1155, 2044, 1134])).
% 88.98/89.24 tff(2046,plain,
% 88.98/89.24 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 88.98/89.24 inference(symmetry,[status(thm)],[2045])).
% 88.98/89.24 tff(2047,plain,
% 88.98/89.24 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2046])).
% 88.98/89.24 tff(2048,plain,
% 88.98/89.24 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2047])).
% 88.98/89.24 tff(2049,plain,
% 88.98/89.24 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.24 inference(symmetry,[status(thm)],[2048])).
% 88.98/89.24 tff(2050,plain,
% 88.98/89.24 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[1205, 2049])).
% 88.98/89.24 tff(2051,plain,
% 88.98/89.24 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[1227, 1183, 1221, 1214, 1159, 1210, 979, 2050])).
% 88.98/89.24 tff(2052,plain,
% 88.98/89.24 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f21(compose(b, a))),
% 88.98/89.24 inference(transitivity,[status(thm)],[2051, 2038])).
% 88.98/89.24 tff(2053,plain,
% 88.98/89.24 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f20(compose(b, a)) = f21(compose(b, a)))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2052])).
% 88.98/89.24 tff(2054,plain,
% 88.98/89.24 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2053])).
% 88.98/89.24 tff(2055,plain,
% 88.98/89.24 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.24 inference(transitivity,[status(thm)],[2054, 1007])).
% 88.98/89.24 tff(2056,plain,
% 88.98/89.24 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2055])).
% 88.98/89.24 tff(2057,plain,
% 88.98/89.24 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[1244, 2056])).
% 88.98/89.24 tff(2058,plain,
% 88.98/89.24 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.24 inference(commutativity,[status(thm)],[])).
% 88.98/89.24 tff(2059,plain,
% 88.98/89.24 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2058])).
% 88.98/89.24 tff(2060,plain,
% 88.98/89.24 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2051])).
% 88.98/89.24 tff(2061,plain,
% 88.98/89.24 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2060])).
% 88.98/89.24 tff(2062,plain,
% 88.98/89.24 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.98/89.24 inference(transitivity,[status(thm)],[2061, 2059])).
% 88.98/89.24 tff(2063,plain,
% 88.98/89.24 ((~(f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2062])).
% 88.98/89.24 tff(2064,plain,
% 88.98/89.24 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[1031, 2038])).
% 88.98/89.24 tff(2065,plain,
% 88.98/89.24 ((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(symmetry,[status(thm)],[2064])).
% 88.98/89.24 tff(2066,plain,
% 88.98/89.24 ((~(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))) <=> (~(f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.24 inference(monotonicity,[status(thm)],[2065])).
% 88.98/89.24 tff(2067,plain,
% 88.98/89.24 (~(f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[862, 2066])).
% 88.98/89.24 tff(2068,plain,
% 88.98/89.24 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 88.98/89.24 inference(modus_ponens,[status(thm)],[2067, 2063])).
% 88.98/89.24 tff(2069,plain,
% 88.98/89.24 ((f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[1260, 188, 1005])).
% 88.98/89.24 tff(2070,plain,
% 88.98/89.24 ($false),
% 88.98/89.24 inference(unit_resolution,[status(thm)],[2069, 2068, 2057])).
% 88.98/89.24 tff(2071,plain,((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))), inference(lemma,lemma(discharge,[]))).
% 88.98/89.25 tff(2072,plain,
% 88.98/89.25 (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.25 inference(unit_resolution,[status(thm)],[2071, 2023, 1006, 862, 1008, 1005])).
% 88.98/89.25 tff(2073,plain,
% 88.98/89.25 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.25 inference(unit_resolution,[status(thm)],[965, 2072])).
% 88.98/89.25 tff(2074,plain,
% 88.98/89.25 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 88.98/89.25 inference(transitivity,[status(thm)],[1009, 2073])).
% 88.98/89.25 tff(2075,plain,
% 88.98/89.25 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 88.98/89.25 inference(monotonicity,[status(thm)],[1008])).
% 88.98/89.25 tff(2076,plain,
% 88.98/89.25 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.25 inference(transitivity,[status(thm)],[2075, 1268])).
% 88.98/89.25 tff(2077,plain,
% 88.98/89.25 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.25 inference(monotonicity,[status(thm)],[2076])).
% 88.98/89.25 tff(2078,plain,
% 88.98/89.25 (~(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.25 inference(modus_ponens,[status(thm)],[2072, 2077])).
% 88.98/89.25 tff(2079,plain,
% 88.98/89.25 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 88.98/89.25 inference(unit_resolution,[status(thm)],[1320, 2078])).
% 88.98/89.25 tff(2080,plain,
% 88.98/89.25 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.25 inference(symmetry,[status(thm)],[2079])).
% 88.98/89.25 tff(2081,plain,
% 88.98/89.25 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 88.98/89.25 inference(transitivity,[status(thm)],[867, 2080])).
% 88.98/89.25 tff(2082,plain,
% 88.98/89.25 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 88.98/89.25 inference(monotonicity,[status(thm)],[2081, 2074])).
% 88.98/89.25 tff(2083,plain,
% 88.98/89.25 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.25 inference(rewrite,[status(thm)],[])).
% 88.98/89.25 tff(2084,plain,
% 88.98/89.25 (((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.25 inference(rewrite,[status(thm)],[])).
% 88.98/89.25 tff(2085,plain,
% 88.98/89.25 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))))),
% 88.98/89.25 inference(monotonicity,[status(thm)],[2084])).
% 88.98/89.25 tff(2086,plain,
% 88.98/89.25 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.25 inference(transitivity,[status(thm)],[2085, 2083])).
% 88.98/89.25 tff(2087,plain,
% 88.98/89.25 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 88.98/89.25 inference(quant_inst,[status(thm)],[])).
% 88.98/89.25 tff(2088,plain,
% 88.98/89.25 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.25 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 88.98/89.25 tff(2089,plain,
% 88.98/89.25 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 88.98/89.25 inference(unit_resolution,[status(thm)],[2088, 163, 988, 814])).
% 88.98/89.25 tff(2090,plain,
% 88.98/89.25 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 88.98/89.25 inference(rewrite,[status(thm)],[])).
% 88.98/89.25 tff(2091,plain,
% 88.98/89.25 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.25 inference(quant_inst,[status(thm)],[])).
% 89.09/89.25 tff(2092,plain,
% 89.09/89.25 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.25 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 89.09/89.25 tff(2093,plain,
% 89.09/89.25 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.25 inference(unit_resolution,[status(thm)],[2092, 332, 2089])).
% 89.09/89.25 tff(2094,plain,
% 89.09/89.25 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.25 inference(rewrite,[status(thm)],[])).
% 89.09/89.25 tff(2095,plain,
% 89.09/89.25 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(rewrite,[status(thm)],[])).
% 89.09/89.26 tff(2096,plain,
% 89.09/89.26 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.26 inference(monotonicity,[status(thm)],[2095])).
% 89.09/89.26 tff(2097,plain,
% 89.09/89.26 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(transitivity,[status(thm)],[2096, 2094])).
% 89.09/89.26 tff(2098,plain,
% 89.09/89.26 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))))),
% 89.09/89.26 inference(quant_inst,[status(thm)],[])).
% 89.09/89.26 tff(2099,plain,
% 89.09/89.26 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.26 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 89.09/89.26 tff(2100,plain,
% 89.09/89.26 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.09/89.26 inference(unit_resolution,[status(thm)],[2099, 188, 2093])).
% 89.09/89.26 tff(2101,plain,
% 89.09/89.26 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(symmetry,[status(thm)],[2100])).
% 89.09/89.26 tff(2102,plain,
% 89.09/89.26 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 89.09/89.26 inference(transitivity,[status(thm)],[2101, 2082, 861])).
% 89.09/89.26 tff(2103,plain,
% 89.09/89.26 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 89.09/89.26 inference(monotonicity,[status(thm)],[2102])).
% 89.09/89.26 tff(2104,plain,
% 89.09/89.26 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.26 inference(symmetry,[status(thm)],[2103])).
% 89.09/89.26 tff(2105,plain,
% 89.09/89.26 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.26 inference(transitivity,[status(thm)],[222, 2104, 866])).
% 89.09/89.26 tff(2106,plain,
% 89.09/89.26 ((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(monotonicity,[status(thm)],[2073])).
% 89.09/89.26 tff(2107,plain,
% 89.09/89.26 ((~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.26 inference(monotonicity,[status(thm)],[2106])).
% 89.09/89.26 tff(2108,plain,
% 89.09/89.26 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(modus_ponens,[status(thm)],[2023, 2107])).
% 89.09/89.26 tff(2109,plain,
% 89.09/89.26 ($false),
% 89.09/89.26 inference(unit_resolution,[status(thm)],[2108, 2105])).
% 89.09/89.26 tff(2110,plain,((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 89.09/89.26 tff(2111,plain,
% 89.09/89.26 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.26 inference(unit_resolution,[status(thm)],[2110, 2019, 756, 862, 2022])).
% 89.09/89.26 tff(2112,plain,
% 89.09/89.26 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(symmetry,[status(thm)],[2111])).
% 89.09/89.26 tff(2113,plain,
% 89.09/89.26 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.26 inference(transitivity,[status(thm)],[866, 2112, 2019])).
% 89.09/89.26 tff(2114,plain,
% 89.09/89.26 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(monotonicity,[status(thm)],[2113])).
% 89.09/89.26 tff(2115,plain,
% 89.09/89.26 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.26 inference(unit_resolution,[status(thm)],[1971, 2111])).
% 89.09/89.26 tff(2116,plain,
% 89.09/89.26 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.26 inference(symmetry,[status(thm)],[2115])).
% 89.09/89.27 tff(2117,plain,
% 89.09/89.27 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.27 inference(transitivity,[status(thm)],[1941, 2116, 2111, 867])).
% 89.09/89.27 tff(2118,plain,
% 89.09/89.27 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2117])).
% 89.09/89.27 tff(2119,plain,
% 89.09/89.27 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2118, 1664])).
% 89.09/89.27 tff(2120,plain,
% 89.09/89.27 ((f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2119, 2114])).
% 89.09/89.27 tff(2121,plain,
% 89.09/89.27 (f23(universal_set, ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2008, 2111, 2115, 198, 862])).
% 89.09/89.27 tff(2122,plain,
% 89.09/89.27 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 89.09/89.27 tff(2123,plain,
% 89.09/89.27 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2122])).
% 89.09/89.27 tff(2124,plain,
% 89.09/89.27 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2116, 2019, 2123])).
% 89.09/89.27 tff(2125,plain,
% 89.09/89.27 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2124])).
% 89.09/89.27 tff(2126,plain,
% 89.09/89.27 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2125])).
% 89.09/89.27 tff(2127,plain,
% 89.09/89.27 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[1027, 2126])).
% 89.09/89.27 tff(2128,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.09/89.27 inference(rewrite,[status(thm)],[])).
% 89.09/89.27 tff(2129,plain,
% 89.09/89.27 (((f21(compose(b, a)) = f19(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.09/89.27 inference(rewrite,[status(thm)],[])).
% 89.09/89.27 tff(2130,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f19(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a)))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2129])).
% 89.09/89.27 tff(2131,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f19(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2130, 2128])).
% 89.09/89.27 tff(2132,plain,
% 89.09/89.27 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f19(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.27 inference(quant_inst,[status(thm)],[])).
% 89.09/89.27 tff(2133,plain,
% 89.09/89.27 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a)))),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 89.09/89.27 tff(2134,plain,
% 89.09/89.27 (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2133, 188, 1997])).
% 89.09/89.27 tff(2135,plain,
% 89.09/89.27 ($false),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2134, 2127])).
% 89.09/89.27 tff(2136,plain,((f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 89.09/89.27 tff(2137,plain,
% 89.09/89.27 (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2136, 198])).
% 89.09/89.27 tff(2138,plain,
% 89.09/89.27 (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2137])).
% 89.09/89.27 tff(2139,plain,
% 89.09/89.27 (f21(compose(b, a)) = f19(compose(b, a))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2138, 861])).
% 89.09/89.27 tff(2140,plain,
% 89.09/89.27 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2139])).
% 89.09/89.27 tff(2141,plain,
% 89.09/89.27 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2140])).
% 89.09/89.27 tff(2142,plain,
% 89.09/89.27 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[222, 2141])).
% 89.09/89.27 tff(2143,plain,
% 89.09/89.27 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2142, 842, 839, 835])).
% 89.09/89.27 tff(2144,plain,
% 89.09/89.27 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[867, 2143])).
% 89.09/89.27 tff(2145,plain,
% 89.09/89.27 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2144])).
% 89.09/89.27 tff(2146,plain,
% 89.09/89.27 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[882, 2145])).
% 89.09/89.27 tff(2147,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.27 inference(rewrite,[status(thm)],[])).
% 89.09/89.27 tff(2148,plain,
% 89.09/89.27 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.27 inference(rewrite,[status(thm)],[])).
% 89.09/89.27 tff(2149,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2148])).
% 89.09/89.27 tff(2150,plain,
% 89.09/89.27 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.27 inference(transitivity,[status(thm)],[2149, 2147])).
% 89.09/89.27 tff(2151,plain,
% 89.09/89.27 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.27 inference(quant_inst,[status(thm)],[])).
% 89.09/89.27 tff(2152,plain,
% 89.09/89.27 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 89.09/89.27 tff(2153,plain,
% 89.09/89.27 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2152, 188])).
% 89.09/89.27 tff(2154,plain,
% 89.09/89.27 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[2153, 2146])).
% 89.09/89.27 tff(2155,plain,
% 89.09/89.27 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2154])).
% 89.09/89.27 tff(2156,plain,
% 89.09/89.27 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.27 inference(symmetry,[status(thm)],[2155])).
% 89.09/89.27 tff(2157,plain,
% 89.09/89.27 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.09/89.27 inference(transitivity,[status(thm)],[779, 2156, 833])).
% 89.09/89.27 tff(2158,plain,
% 89.09/89.27 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2157])).
% 89.09/89.27 tff(2159,plain,
% 89.09/89.27 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.09/89.27 inference(monotonicity,[status(thm)],[2158])).
% 89.09/89.27 tff(2160,plain,
% 89.09/89.27 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.09/89.27 inference(symmetry,[status(thm)],[2159])).
% 89.09/89.27 tff(2161,plain,
% 89.09/89.27 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.09/89.27 inference(modus_ponens,[status(thm)],[1143, 2160])).
% 89.09/89.27 tff(2162,plain,
% 89.09/89.27 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.09/89.27 inference(unit_resolution,[status(thm)],[1189, 1183, 1173, 273, 1159, 1155, 2161, 795])).
% 89.09/89.28 tff(2163,plain,
% 89.09/89.28 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.09/89.28 inference(symmetry,[status(thm)],[2162])).
% 89.09/89.28 tff(2164,plain,
% 89.09/89.28 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2163])).
% 89.09/89.28 tff(2165,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2164])).
% 89.09/89.28 tff(2166,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 89.09/89.28 inference(symmetry,[status(thm)],[2165])).
% 89.09/89.28 tff(2167,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[1205, 2166])).
% 89.09/89.28 tff(2168,plain,
% 89.09/89.28 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2143])).
% 89.09/89.28 tff(2169,plain,
% 89.09/89.28 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.28 inference(symmetry,[status(thm)],[2168])).
% 89.09/89.28 tff(2170,plain,
% 89.09/89.28 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[1283, 2169])).
% 89.09/89.28 tff(2171,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.28 inference(rewrite,[status(thm)],[])).
% 89.09/89.28 tff(2172,plain,
% 89.09/89.28 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.28 inference(rewrite,[status(thm)],[])).
% 89.09/89.28 tff(2173,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2172])).
% 89.09/89.28 tff(2174,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.28 inference(transitivity,[status(thm)],[2173, 2171])).
% 89.09/89.28 tff(2175,plain,
% 89.09/89.28 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.09/89.28 inference(quant_inst,[status(thm)],[])).
% 89.09/89.28 tff(2176,plain,
% 89.09/89.28 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 89.09/89.28 tff(2177,plain,
% 89.09/89.28 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.28 inference(unit_resolution,[status(thm)],[2176, 188])).
% 89.09/89.28 tff(2178,plain,
% 89.09/89.28 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.28 inference(unit_resolution,[status(thm)],[2177, 2170])).
% 89.09/89.28 tff(2179,plain,
% 89.09/89.28 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.28 inference(symmetry,[status(thm)],[2178])).
% 89.09/89.28 tff(2180,plain,
% 89.09/89.28 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2179])).
% 89.09/89.28 tff(2181,plain,
% 89.09/89.28 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.28 inference(symmetry,[status(thm)],[2180])).
% 89.09/89.28 tff(2182,plain,
% 89.09/89.28 (((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.28 inference(rewrite,[status(thm)],[])).
% 89.09/89.28 tff(2183,plain,
% 89.09/89.28 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | ((~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.09/89.28 inference(quant_inst,[status(thm)],[])).
% 89.09/89.28 tff(2184,plain,
% 89.09/89.28 ((~![Y: $i, X: $i] : ((~little_set(Y)) | member(Y, non_ordered_pair(X, Y)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 89.09/89.28 tff(2185,plain,
% 89.09/89.28 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.09/89.28 inference(unit_resolution,[status(thm)],[2184, 256, 1210])).
% 89.09/89.28 tff(2186,plain,
% 89.09/89.28 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[2185, 2181])).
% 89.09/89.28 tff(2187,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))))),
% 89.09/89.28 inference(rewrite,[status(thm)],[])).
% 89.09/89.28 tff(2188,plain,
% 89.09/89.28 (((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))) <=> ((~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))))),
% 89.09/89.28 inference(rewrite,[status(thm)],[])).
% 89.09/89.28 tff(2189,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2188])).
% 89.09/89.28 tff(2190,plain,
% 89.09/89.28 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))))),
% 89.09/89.28 inference(transitivity,[status(thm)],[2189, 2187])).
% 89.09/89.28 tff(2191,plain,
% 89.09/89.28 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.09/89.28 inference(quant_inst,[status(thm)],[])).
% 89.09/89.28 tff(2192,plain,
% 89.09/89.28 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 89.09/89.28 tff(2193,plain,
% 89.09/89.28 ((~member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) | (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a)))),
% 89.09/89.28 inference(unit_resolution,[status(thm)],[2192, 188])).
% 89.09/89.28 tff(2194,plain,
% 89.09/89.28 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 89.09/89.28 inference(unit_resolution,[status(thm)],[2193, 2186])).
% 89.09/89.28 tff(2195,plain,
% 89.09/89.28 (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.09/89.28 inference(symmetry,[status(thm)],[2194])).
% 89.09/89.28 tff(2196,plain,
% 89.09/89.28 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2195])).
% 89.09/89.28 tff(2197,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.09/89.28 inference(monotonicity,[status(thm)],[2196])).
% 89.09/89.28 tff(2198,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)),
% 89.09/89.28 inference(symmetry,[status(thm)],[2197])).
% 89.09/89.28 tff(2199,plain,
% 89.09/89.28 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)),
% 89.09/89.28 inference(modus_ponens,[status(thm)],[1214, 2198])).
% 89.09/89.28 tff(2200,plain,
% 89.09/89.28 (member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2020])).
% 89.09/89.29 tff(2201,plain,
% 89.09/89.29 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2200])).
% 89.09/89.29 tff(2202,plain,
% 89.09/89.29 (member(f20(compose(b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[450, 2201])).
% 89.09/89.29 tff(2203,plain,
% 89.09/89.29 ((f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 89.09/89.29 inference(commutativity,[status(thm)],[])).
% 89.09/89.29 tff(2204,plain,
% 89.09/89.29 ((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) <=> (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2203])).
% 89.09/89.29 tff(2205,plain,
% 89.09/89.29 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.29 inference(transitivity,[status(thm)],[1611, 758, 778, 398])).
% 89.09/89.29 tff(2206,plain,
% 89.09/89.29 ((f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2205])).
% 89.09/89.29 tff(2207,plain,
% 89.09/89.29 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a)))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2206])).
% 89.09/89.29 tff(2208,plain,
% 89.09/89.29 (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2138, 861, 398])).
% 89.09/89.29 tff(2209,plain,
% 89.09/89.29 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2208])).
% 89.09/89.29 tff(2210,plain,
% 89.09/89.29 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2209, 426])).
% 89.09/89.29 tff(2211,plain,
% 89.09/89.29 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2210, 2207, 2204])).
% 89.09/89.29 tff(2212,plain,
% 89.09/89.29 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2211])).
% 89.09/89.29 tff(2213,plain,
% 89.09/89.29 (~(f20(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[1244, 2212])).
% 89.09/89.29 tff(2214,plain,
% 89.09/89.29 (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[1775, 2213, 2202])).
% 89.09/89.29 tff(2215,plain,
% 89.09/89.29 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2214])).
% 89.09/89.29 tff(2216,plain,
% 89.09/89.29 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[398, 2215])).
% 89.09/89.29 tff(2217,plain,
% 89.09/89.29 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2216])).
% 89.09/89.29 tff(2218,plain,
% 89.09/89.29 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2217, 2059])).
% 89.09/89.29 tff(2219,plain,
% 89.09/89.29 ((~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))) <=> (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2218])).
% 89.09/89.29 tff(2220,plain,
% 89.09/89.29 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2210])).
% 89.09/89.29 tff(2221,plain,
% 89.09/89.29 (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[1244, 2220])).
% 89.09/89.29 tff(2222,plain,
% 89.09/89.29 (~(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a)))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[2221, 2219])).
% 89.09/89.29 tff(2223,plain,
% 89.09/89.29 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)))),
% 89.09/89.29 inference(rewrite,[status(thm)],[])).
% 89.09/89.29 tff(2224,plain,
% 89.09/89.29 (((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a))) <=> ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)))),
% 89.09/89.29 inference(rewrite,[status(thm)],[])).
% 89.09/89.29 tff(2225,plain,
% 89.09/89.29 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2224])).
% 89.09/89.29 tff(2226,plain,
% 89.09/89.29 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2225, 2223])).
% 89.09/89.29 tff(2227,plain,
% 89.09/89.29 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~single_valued_set(a)))),
% 89.09/89.29 inference(quant_inst,[status(thm)],[])).
% 89.09/89.29 tff(2228,plain,
% 89.09/89.29 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f19(compose(b, a))), a)) | (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))) | (~single_valued_set(a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 89.09/89.29 tff(2229,plain,
% 89.09/89.29 ($false),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[2228, 1183, 1221, 273, 1159, 979, 2222, 2199, 2167])).
% 89.09/89.29 tff(2230,plain,(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 89.09/89.29 tff(2231,plain,
% 89.09/89.29 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2230])).
% 89.09/89.29 tff(2232,plain,
% 89.09/89.29 (f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[1463, 2230])).
% 89.09/89.29 tff(2233,plain,
% 89.09/89.29 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2232, 2231])).
% 89.09/89.29 tff(2234,plain,
% 89.09/89.29 ((f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.29 inference(transitivity,[status(thm)],[2233, 1])).
% 89.09/89.29 tff(2235,plain,
% 89.09/89.29 ((~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2234])).
% 89.09/89.29 tff(2236,plain,
% 89.09/89.29 ((~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[196])).
% 89.09/89.29 tff(2237,assumption,(~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), introduced(assumption)).
% 89.09/89.29 tff(2238,plain,
% 89.09/89.29 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 89.09/89.29 tff(2239,plain,
% 89.09/89.29 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[670, 2238])).
% 89.09/89.29 tff(2240,plain,
% 89.09/89.29 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2239])).
% 89.09/89.29 tff(2241,plain,
% 89.09/89.29 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(symmetry,[status(thm)],[2240])).
% 89.09/89.29 tff(2242,plain,
% 89.09/89.29 ((~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.29 inference(monotonicity,[status(thm)],[2241])).
% 89.09/89.29 tff(2243,plain,
% 89.09/89.29 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[932, 2023])).
% 89.09/89.29 tff(2244,plain,
% 89.09/89.29 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[755, 2237])).
% 89.09/89.29 tff(2245,plain,
% 89.09/89.29 (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[2110, 2244, 2023, 862, 2243])).
% 89.09/89.29 tff(2246,plain,
% 89.09/89.29 (~member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.29 inference(modus_ponens,[status(thm)],[2245, 2242])).
% 89.09/89.29 tff(2247,plain,
% 89.09/89.29 ($false),
% 89.09/89.29 inference(unit_resolution,[status(thm)],[983, 2246])).
% 89.09/89.29 tff(2248,plain,((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 89.09/89.30 tff(2249,plain,
% 89.09/89.30 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.30 inference(unit_resolution,[status(thm)],[2248, 2023, 862])).
% 89.09/89.30 tff(2250,plain,
% 89.09/89.30 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2249])).
% 89.09/89.30 tff(2251,plain,
% 89.09/89.30 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2250])).
% 89.09/89.30 tff(2252,plain,
% 89.09/89.30 (member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.30 inference(modus_ponens,[status(thm)],[503, 2251])).
% 89.09/89.30 tff(2253,plain,
% 89.09/89.30 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 89.09/89.30 inference(unit_resolution,[status(thm)],[1555, 2252])).
% 89.09/89.30 tff(2254,plain,
% 89.09/89.30 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2253])).
% 89.09/89.30 tff(2255,plain,
% 89.09/89.30 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2254])).
% 89.09/89.30 tff(2256,plain,
% 89.09/89.30 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.30 inference(transitivity,[status(thm)],[222, 2255, 524])).
% 89.09/89.30 tff(2257,plain,
% 89.09/89.30 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2249])).
% 89.09/89.30 tff(2258,plain,
% 89.09/89.30 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(transitivity,[status(thm)],[2257, 2231])).
% 89.09/89.30 tff(2259,plain,
% 89.09/89.30 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2258])).
% 89.09/89.30 tff(2260,plain,
% 89.09/89.30 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.30 inference(transitivity,[status(thm)],[2259, 1])).
% 89.09/89.30 tff(2261,plain,
% 89.09/89.30 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2260])).
% 89.09/89.30 tff(2262,assumption,(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), introduced(assumption)).
% 89.09/89.30 tff(2263,plain,
% 89.09/89.30 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2262])).
% 89.09/89.30 tff(2264,plain,
% 89.09/89.30 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(transitivity,[status(thm)],[2263, 2231])).
% 89.09/89.30 tff(2265,plain,
% 89.09/89.30 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2264])).
% 89.09/89.30 tff(2266,plain,
% 89.09/89.30 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.09/89.30 inference(transitivity,[status(thm)],[2265, 1])).
% 89.09/89.30 tff(2267,plain,
% 89.09/89.30 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2266])).
% 89.09/89.30 tff(2268,plain,
% 89.09/89.30 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2267])).
% 89.09/89.30 tff(2269,plain,
% 89.09/89.30 (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.30 inference(modus_ponens,[status(thm)],[1471, 2268])).
% 89.09/89.30 tff(2270,plain,
% 89.09/89.30 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.09/89.30 inference(unit_resolution,[status(thm)],[1575, 2269])).
% 89.09/89.30 tff(2271,plain,
% 89.09/89.30 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.09/89.30 inference(symmetry,[status(thm)],[2270])).
% 89.09/89.30 tff(2272,plain,
% 89.09/89.30 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.09/89.30 inference(transitivity,[status(thm)],[525, 2271])).
% 89.09/89.30 tff(2273,plain,
% 89.09/89.30 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2272, 2263])).
% 89.09/89.30 tff(2274,plain,
% 89.09/89.30 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.09/89.30 inference(rewrite,[status(thm)],[])).
% 89.09/89.30 tff(2275,plain,
% 89.09/89.30 (((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.09/89.30 inference(rewrite,[status(thm)],[])).
% 89.09/89.30 tff(2276,plain,
% 89.09/89.30 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))))),
% 89.09/89.30 inference(monotonicity,[status(thm)],[2275])).
% 89.09/89.30 tff(2277,plain,
% 89.09/89.30 (((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.09/89.31 inference(transitivity,[status(thm)],[2276, 2274])).
% 89.09/89.31 tff(2278,plain,
% 89.09/89.31 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | ((~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.09/89.31 inference(quant_inst,[status(thm)],[])).
% 89.09/89.31 tff(2279,plain,
% 89.09/89.31 ((~![Y: $i, U: $i, X: $i] : ((~member(U, X)) | (~member(U, Y)) | (~disjoint(X, Y)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~member(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.31 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 89.09/89.31 tff(2280,plain,
% 89.09/89.31 (~disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.31 inference(unit_resolution,[status(thm)],[2279, 163, 503, 139])).
% 89.09/89.31 tff(2281,plain,
% 89.09/89.31 (((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.31 inference(rewrite,[status(thm)],[])).
% 89.09/89.31 tff(2282,plain,
% 89.09/89.31 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | (disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.09/89.31 inference(quant_inst,[status(thm)],[])).
% 89.09/89.31 tff(2283,plain,
% 89.09/89.31 ((~![Y: $i, X: $i] : (disjoint(X, Y) | member(f23(X, Y), X))) | disjoint(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.31 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 89.09/89.31 tff(2284,plain,
% 89.09/89.31 (member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.09/89.31 inference(unit_resolution,[status(thm)],[2283, 332, 2280])).
% 89.09/89.31 tff(2285,plain,
% 89.09/89.31 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.31 inference(rewrite,[status(thm)],[])).
% 89.14/89.31 tff(2286,plain,
% 89.14/89.31 (((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.31 inference(rewrite,[status(thm)],[])).
% 89.14/89.31 tff(2287,plain,
% 89.14/89.31 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.31 inference(monotonicity,[status(thm)],[2286])).
% 89.14/89.31 tff(2288,plain,
% 89.14/89.31 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.31 inference(transitivity,[status(thm)],[2287, 2285])).
% 89.14/89.31 tff(2289,plain,
% 89.14/89.31 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.14/89.31 inference(quant_inst,[status(thm)],[])).
% 89.14/89.31 tff(2290,plain,
% 89.14/89.31 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.31 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 89.14/89.31 tff(2291,plain,
% 89.14/89.31 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.31 inference(unit_resolution,[status(thm)],[2290, 188, 2284])).
% 89.14/89.31 tff(2292,plain,
% 89.14/89.31 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.31 inference(symmetry,[status(thm)],[2291])).
% 89.14/89.31 tff(2293,plain,
% 89.14/89.31 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.31 inference(transitivity,[status(thm)],[2270, 524])).
% 89.14/89.31 tff(2294,plain,
% 89.14/89.31 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.31 inference(monotonicity,[status(thm)],[2293])).
% 89.14/89.31 tff(2295,plain,
% 89.14/89.31 (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))),
% 89.14/89.31 inference(transitivity,[status(thm)],[2294, 640, 2292, 2273, 397])).
% 89.14/89.31 tff(2296,assumption,(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a))), introduced(assumption)).
% 89.14/89.31 tff(2297,assumption,(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))), introduced(assumption)).
% 89.14/89.31 tff(2298,plain,
% 89.14/89.31 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.31 inference(symmetry,[status(thm)],[2297])).
% 89.14/89.31 tff(2299,plain,
% 89.14/89.31 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.32 inference(transitivity,[status(thm)],[525, 2298])).
% 89.14/89.32 tff(2300,plain,
% 89.14/89.32 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2299])).
% 89.14/89.32 tff(2301,plain,
% 89.14/89.32 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.32 inference(symmetry,[status(thm)],[640])).
% 89.14/89.32 tff(2302,plain,
% 89.14/89.32 (f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f19(compose(b, a))),
% 89.14/89.32 inference(transitivity,[status(thm)],[2301, 2300, 2296])).
% 89.14/89.32 tff(2303,plain,
% 89.14/89.32 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = singleton_set(f19(compose(b, a)))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2302])).
% 89.14/89.32 tff(2304,plain,
% 89.14/89.32 (singleton_set(f19(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2303])).
% 89.14/89.32 tff(2305,plain,
% 89.14/89.32 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[312, 1471])).
% 89.14/89.32 tff(2306,plain,
% 89.14/89.32 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(transitivity,[status(thm)],[2305, 222, 2304, 524])).
% 89.14/89.32 tff(2307,plain,
% 89.14/89.32 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2299])).
% 89.14/89.32 tff(2308,plain,
% 89.14/89.32 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2307])).
% 89.14/89.32 tff(2309,plain,
% 89.14/89.32 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2308])).
% 89.14/89.32 tff(2310,plain,
% 89.14/89.32 (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[1471, 2309])).
% 89.14/89.32 tff(2311,plain,
% 89.14/89.32 ($false),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2310, 2306])).
% 89.14/89.32 tff(2312,plain,((~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.32 tff(2313,plain,
% 89.14/89.32 (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), sigma(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) = f19(compose(b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2312, 2270, 1471])).
% 89.14/89.32 tff(2314,plain,
% 89.14/89.32 ($false),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2313, 2295])).
% 89.14/89.32 tff(2315,plain,((~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.32 tff(2316,plain,
% 89.14/89.32 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2315, 2249])).
% 89.14/89.32 tff(2317,plain,
% 89.14/89.32 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[2316, 2261])).
% 89.14/89.32 tff(2318,plain,
% 89.14/89.32 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2317])).
% 89.14/89.32 tff(2319,plain,
% 89.14/89.32 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2318])).
% 89.14/89.32 tff(2320,plain,
% 89.14/89.32 (member(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[983, 2319])).
% 89.14/89.32 tff(2321,plain,
% 89.14/89.32 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2110, 2320, 2023, 862, 2243])).
% 89.14/89.32 tff(2322,plain,
% 89.14/89.32 ($false),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2321, 2256])).
% 89.14/89.32 tff(2323,plain,((f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) | (f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.32 tff(2324,plain,
% 89.14/89.32 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2323, 862])).
% 89.14/89.32 tff(2325,plain,
% 89.14/89.32 (~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[2315, 1471])).
% 89.14/89.32 tff(2326,plain,
% 89.14/89.32 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[755, 2325])).
% 89.14/89.32 tff(2327,plain,
% 89.14/89.32 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2326])).
% 89.14/89.32 tff(2328,plain,
% 89.14/89.32 (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(transitivity,[status(thm)],[524, 2327, 2231])).
% 89.14/89.32 tff(2329,plain,
% 89.14/89.32 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2328])).
% 89.14/89.32 tff(2330,plain,
% 89.14/89.32 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.32 inference(transitivity,[status(thm)],[2329, 1])).
% 89.14/89.32 tff(2331,plain,
% 89.14/89.32 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2330])).
% 89.14/89.32 tff(2332,plain,
% 89.14/89.32 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2331])).
% 89.14/89.32 tff(2333,plain,
% 89.14/89.32 (~(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[1471, 2332])).
% 89.14/89.32 tff(2334,plain,
% 89.14/89.32 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[1575, 2333])).
% 89.14/89.32 tff(2335,plain,
% 89.14/89.32 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2334])).
% 89.14/89.32 tff(2336,plain,
% 89.14/89.32 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2327])).
% 89.14/89.32 tff(2337,plain,
% 89.14/89.32 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2336])).
% 89.14/89.32 tff(2338,plain,
% 89.14/89.32 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.32 inference(transitivity,[status(thm)],[779, 2337, 195])).
% 89.14/89.32 tff(2339,plain,
% 89.14/89.32 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2338])).
% 89.14/89.32 tff(2340,plain,
% 89.14/89.32 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2339])).
% 89.14/89.32 tff(2341,plain,
% 89.14/89.32 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(symmetry,[status(thm)],[2340])).
% 89.14/89.32 tff(2342,plain,
% 89.14/89.32 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[794, 2341])).
% 89.14/89.32 tff(2343,plain,
% 89.14/89.32 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[1971, 967])).
% 89.14/89.32 tff(2344,plain,
% 89.14/89.32 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.32 inference(transitivity,[status(thm)],[968, 2343])).
% 89.14/89.32 tff(2345,plain,
% 89.14/89.32 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2344])).
% 89.14/89.32 tff(2346,plain,
% 89.14/89.32 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.32 inference(symmetry,[status(thm)],[2345])).
% 89.14/89.32 tff(2347,plain,
% 89.14/89.32 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.32 inference(transitivity,[status(thm)],[779, 2346, 833])).
% 89.14/89.32 tff(2348,plain,
% 89.14/89.32 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2347])).
% 89.14/89.32 tff(2349,plain,
% 89.14/89.32 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2348])).
% 89.14/89.32 tff(2350,plain,
% 89.14/89.32 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(symmetry,[status(thm)],[2349])).
% 89.14/89.32 tff(2351,plain,
% 89.14/89.32 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[1143, 2350])).
% 89.14/89.32 tff(2352,plain,
% 89.14/89.32 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[1405, 1183, 1173, 273, 1159, 1155, 2351, 2342])).
% 89.14/89.32 tff(2353,plain,
% 89.14/89.32 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.32 inference(symmetry,[status(thm)],[2352])).
% 89.14/89.32 tff(2354,plain,
% 89.14/89.32 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2353])).
% 89.14/89.32 tff(2355,plain,
% 89.14/89.32 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.32 inference(monotonicity,[status(thm)],[2354])).
% 89.14/89.32 tff(2356,plain,
% 89.14/89.32 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.32 inference(symmetry,[status(thm)],[2355])).
% 89.14/89.32 tff(2357,plain,
% 89.14/89.32 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.32 inference(modus_ponens,[status(thm)],[1214, 2356])).
% 89.14/89.32 tff(2358,plain,
% 89.14/89.32 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.32 inference(unit_resolution,[status(thm)],[1417, 1183, 1221, 1210, 1205, 1155, 979, 2357])).
% 89.14/89.32 tff(2359,plain,
% 89.14/89.32 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.32 inference(transitivity,[status(thm)],[1102, 2345, 2337, 195])).
% 89.14/89.32 tff(2360,plain,
% 89.14/89.32 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2359, 2358])).
% 89.14/89.33 tff(2361,plain,
% 89.14/89.33 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2360, 2335])).
% 89.14/89.33 tff(2362,plain,
% 89.14/89.33 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2361, 2231])).
% 89.14/89.33 tff(2363,plain,
% 89.14/89.33 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2362, 1])).
% 89.14/89.33 tff(2364,plain,
% 89.14/89.33 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2363])).
% 89.14/89.33 tff(2365,plain,
% 89.14/89.33 ((~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2364])).
% 89.14/89.33 tff(2366,plain,
% 89.14/89.33 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[1471, 2365])).
% 89.14/89.33 tff(2367,plain,
% 89.14/89.33 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.14/89.33 inference(unit_resolution,[status(thm)],[1289, 2366])).
% 89.14/89.33 tff(2368,plain,
% 89.14/89.33 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2360])).
% 89.14/89.33 tff(2369,plain,
% 89.14/89.33 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2334, 2368, 2367])).
% 89.14/89.33 tff(2370,plain,
% 89.14/89.33 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2369])).
% 89.14/89.33 tff(2371,plain,
% 89.14/89.33 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2370])).
% 89.14/89.33 tff(2372,plain,
% 89.14/89.33 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[1027, 2371])).
% 89.14/89.33 tff(2373,assumption,(~(f21(compose(b, a)) = f19(compose(b, a)))), introduced(assumption)).
% 89.14/89.33 tff(2374,plain,
% 89.14/89.33 ((f21(compose(b, a)) = f20(compose(b, a))) <=> (f20(compose(b, a)) = f21(compose(b, a)))),
% 89.14/89.33 inference(commutativity,[status(thm)],[])).
% 89.14/89.33 tff(2375,plain,
% 89.14/89.33 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f21(compose(b, a)) = f20(compose(b, a)))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2374])).
% 89.14/89.33 tff(2376,plain,
% 89.14/89.33 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f21(compose(b, a)) = f20(compose(b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2375])).
% 89.14/89.33 tff(2377,plain,
% 89.14/89.33 (~(f21(compose(b, a)) = f20(compose(b, a)))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[1244, 2376])).
% 89.14/89.33 tff(2378,plain,
% 89.14/89.33 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.33 inference(rewrite,[status(thm)],[])).
% 89.14/89.33 tff(2379,plain,
% 89.14/89.33 (((f21(compose(b, a)) = f20(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.33 inference(rewrite,[status(thm)],[])).
% 89.14/89.33 tff(2380,plain,
% 89.14/89.33 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f20(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a)))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2379])).
% 89.14/89.33 tff(2381,plain,
% 89.14/89.33 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f20(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2380, 2378])).
% 89.14/89.33 tff(2382,plain,
% 89.14/89.33 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f21(compose(b, a)) = f20(compose(b, a))) | (f21(compose(b, a)) = f19(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 89.14/89.33 inference(quant_inst,[status(thm)],[])).
% 89.14/89.33 tff(2383,plain,
% 89.14/89.33 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f21(compose(b, a)) = f20(compose(b, a))) | (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) | (f21(compose(b, a)) = f19(compose(b, a)))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 89.14/89.33 tff(2384,plain,
% 89.14/89.33 (~member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(unit_resolution,[status(thm)],[2383, 188, 2377, 2373])).
% 89.14/89.33 tff(2385,plain,
% 89.14/89.33 ($false),
% 89.14/89.33 inference(unit_resolution,[status(thm)],[2384, 2372])).
% 89.14/89.33 tff(2386,plain,((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (~(f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) | (f21(compose(b, a)) = f19(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.33 tff(2387,plain,
% 89.14/89.33 (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.33 inference(unit_resolution,[status(thm)],[2386, 2324, 1997])).
% 89.14/89.33 tff(2388,plain,
% 89.14/89.33 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[525])).
% 89.14/89.33 tff(2389,plain,
% 89.14/89.33 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2388, 1470])).
% 89.14/89.33 tff(2390,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2389])).
% 89.14/89.33 tff(2391,assumption,(~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))), introduced(assumption)).
% 89.14/89.33 tff(2392,plain,
% 89.14/89.33 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.33 inference(unit_resolution,[status(thm)],[755, 2391])).
% 89.14/89.33 tff(2393,plain,
% 89.14/89.33 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2392])).
% 89.14/89.33 tff(2394,plain,
% 89.14/89.33 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2393, 2231])).
% 89.14/89.33 tff(2395,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2394])).
% 89.14/89.33 tff(2396,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2395, 1])).
% 89.14/89.33 tff(2397,plain,
% 89.14/89.33 ((f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2396])).
% 89.14/89.33 tff(2398,plain,
% 89.14/89.33 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[315, 2397])).
% 89.14/89.33 tff(2399,plain,
% 89.14/89.33 (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2398, 2393])).
% 89.14/89.33 tff(2400,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2399, 524])).
% 89.14/89.33 tff(2401,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))) = singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2400])).
% 89.14/89.33 tff(2402,plain,
% 89.14/89.33 ((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(transitivity,[status(thm)],[2401, 2390])).
% 89.14/89.33 tff(2403,plain,
% 89.14/89.33 ((~(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[2402])).
% 89.14/89.33 tff(2404,plain,
% 89.14/89.33 (~(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[2391, 2403])).
% 89.14/89.33 tff(2405,plain,
% 89.14/89.33 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.33 inference(monotonicity,[status(thm)],[525, 659])).
% 89.14/89.33 tff(2406,plain,
% 89.14/89.33 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.33 inference(symmetry,[status(thm)],[2405])).
% 89.14/89.33 tff(2407,plain,
% 89.14/89.33 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.33 inference(modus_ponens,[status(thm)],[1902, 2406])).
% 89.14/89.33 tff(2408,plain,
% 89.14/89.33 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.34 inference(rewrite,[status(thm)],[])).
% 89.14/89.34 tff(2409,plain,
% 89.14/89.34 (((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))) <=> ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.34 inference(rewrite,[status(thm)],[])).
% 89.14/89.34 tff(2410,plain,
% 89.14/89.34 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2409])).
% 89.14/89.34 tff(2411,plain,
% 89.14/89.34 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))),
% 89.14/89.34 inference(transitivity,[status(thm)],[2410, 2408])).
% 89.14/89.34 tff(2412,plain,
% 89.14/89.34 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))))),
% 89.14/89.34 inference(quant_inst,[status(thm)],[])).
% 89.14/89.34 tff(2413,plain,
% 89.14/89.34 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.34 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 89.14/89.34 tff(2414,plain,
% 89.14/89.34 ((~member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[2413, 188])).
% 89.14/89.34 tff(2415,plain,
% 89.14/89.34 ((non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[2414, 2407])).
% 89.14/89.34 tff(2416,plain,
% 89.14/89.34 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[2415, 2404])).
% 89.14/89.34 tff(2417,plain,
% 89.14/89.34 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.34 inference(modus_ponens,[status(thm)],[2416, 1617])).
% 89.14/89.34 tff(2418,plain,
% 89.14/89.34 ($false),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[2391, 2417])).
% 89.14/89.34 tff(2419,plain,((non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.34 tff(2420,plain,
% 89.14/89.34 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[2419, 2387])).
% 89.14/89.34 tff(2421,plain,
% 89.14/89.34 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.34 inference(symmetry,[status(thm)],[2420])).
% 89.14/89.34 tff(2422,plain,
% 89.14/89.34 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2421])).
% 89.14/89.34 tff(2423,plain,
% 89.14/89.34 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.34 inference(symmetry,[status(thm)],[2422])).
% 89.14/89.34 tff(2424,plain,
% 89.14/89.34 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.34 inference(transitivity,[status(thm)],[779, 2423, 195])).
% 89.14/89.34 tff(2425,plain,
% 89.14/89.34 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2424])).
% 89.14/89.34 tff(2426,plain,
% 89.14/89.34 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2425])).
% 89.14/89.34 tff(2427,plain,
% 89.14/89.34 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(symmetry,[status(thm)],[2426])).
% 89.14/89.34 tff(2428,plain,
% 89.14/89.34 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(modus_ponens,[status(thm)],[794, 2427])).
% 89.14/89.34 tff(2429,plain,
% 89.14/89.34 (f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[1971, 2324])).
% 89.14/89.34 tff(2430,plain,
% 89.14/89.34 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = f23(f16(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), universal_set), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.34 inference(symmetry,[status(thm)],[2324])).
% 89.14/89.34 tff(2431,plain,
% 89.14/89.34 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.34 inference(transitivity,[status(thm)],[2430, 2429])).
% 89.14/89.34 tff(2432,plain,
% 89.14/89.34 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2431])).
% 89.14/89.34 tff(2433,plain,
% 89.14/89.34 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.34 inference(symmetry,[status(thm)],[2432])).
% 89.14/89.34 tff(2434,plain,
% 89.14/89.34 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.34 inference(transitivity,[status(thm)],[779, 2433, 833])).
% 89.14/89.34 tff(2435,plain,
% 89.14/89.34 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2434])).
% 89.14/89.34 tff(2436,plain,
% 89.14/89.34 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2435])).
% 89.14/89.34 tff(2437,plain,
% 89.14/89.34 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(symmetry,[status(thm)],[2436])).
% 89.14/89.34 tff(2438,plain,
% 89.14/89.34 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.34 inference(modus_ponens,[status(thm)],[1143, 2437])).
% 89.14/89.34 tff(2439,plain,
% 89.14/89.34 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[1405, 1183, 1173, 273, 1159, 1155, 2438, 2428])).
% 89.14/89.34 tff(2440,plain,
% 89.14/89.34 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.34 inference(symmetry,[status(thm)],[2439])).
% 89.14/89.34 tff(2441,plain,
% 89.14/89.34 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2440])).
% 89.14/89.34 tff(2442,plain,
% 89.14/89.34 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.34 inference(monotonicity,[status(thm)],[2441])).
% 89.14/89.34 tff(2443,plain,
% 89.14/89.34 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.34 inference(symmetry,[status(thm)],[2442])).
% 89.14/89.34 tff(2444,plain,
% 89.14/89.34 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.34 inference(modus_ponens,[status(thm)],[1214, 2443])).
% 89.14/89.34 tff(2445,plain,
% 89.14/89.34 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.34 inference(unit_resolution,[status(thm)],[1417, 1183, 1221, 1210, 1205, 1155, 979, 2444])).
% 89.14/89.34 tff(2446,plain,
% 89.14/89.34 (f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.34 inference(transitivity,[status(thm)],[1102, 2432, 2423, 195])).
% 89.14/89.34 tff(2447,plain,
% 89.14/89.34 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2446, 2445])).
% 89.14/89.35 tff(2448,plain,
% 89.14/89.35 (ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2447])).
% 89.14/89.35 tff(2449,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2231, 2387])).
% 89.14/89.35 tff(2450,plain,
% 89.14/89.35 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[222, 2449])).
% 89.14/89.35 tff(2451,plain,
% 89.14/89.35 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2450, 212, 202, 2448, 884, 841])).
% 89.14/89.35 tff(2452,plain,
% 89.14/89.35 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2451])).
% 89.14/89.35 tff(2453,plain,
% 89.14/89.35 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))) <=> member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2452])).
% 89.14/89.35 tff(2454,plain,
% 89.14/89.35 (member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[1062, 2453])).
% 89.14/89.35 tff(2455,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.14/89.35 inference(rewrite,[status(thm)],[])).
% 89.14/89.35 tff(2456,plain,
% 89.14/89.35 (((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))) <=> ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.14/89.35 inference(rewrite,[status(thm)],[])).
% 89.14/89.35 tff(2457,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2456])).
% 89.14/89.35 tff(2458,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2457, 2455])).
% 89.14/89.35 tff(2459,plain,
% 89.14/89.35 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))))),
% 89.14/89.35 inference(quant_inst,[status(thm)],[])).
% 89.14/89.35 tff(2460,plain,
% 89.14/89.35 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 89.14/89.35 tff(2461,plain,
% 89.14/89.35 ((non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) | (~member(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))))),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[2460, 188])).
% 89.14/89.35 tff(2462,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[2461, 2454])).
% 89.14/89.35 tff(2463,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2462])).
% 89.14/89.35 tff(2464,plain,
% 89.14/89.35 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2463])).
% 89.14/89.35 tff(2465,plain,
% 89.14/89.35 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))) <=> member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2464])).
% 89.14/89.35 tff(2466,plain,
% 89.14/89.35 (member(f21(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[1027, 2465])).
% 89.14/89.35 tff(2467,plain,
% 89.14/89.35 ($false),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[2134, 2466])).
% 89.14/89.35 tff(2468,plain,(f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f21(compose(b, a))), inference(lemma,lemma(discharge,[]))).
% 89.14/89.35 tff(2469,plain,
% 89.14/89.35 (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2468])).
% 89.14/89.35 tff(2470,plain,
% 89.14/89.35 (f21(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2469, 861, 398])).
% 89.14/89.35 tff(2471,plain,
% 89.14/89.35 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f20(compose(b, a)) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2470])).
% 89.14/89.35 tff(2472,plain,
% 89.14/89.35 ((f20(compose(b, a)) = f21(compose(b, a))) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2471, 426])).
% 89.14/89.35 tff(2473,plain,
% 89.14/89.35 ((~(f20(compose(b, a)) = f21(compose(b, a)))) <=> (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2472])).
% 89.14/89.35 tff(2474,plain,
% 89.14/89.35 (~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[1244, 2473])).
% 89.14/89.35 tff(2475,plain,
% 89.14/89.35 (~(f16(f20(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[469, 2474])).
% 89.14/89.35 tff(2476,plain,
% 89.14/89.35 (~(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[2475, 2235])).
% 89.14/89.35 tff(2477,plain,
% 89.14/89.35 (f19(compose(b, a)) = f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.35 inference(transitivity,[status(thm)],[779, 2337, 195, 1829])).
% 89.14/89.35 tff(2478,plain,
% 89.14/89.35 ((f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2477])).
% 89.14/89.35 tff(2479,plain,
% 89.14/89.35 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2478])).
% 89.14/89.35 tff(2480,plain,
% 89.14/89.35 (~(f20(compose(b, a)) = f19(compose(b, a)))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[2474, 430])).
% 89.14/89.35 tff(2481,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2338])).
% 89.14/89.35 tff(2482,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2481, 2335])).
% 89.14/89.35 tff(2483,plain,
% 89.14/89.35 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) <=> member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2482])).
% 89.14/89.35 tff(2484,plain,
% 89.14/89.35 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))) <=> member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2483])).
% 89.14/89.35 tff(2485,plain,
% 89.14/89.35 (member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[450, 2484])).
% 89.14/89.35 tff(2486,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.35 inference(rewrite,[status(thm)],[])).
% 89.14/89.35 tff(2487,plain,
% 89.14/89.35 (((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))) <=> ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.35 inference(rewrite,[status(thm)],[])).
% 89.14/89.35 tff(2488,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a)))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2487])).
% 89.14/89.35 tff(2489,plain,
% 89.14/89.35 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a))))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2488, 2486])).
% 89.14/89.35 tff(2490,plain,
% 89.14/89.35 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (f20(compose(b, a)) = f19(compose(b, a))) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))))),
% 89.14/89.35 inference(quant_inst,[status(thm)],[])).
% 89.14/89.35 tff(2491,plain,
% 89.14/89.35 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, non_ordered_pair(X, Y))))) | (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a)))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 89.14/89.35 tff(2492,plain,
% 89.14/89.35 ((f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(f20(compose(b, a)), non_ordered_pair(f19(compose(b, a)), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) | (f20(compose(b, a)) = f19(compose(b, a)))),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[2491, 188])).
% 89.14/89.35 tff(2493,plain,
% 89.14/89.35 (f20(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.35 inference(unit_resolution,[status(thm)],[2492, 2485, 2480])).
% 89.14/89.35 tff(2494,plain,
% 89.14/89.35 (f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f20(compose(b, a))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2493])).
% 89.14/89.35 tff(2495,plain,
% 89.14/89.35 (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.35 inference(transitivity,[status(thm)],[518, 1611, 2336, 778, 398])).
% 89.14/89.35 tff(2496,plain,
% 89.14/89.35 ((f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) <=> (f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2495, 2494])).
% 89.14/89.35 tff(2497,plain,
% 89.14/89.35 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f23(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2496])).
% 89.14/89.35 tff(2498,plain,
% 89.14/89.35 ((f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a))) <=> (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2497, 2479])).
% 89.14/89.35 tff(2499,plain,
% 89.14/89.35 ((~(f23(non_ordered_pair(f19(compose(b, a)), f20(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f20(compose(b, a)))) <=> (~(f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2498])).
% 89.14/89.35 tff(2500,plain,
% 89.14/89.35 (~(f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[2474, 2499])).
% 89.14/89.35 tff(2501,plain,
% 89.14/89.35 (f21(compose(b, a)) = f19(compose(b, a))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2469, 861])).
% 89.14/89.35 tff(2502,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2501])).
% 89.14/89.35 tff(2503,plain,
% 89.14/89.35 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f19(compose(b, a)), f21(compose(b, a)))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2502])).
% 89.14/89.35 tff(2504,plain,
% 89.14/89.35 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f21(compose(b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[222, 2503])).
% 89.14/89.35 tff(2505,plain,
% 89.14/89.35 (non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.35 inference(transitivity,[status(thm)],[2504, 842, 839, 835])).
% 89.14/89.35 tff(2506,plain,
% 89.14/89.35 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.14/89.35 inference(monotonicity,[status(thm)],[2505])).
% 89.14/89.35 tff(2507,plain,
% 89.14/89.35 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.35 inference(symmetry,[status(thm)],[2506])).
% 89.14/89.35 tff(2508,plain,
% 89.14/89.35 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.35 inference(modus_ponens,[status(thm)],[1283, 2507])).
% 89.14/89.35 tff(2509,plain,
% 89.14/89.35 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.36 inference(unit_resolution,[status(thm)],[2177, 2508])).
% 89.14/89.36 tff(2510,plain,
% 89.14/89.36 (non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))) = non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.36 inference(symmetry,[status(thm)],[2509])).
% 89.14/89.36 tff(2511,plain,
% 89.14/89.36 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) <=> member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2510])).
% 89.14/89.36 tff(2512,plain,
% 89.14/89.36 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) <=> member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.36 inference(symmetry,[status(thm)],[2511])).
% 89.14/89.36 tff(2513,plain,
% 89.14/89.36 (member(f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.36 inference(modus_ponens,[status(thm)],[2185, 2512])).
% 89.14/89.36 tff(2514,plain,
% 89.14/89.36 (f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f19(compose(b, a))),
% 89.14/89.36 inference(unit_resolution,[status(thm)],[2193, 2513])).
% 89.14/89.36 tff(2515,plain,
% 89.14/89.36 (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.36 inference(symmetry,[status(thm)],[2514])).
% 89.14/89.36 tff(2516,plain,
% 89.14/89.36 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))) <=> member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[867, 2505])).
% 89.14/89.36 tff(2517,plain,
% 89.14/89.36 (member(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(singleton_set(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))) <=> member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.36 inference(symmetry,[status(thm)],[2516])).
% 89.14/89.36 tff(2518,plain,
% 89.14/89.36 (member(non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), non_ordered_pair(non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))), non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))))),
% 89.14/89.36 inference(modus_ponens,[status(thm)],[882, 2517])).
% 89.14/89.36 tff(2519,plain,
% 89.14/89.36 (non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))),
% 89.14/89.36 inference(unit_resolution,[status(thm)],[2153, 2518])).
% 89.14/89.36 tff(2520,plain,
% 89.14/89.36 (f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))) = f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a))))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2519])).
% 89.14/89.36 tff(2521,plain,
% 89.14/89.36 (f23(universal_set, non_ordered_pair(f19(compose(b, a)), f19(compose(b, a)))) = f23(universal_set, non_ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)))),
% 89.14/89.36 inference(symmetry,[status(thm)],[2520])).
% 89.14/89.36 tff(2522,plain,
% 89.14/89.36 (f19(compose(b, a)) = f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.36 inference(transitivity,[status(thm)],[779, 2521, 833])).
% 89.14/89.36 tff(2523,plain,
% 89.14/89.36 (ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)) = ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2522])).
% 89.14/89.36 tff(2524,plain,
% 89.14/89.36 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2523])).
% 89.14/89.36 tff(2525,plain,
% 89.14/89.36 (member(ordered_pair(f29(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b) <=> member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.36 inference(symmetry,[status(thm)],[2524])).
% 89.14/89.36 tff(2526,plain,
% 89.14/89.36 (member(ordered_pair(f19(compose(b, a)), f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), b)),
% 89.14/89.36 inference(modus_ponens,[status(thm)],[1143, 2525])).
% 89.14/89.36 tff(2527,plain,
% 89.14/89.36 (f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)),
% 89.14/89.36 inference(unit_resolution,[status(thm)],[1405, 1183, 1173, 273, 1159, 1155, 2526, 2342])).
% 89.14/89.36 tff(2528,plain,
% 89.14/89.36 (f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a) = f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)),
% 89.14/89.36 inference(symmetry,[status(thm)],[2527])).
% 89.14/89.36 tff(2529,plain,
% 89.14/89.36 (ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))) = ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2528, 2515])).
% 89.14/89.36 tff(2530,plain,
% 89.14/89.36 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a)),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2529])).
% 89.14/89.36 tff(2531,plain,
% 89.14/89.36 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f21(compose(b, a))), b, a)), a) <=> member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)),
% 89.14/89.36 inference(symmetry,[status(thm)],[2530])).
% 89.14/89.36 tff(2532,plain,
% 89.14/89.36 (member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)),
% 89.14/89.36 inference(modus_ponens,[status(thm)],[1214, 2531])).
% 89.14/89.36 tff(2533,plain,
% 89.14/89.36 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.36 inference(rewrite,[status(thm)],[])).
% 89.14/89.36 tff(2534,plain,
% 89.14/89.36 (((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a))) <=> ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.14/89.36 inference(rewrite,[status(thm)],[])).
% 89.14/89.36 tff(2535,plain,
% 89.14/89.36 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))))),
% 89.14/89.36 inference(monotonicity,[status(thm)],[2534])).
% 89.14/89.36 tff(2536,plain,
% 89.14/89.36 (((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)))),
% 89.20/89.38 inference(transitivity,[status(thm)],[2535, 2533])).
% 89.20/89.38 tff(2537,plain,
% 89.20/89.38 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | ((~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f19(compose(b, a)))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)))),
% 89.20/89.38 inference(quant_inst,[status(thm)],[])).
% 89.20/89.38 tff(2538,plain,
% 89.20/89.38 ((~![W: $i, V: $i, U: $i, X: $i] : ((~little_set(U)) | (~little_set(V)) | (~little_set(W)) | (V = W) | (~member(ordered_pair(U, W), X)) | (~member(ordered_pair(U, V), X)) | (~single_valued_set(X)))) | (~little_set(f19(compose(b, a)))) | (~little_set(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~little_set(f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a)), a)) | (~member(ordered_pair(f31(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f19(compose(b, a))), a)) | (~single_valued_set(a)) | (f19(compose(b, a)) = f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))),
% 89.20/89.38 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 89.20/89.38 tff(2539,plain,
% 89.20/89.38 ($false),
% 89.20/89.38 inference(unit_resolution,[status(thm)],[2538, 1183, 1221, 273, 1205, 1155, 979, 2532, 2500])).
% 89.20/89.38 tff(2540,plain,(f16(f19(compose(b, a)), ordered_pair(f29(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a), f30(ordered_pair(f19(compose(b, a)), f20(compose(b, a))), b, a))) = non_ordered_pair(f19(compose(b, a)), f20(compose(b, a)))), inference(lemma,lemma(discharge,[]))).
% 89.20/89.38 tff(2541,plain,
% 89.20/89.38 ($false),
% 89.20/89.38 inference(unit_resolution,[status(thm)],[2540, 2476])).
% 89.20/89.38 % SZS output end Proof
% 89.20/89.39 % E exiting
%------------------------------------------------------------------------------