TSTP Solution File: SET020-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET020-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Tue Sep 20 05:04:53 EDT 2022
% Result : Unsatisfiable 0.16s 0.44s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET020-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n004.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Sep 3 01:12:34 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.16/0.44 % SZS status Unsatisfiable
% 0.16/0.44 % SZS output start Proof
% 0.16/0.44 tff(member_type, type, (
% 0.16/0.44 member: ( $i * $i ) > $o)).
% 0.16/0.44 tff(unordered_pair_type, type, (
% 0.16/0.44 unordered_pair: ( $i * $i ) > $i)).
% 0.16/0.44 tff(u_type, type, (
% 0.16/0.44 u: $i)).
% 0.16/0.44 tff(first_type, type, (
% 0.16/0.44 first: $i > $i)).
% 0.16/0.44 tff(ordered_pair_type, type, (
% 0.16/0.44 ordered_pair: ( $i * $i ) > $i)).
% 0.16/0.44 tff(v_type, type, (
% 0.16/0.44 v: $i)).
% 0.16/0.44 tff(singleton_type, type, (
% 0.16/0.44 singleton: $i > $i)).
% 0.16/0.44 tff(second_type, type, (
% 0.16/0.44 second: $i > $i)).
% 0.16/0.44 tff(universal_class_type, type, (
% 0.16/0.44 universal_class: $i)).
% 0.16/0.44 tff(cross_product_type, type, (
% 0.16/0.44 cross_product: ( $i * $i ) > $i)).
% 0.16/0.44 tff(1,plain,
% 0.16/0.44 (^[X: $i] : refl((unordered_pair(X, X) = singleton(X)) <=> (unordered_pair(X, X) = singleton(X)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(2,plain,
% 0.16/0.44 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.44 tff(3,plain,
% 0.16/0.44 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(4,axiom,(![X: $i] : (unordered_pair(X, X) = singleton(X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','singleton_set')).
% 0.16/0.44 tff(5,plain,
% 0.16/0.44 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.44 tff(6,plain,(
% 0.16/0.44 ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 0.16/0.44 inference(skolemize,[status(sab)],[5])).
% 0.16/0.44 tff(7,plain,
% 0.16/0.44 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.44 tff(8,plain,
% 0.16/0.44 ((~![X: $i] : (unordered_pair(X, X) = singleton(X))) | (unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v))) = singleton(first(ordered_pair(u, v))))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(9,plain,
% 0.16/0.44 (unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v))) = singleton(first(ordered_pair(u, v)))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.16/0.44 tff(10,plain,
% 0.16/0.44 (singleton(first(ordered_pair(u, v))) = unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))),
% 0.16/0.44 inference(symmetry,[status(thm)],[9])).
% 0.16/0.44 tff(11,assumption,(singleton(u) = singleton(first(ordered_pair(u, v)))), introduced(assumption)).
% 0.16/0.44 tff(12,plain,
% 0.16/0.44 ((~![X: $i] : (unordered_pair(X, X) = singleton(X))) | (unordered_pair(u, u) = singleton(u))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(13,plain,
% 0.16/0.44 (unordered_pair(u, u) = singleton(u)),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[12, 7])).
% 0.16/0.44 tff(14,plain,
% 0.16/0.44 (unordered_pair(u, u) = unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))),
% 0.16/0.44 inference(transitivity,[status(thm)],[13, 11, 10])).
% 0.16/0.44 tff(15,plain,
% 0.16/0.44 (member(first(ordered_pair(u, v)), unordered_pair(u, u)) <=> member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[14])).
% 0.16/0.44 tff(16,plain,
% 0.16/0.44 (member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))) <=> member(first(ordered_pair(u, v)), unordered_pair(u, u))),
% 0.16/0.44 inference(symmetry,[status(thm)],[15])).
% 0.16/0.44 tff(17,plain,
% 0.16/0.44 (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) <=> member(ordered_pair(u, v), cross_product(universal_class, universal_class))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(18,axiom,(member(ordered_pair(u, v), cross_product(universal_class, universal_class))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_unique_1st_and_2nd_in_pair_of_sets1_1')).
% 0.16/0.44 tff(19,plain,
% 0.16/0.44 (member(ordered_pair(u, v), cross_product(universal_class, universal_class))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.16/0.44 tff(20,plain,
% 0.16/0.44 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(21,plain,
% 0.16/0.44 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[20])).
% 0.16/0.44 tff(22,plain,
% 0.16/0.44 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(23,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product4')).
% 0.16/0.44 tff(24,plain,
% 0.16/0.44 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.16/0.44 tff(25,plain,(
% 0.16/0.44 ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 0.16/0.44 inference(skolemize,[status(sab)],[24])).
% 0.16/0.44 tff(26,plain,
% 0.16/0.44 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.16/0.44 tff(27,plain,
% 0.16/0.44 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) | (ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))) = ordered_pair(u, v)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) | (ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))) = ordered_pair(u, v)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(28,plain,
% 0.16/0.44 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) | (ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))) = ordered_pair(u, v)))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(29,plain,
% 0.16/0.44 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) | (ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))) = ordered_pair(u, v))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.16/0.44 tff(30,plain,
% 0.16/0.44 (ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))) = ordered_pair(u, v)),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 0.16/0.44 tff(31,plain,
% 0.16/0.44 (member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class)) <=> member(ordered_pair(u, v), cross_product(universal_class, universal_class))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.16/0.44 tff(32,plain,
% 0.16/0.44 (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) <=> member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))),
% 0.16/0.44 inference(symmetry,[status(thm)],[31])).
% 0.16/0.44 tff(33,plain,
% 0.16/0.44 (member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[19, 32])).
% 0.16/0.44 tff(34,plain,
% 0.16/0.44 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(35,plain,
% 0.16/0.44 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.16/0.44 tff(36,plain,
% 0.16/0.44 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(37,axiom,(![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product1')).
% 0.16/0.45 tff(38,plain,
% 0.16/0.45 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.16/0.45 tff(39,plain,(
% 0.16/0.45 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 0.16/0.45 inference(skolemize,[status(sab)],[38])).
% 0.16/0.45 tff(40,plain,
% 0.16/0.45 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.16/0.45 tff(41,plain,
% 0.16/0.45 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))) | member(first(ordered_pair(u, v)), universal_class))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))) | member(first(ordered_pair(u, v)), universal_class))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(42,plain,
% 0.16/0.45 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))) | member(first(ordered_pair(u, v)), universal_class))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(43,plain,
% 0.16/0.45 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))) | member(first(ordered_pair(u, v)), universal_class)),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.16/0.45 tff(44,plain,
% 0.16/0.45 ((~member(ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))), cross_product(universal_class, universal_class))) | member(first(ordered_pair(u, v)), universal_class)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.16/0.45 tff(45,plain,
% 0.16/0.45 (member(first(ordered_pair(u, v)), universal_class)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[44, 33])).
% 0.16/0.45 tff(46,plain,
% 0.16/0.45 (^[Y: $i, X: $i] : refl(((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(47,plain,
% 0.16/0.45 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.16/0.45 tff(48,plain,
% 0.16/0.45 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(49,axiom,(![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','unordered_pair2')).
% 0.16/0.45 tff(50,plain,
% 0.16/0.45 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.16/0.45 tff(51,plain,(
% 0.16/0.45 ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 0.16/0.45 inference(skolemize,[status(sab)],[50])).
% 0.16/0.45 tff(52,plain,
% 0.16/0.45 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.16/0.45 tff(53,plain,
% 0.16/0.45 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(54,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v)))))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(55,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.16/0.45 tff(56,plain,
% 0.16/0.45 (member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), first(ordered_pair(u, v))))),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[55, 52, 45])).
% 0.16/0.45 tff(57,plain,
% 0.16/0.45 (member(first(ordered_pair(u, v)), unordered_pair(u, u))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[56, 16])).
% 0.16/0.45 tff(58,plain,
% 0.16/0.45 ((~(first(ordered_pair(u, v)) = u)) <=> (~(first(ordered_pair(u, v)) = u))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(59,axiom,(~(first(ordered_pair(u, v)) = u)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_unique_1st_and_2nd_in_pair_of_sets1_2')).
% 0.16/0.45 tff(60,plain,
% 0.16/0.45 (~(first(ordered_pair(u, v)) = u)),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.16/0.45 tff(61,plain,
% 0.16/0.45 (^[Y: $i, U: $i, X: $i] : refl(((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(62,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.16/0.45 tff(63,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(64,plain,
% 0.16/0.45 (^[Y: $i, U: $i, X: $i] : rewrite((((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(65,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.16/0.45 tff(66,axiom,(![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','unordered_pair_member')).
% 0.16/0.45 tff(67,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.16/0.45 tff(68,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.16/0.45 tff(69,plain,(
% 0.16/0.45 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(skolemize,[status(sab)],[68])).
% 0.16/0.45 tff(70,plain,
% 0.16/0.45 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.16/0.45 tff(71,plain,
% 0.16/0.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(72,plain,
% 0.16/0.45 (((first(ordered_pair(u, v)) = u) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u)))) <=> ((first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(73,plain,
% 0.16/0.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((first(ordered_pair(u, v)) = u) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u)))))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[72])).
% 0.16/0.45 tff(74,plain,
% 0.16/0.45 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((first(ordered_pair(u, v)) = u) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))),
% 0.16/0.45 inference(transitivity,[status(thm)],[73, 71])).
% 0.16/0.45 tff(75,plain,
% 0.16/0.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((first(ordered_pair(u, v)) = u) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u))))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(76,plain,
% 0.16/0.45 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (first(ordered_pair(u, v)) = u) | (~member(first(ordered_pair(u, v)), unordered_pair(u, u)))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.16/0.45 tff(77,plain,
% 0.16/0.45 (~member(first(ordered_pair(u, v)), unordered_pair(u, u))),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 0.16/0.45 tff(78,plain,
% 0.16/0.45 ($false),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[77, 57])).
% 0.16/0.45 tff(79,plain,(~(singleton(u) = singleton(first(ordered_pair(u, v))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.45 tff(80,plain,
% 0.16/0.45 (^[Y: $i, X: $i] : refl((unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(81,plain,
% 0.16/0.45 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.16/0.45 tff(82,plain,
% 0.16/0.45 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(83,axiom,(![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','ordered_pair')).
% 0.16/0.45 tff(84,plain,
% 0.16/0.45 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.16/0.45 tff(85,plain,(
% 0.16/0.45 ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 0.16/0.45 inference(skolemize,[status(sab)],[84])).
% 0.16/0.45 tff(86,plain,
% 0.16/0.45 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.16/0.45 tff(87,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))) | (unordered_pair(singleton(u), unordered_pair(u, singleton(v))) = ordered_pair(u, v))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(88,plain,
% 0.16/0.45 (unordered_pair(singleton(u), unordered_pair(u, singleton(v))) = ordered_pair(u, v)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.16/0.45 tff(89,plain,
% 0.16/0.45 (ordered_pair(u, v) = unordered_pair(singleton(u), unordered_pair(u, singleton(v)))),
% 0.16/0.45 inference(symmetry,[status(thm)],[88])).
% 0.16/0.45 tff(90,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))) | (unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) = ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v))))),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(91,plain,
% 0.16/0.45 (unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) = ordered_pair(first(ordered_pair(u, v)), second(ordered_pair(u, v)))),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[90, 86])).
% 0.16/0.45 tff(92,plain,
% 0.16/0.45 (unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) = unordered_pair(singleton(u), unordered_pair(u, singleton(v)))),
% 0.16/0.45 inference(transitivity,[status(thm)],[91, 30, 89])).
% 0.16/0.45 tff(93,plain,
% 0.16/0.45 (member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))) <=> member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v))))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[92])).
% 0.16/0.45 tff(94,plain,
% 0.16/0.45 (member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v)))) <=> member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))),
% 0.16/0.45 inference(symmetry,[status(thm)],[93])).
% 0.16/0.45 tff(95,plain,
% 0.16/0.45 (member(unordered_pair(u, u), universal_class) <=> member(singleton(u), universal_class)),
% 0.16/0.45 inference(monotonicity,[status(thm)],[13])).
% 0.16/0.45 tff(96,plain,
% 0.16/0.45 (^[Y: $i, X: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(97,plain,
% 0.16/0.45 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class) <=> ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.16/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.16/0.45 tff(98,plain,
% 0.16/0.45 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class) <=> ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(99,axiom,(![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','unordered_pairs_in_universal')).
% 0.16/0.45 tff(100,plain,
% 0.16/0.45 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.16/0.45 tff(101,plain,(
% 0.16/0.45 ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.16/0.45 inference(skolemize,[status(sab)],[100])).
% 0.16/0.45 tff(102,plain,
% 0.16/0.45 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.16/0.45 tff(103,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(u, u), universal_class)),
% 0.16/0.45 inference(quant_inst,[status(thm)],[])).
% 0.16/0.45 tff(104,plain,
% 0.16/0.45 (member(unordered_pair(u, u), universal_class)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.16/0.45 tff(105,plain,
% 0.16/0.45 (member(singleton(u), universal_class)),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[104, 95])).
% 0.16/0.45 tff(106,plain,
% 0.16/0.45 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(singleton(u), universal_class)) | member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v)))))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(singleton(u), universal_class)) | member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v)))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(107,plain,
% 0.16/0.45 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(singleton(u), universal_class)) | member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v)))))),
% 0.16/0.46 inference(quant_inst,[status(thm)],[])).
% 0.16/0.46 tff(108,plain,
% 0.16/0.46 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(singleton(u), universal_class)) | member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v))))),
% 0.16/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.16/0.46 tff(109,plain,
% 0.16/0.46 ((~member(singleton(u), universal_class)) | member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[108, 52])).
% 0.16/0.46 tff(110,plain,
% 0.16/0.46 (member(singleton(u), unordered_pair(singleton(u), unordered_pair(u, singleton(v))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.16/0.46 tff(111,plain,
% 0.16/0.46 (member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))),
% 0.16/0.46 inference(modus_ponens,[status(thm)],[110, 94])).
% 0.16/0.46 tff(112,plain,
% 0.16/0.46 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v)))) | (~member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v)))) | (~member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(113,plain,
% 0.16/0.46 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v)))) | (~member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))))),
% 0.16/0.46 inference(quant_inst,[status(thm)],[])).
% 0.16/0.46 tff(114,plain,
% 0.16/0.46 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v)))) | (~member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))))),
% 0.16/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.16/0.46 tff(115,plain,
% 0.16/0.46 ((singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v)))) | (~member(singleton(u), unordered_pair(singleton(first(ordered_pair(u, v))), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[114, 70])).
% 0.16/0.46 tff(116,plain,
% 0.16/0.46 ((singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) | (singleton(u) = singleton(first(ordered_pair(u, v))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[115, 111])).
% 0.16/0.46 tff(117,plain,
% 0.16/0.46 (singleton(u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[116, 79])).
% 0.16/0.46 tff(118,plain,
% 0.16/0.46 (unordered_pair(u, u) = unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[13, 117])).
% 0.16/0.46 tff(119,plain,
% 0.16/0.46 (member(first(ordered_pair(u, v)), unordered_pair(u, u)) <=> member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[118])).
% 0.16/0.46 tff(120,plain,
% 0.16/0.46 (member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))) <=> member(first(ordered_pair(u, v)), unordered_pair(u, u))),
% 0.16/0.46 inference(symmetry,[status(thm)],[119])).
% 0.16/0.46 tff(121,plain,
% 0.16/0.46 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(122,plain,
% 0.16/0.46 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v))))))),
% 0.16/0.46 inference(quant_inst,[status(thm)],[])).
% 0.16/0.46 tff(123,plain,
% 0.16/0.46 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))),
% 0.16/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.16/0.46 tff(124,plain,
% 0.16/0.46 ((~member(first(ordered_pair(u, v)), universal_class)) | member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[123, 52])).
% 0.16/0.46 tff(125,plain,
% 0.16/0.46 (member(first(ordered_pair(u, v)), unordered_pair(first(ordered_pair(u, v)), singleton(second(ordered_pair(u, v)))))),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[124, 45])).
% 0.16/0.46 tff(126,plain,
% 0.16/0.46 (member(first(ordered_pair(u, v)), unordered_pair(u, u))),
% 0.16/0.46 inference(modus_ponens,[status(thm)],[125, 120])).
% 0.16/0.46 tff(127,plain,
% 0.16/0.46 ($false),
% 0.16/0.46 inference(unit_resolution,[status(thm)],[77, 126])).
% 0.16/0.46 % SZS output end Proof
%------------------------------------------------------------------------------