TSTP Solution File: SET199-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET199-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:06:07 EDT 2022
% Result : Unsatisfiable 102.52s 66.36s
% Output : Proof 102.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET199-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 03:44:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 102.52/66.36 % SZS status Unsatisfiable
% 102.52/66.36 % SZS output start Proof
% 102.52/66.36 tff(member_type, type, (
% 102.52/66.36 member: ( $i * $i ) > $o)).
% 102.52/66.36 tff(y_type, type, (
% 102.52/66.36 y: $i)).
% 102.52/66.36 tff(not_subclass_element_type, type, (
% 102.52/66.36 not_subclass_element: ( $i * $i ) > $i)).
% 102.52/66.36 tff(intersection_type, type, (
% 102.52/66.36 intersection: ( $i * $i ) > $i)).
% 102.52/66.36 tff(x_type, type, (
% 102.52/66.36 x: $i)).
% 102.52/66.36 tff(z_type, type, (
% 102.52/66.36 z: $i)).
% 102.52/66.36 tff(subclass_type, type, (
% 102.52/66.36 subclass: ( $i * $i ) > $o)).
% 102.52/66.36 tff(1,assumption,(~member(not_subclass_element(z, intersection(x, y)), x)), introduced(assumption)).
% 102.52/66.36 tff(2,plain,
% 102.52/66.36 ((~subclass(z, intersection(x, y))) <=> (~subclass(z, intersection(x, y)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(3,axiom,(~subclass(z, intersection(x, y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_greatest_lower_bound_3')).
% 102.52/66.36 tff(4,plain,
% 102.52/66.36 (~subclass(z, intersection(x, y))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 102.52/66.36 tff(5,plain,
% 102.52/66.36 (^[Y: $i, X: $i] : refl((subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(6,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[5])).
% 102.52/66.36 tff(7,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(8,plain,
% 102.52/66.36 (^[Y: $i, X: $i] : rewrite((member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(9,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[8])).
% 102.52/66.36 tff(10,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 102.52/66.36 tff(11,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[10, 9])).
% 102.52/66.36 tff(12,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[11, 7])).
% 102.52/66.36 tff(13,plain,(
% 102.52/66.36 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(skolemize,[status(sab)],[12])).
% 102.52/66.36 tff(14,plain,
% 102.52/66.36 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[13, 6])).
% 102.52/66.36 tff(15,plain,
% 102.52/66.36 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(z, intersection(x, y)) | member(not_subclass_element(z, intersection(x, y)), z))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(z, intersection(x, y)) | member(not_subclass_element(z, intersection(x, y)), z))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(16,plain,
% 102.52/66.36 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(z, intersection(x, y)) | member(not_subclass_element(z, intersection(x, y)), z))),
% 102.52/66.36 inference(quant_inst,[status(thm)],[])).
% 102.52/66.36 tff(17,plain,
% 102.52/66.36 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(z, intersection(x, y)) | member(not_subclass_element(z, intersection(x, y)), z)),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 102.52/66.36 tff(18,plain,
% 102.52/66.36 (member(not_subclass_element(z, intersection(x, y)), z)),
% 102.52/66.36 inference(unit_resolution,[status(thm)],[17, 14, 4])).
% 102.52/66.36 tff(19,plain,
% 102.52/66.36 (subclass(z, x) <=> subclass(z, x)),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(20,axiom,(subclass(z, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_greatest_lower_bound_1')).
% 102.52/66.36 tff(21,plain,
% 102.52/66.36 (subclass(z, x)),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 102.52/66.36 tff(22,plain,
% 102.52/66.36 (^[Y: $i, U: $i, X: $i] : refl((member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(23,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[22])).
% 102.52/66.36 tff(24,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(25,plain,
% 102.52/66.36 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | (~member(U, X))) <=> ((~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)))), rewrite((((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(26,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[25])).
% 102.52/66.36 tff(27,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 102.52/66.36 tff(28,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 102.52/66.36 tff(29,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[28, 24])).
% 102.52/66.36 tff(30,plain,(
% 102.52/66.36 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(skolemize,[status(sab)],[29])).
% 102.52/66.36 tff(31,plain,
% 102.52/66.36 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[30, 23])).
% 102.52/66.36 tff(32,plain,
% 102.52/66.36 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), x) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, x)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(z, intersection(x, y)), x) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, x)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(33,plain,
% 102.52/66.36 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), x) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, x)))),
% 102.52/66.36 inference(quant_inst,[status(thm)],[])).
% 102.52/66.36 tff(34,plain,
% 102.52/66.36 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(z, intersection(x, y)), x) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, x))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 102.52/66.36 tff(35,plain,
% 102.52/66.36 ($false),
% 102.52/66.36 inference(unit_resolution,[status(thm)],[34, 31, 21, 18, 1])).
% 102.52/66.36 tff(36,plain,(member(not_subclass_element(z, intersection(x, y)), x)), inference(lemma,lemma(discharge,[]))).
% 102.52/66.36 tff(37,plain,
% 102.52/66.36 (^[Y: $i, X: $i] : refl(((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(38,plain,
% 102.52/66.36 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[37])).
% 102.52/66.36 tff(39,plain,
% 102.52/66.36 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(40,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 102.52/66.36 tff(41,plain,
% 102.52/66.36 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[40, 39])).
% 102.52/66.36 tff(42,plain,(
% 102.52/66.36 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 102.52/66.36 inference(skolemize,[status(sab)],[41])).
% 102.52/66.36 tff(43,plain,
% 102.52/66.36 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[42, 38])).
% 102.52/66.36 tff(44,plain,
% 102.52/66.36 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(z, intersection(x, y)), intersection(x, y))) | subclass(z, intersection(x, y)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(z, intersection(x, y)), intersection(x, y))) | subclass(z, intersection(x, y)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(45,plain,
% 102.52/66.36 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(z, intersection(x, y)), intersection(x, y))) | subclass(z, intersection(x, y)))),
% 102.52/66.36 inference(quant_inst,[status(thm)],[])).
% 102.52/66.36 tff(46,plain,
% 102.52/66.36 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(z, intersection(x, y)), intersection(x, y))) | subclass(z, intersection(x, y))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[45, 44])).
% 102.52/66.36 tff(47,plain,
% 102.52/66.36 (~member(not_subclass_element(z, intersection(x, y)), intersection(x, y))),
% 102.52/66.36 inference(unit_resolution,[status(thm)],[46, 43, 4])).
% 102.52/66.36 tff(48,plain,
% 102.52/66.36 (^[Z: $i, Y: $i, X: $i] : refl((member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(49,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[48])).
% 102.52/66.36 tff(50,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(51,plain,
% 102.52/66.36 (^[Z: $i, Y: $i, X: $i] : rewrite((((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 102.52/66.36 inference(bind,[status(th)],[])).
% 102.52/66.36 tff(52,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(quant_intro,[status(thm)],[51])).
% 102.52/66.36 tff(53,axiom,(![Z: $i, Y: $i, X: $i] : (((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','intersection3')).
% 102.52/66.36 tff(54,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[53, 52])).
% 102.52/66.36 tff(55,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[54, 50])).
% 102.52/66.36 tff(56,plain,(
% 102.52/66.36 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(skolemize,[status(sab)],[55])).
% 102.52/66.36 tff(57,plain,
% 102.52/66.36 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[56, 49])).
% 102.52/66.36 tff(58,plain,
% 102.52/66.36 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(not_subclass_element(z, intersection(x, y)), intersection(x, y)) | (~member(not_subclass_element(z, intersection(x, y)), y)) | (~member(not_subclass_element(z, intersection(x, y)), x)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(not_subclass_element(z, intersection(x, y)), intersection(x, y)) | (~member(not_subclass_element(z, intersection(x, y)), y)) | (~member(not_subclass_element(z, intersection(x, y)), x)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(59,plain,
% 102.52/66.36 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(not_subclass_element(z, intersection(x, y)), intersection(x, y)) | (~member(not_subclass_element(z, intersection(x, y)), y)) | (~member(not_subclass_element(z, intersection(x, y)), x)))),
% 102.52/66.36 inference(quant_inst,[status(thm)],[])).
% 102.52/66.36 tff(60,plain,
% 102.52/66.36 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(not_subclass_element(z, intersection(x, y)), intersection(x, y)) | (~member(not_subclass_element(z, intersection(x, y)), y)) | (~member(not_subclass_element(z, intersection(x, y)), x))),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[59, 58])).
% 102.52/66.36 tff(61,plain,
% 102.52/66.36 ((~member(not_subclass_element(z, intersection(x, y)), y)) | (~member(not_subclass_element(z, intersection(x, y)), x))),
% 102.52/66.36 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 102.52/66.36 tff(62,plain,
% 102.52/66.36 (~member(not_subclass_element(z, intersection(x, y)), y)),
% 102.52/66.36 inference(unit_resolution,[status(thm)],[61, 36])).
% 102.52/66.36 tff(63,plain,
% 102.52/66.36 (subclass(z, y) <=> subclass(z, y)),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(64,axiom,(subclass(z, y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_greatest_lower_bound_2')).
% 102.52/66.36 tff(65,plain,
% 102.52/66.36 (subclass(z, y)),
% 102.52/66.36 inference(modus_ponens,[status(thm)],[64, 63])).
% 102.52/66.36 tff(66,plain,
% 102.52/66.36 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(67,plain,
% 102.52/66.36 ((member(not_subclass_element(z, intersection(x, y)), y) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, y))) <=> (member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z)))),
% 102.52/66.36 inference(rewrite,[status(thm)],[])).
% 102.52/66.36 tff(68,plain,
% 102.52/66.36 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), y) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, y)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z))))),
% 102.52/66.36 inference(monotonicity,[status(thm)],[67])).
% 102.52/66.36 tff(69,plain,
% 102.52/66.36 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), y) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, y)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z)))),
% 102.52/66.36 inference(transitivity,[status(thm)],[68, 66])).
% 102.52/66.36 tff(70,plain,
% 102.52/66.36 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(z, intersection(x, y)), y) | (~member(not_subclass_element(z, intersection(x, y)), z)) | (~subclass(z, y)))),
% 102.52/66.36 inference(quant_inst,[status(thm)],[])).
% 102.52/66.36 tff(71,plain,
% 102.52/66.36 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(z, intersection(x, y)), y) | (~subclass(z, y)) | (~member(not_subclass_element(z, intersection(x, y)), z))),
% 102.52/66.37 inference(modus_ponens,[status(thm)],[70, 69])).
% 102.52/66.37 tff(72,plain,
% 102.52/66.37 ($false),
% 102.52/66.37 inference(unit_resolution,[status(thm)],[71, 31, 65, 18, 62])).
% 102.52/66.37 % SZS output end Proof
%------------------------------------------------------------------------------