TSTP Solution File: SET201-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET201-6 : 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 05:06:09 EDT 2022
% Result : Unsatisfiable 34.74s 22.45s
% Output : Proof 34.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET201-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 03:18:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 34.74/22.45 % SZS status Unsatisfiable
% 34.74/22.45 % SZS output start Proof
% 34.74/22.45 tff(member_type, type, (
% 34.74/22.45 member: ( $i * $i ) > $o)).
% 34.74/22.45 tff(w_type, type, (
% 34.74/22.45 w: $i)).
% 34.74/22.45 tff(not_subclass_element_type, type, (
% 34.74/22.45 not_subclass_element: ( $i * $i ) > $i)).
% 34.74/22.45 tff(intersection_type, type, (
% 34.74/22.45 intersection: ( $i * $i ) > $i)).
% 34.74/22.45 tff(y_type, type, (
% 34.74/22.45 y: $i)).
% 34.74/22.45 tff(z_type, type, (
% 34.74/22.45 z: $i)).
% 34.74/22.45 tff(x_type, type, (
% 34.74/22.45 x: $i)).
% 34.74/22.45 tff(subclass_type, type, (
% 34.74/22.45 subclass: ( $i * $i ) > $o)).
% 34.74/22.45 tff(1,assumption,(~member(not_subclass_element(intersection(x, z), intersection(y, w)), y)), introduced(assumption)).
% 34.74/22.45 tff(2,plain,
% 34.74/22.45 ((~subclass(intersection(x, z), intersection(y, w))) <=> (~subclass(intersection(x, z), intersection(y, w)))),
% 34.74/22.45 inference(rewrite,[status(thm)],[])).
% 34.74/22.45 tff(3,axiom,(~subclass(intersection(x, z), intersection(y, w))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_is_monotonic_3')).
% 34.74/22.45 tff(4,plain,
% 34.74/22.45 (~subclass(intersection(x, z), intersection(y, w))),
% 34.74/22.45 inference(modus_ponens,[status(thm)],[3, 2])).
% 34.74/22.45 tff(5,plain,
% 34.74/22.45 (^[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)))),
% 34.74/22.45 inference(bind,[status(th)],[])).
% 34.74/22.45 tff(6,plain,
% 34.74/22.45 (![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))),
% 34.74/22.45 inference(quant_intro,[status(thm)],[5])).
% 34.74/22.45 tff(7,plain,
% 34.74/22.45 (![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))),
% 34.74/22.45 inference(rewrite,[status(thm)],[])).
% 34.74/22.45 tff(8,plain,
% 34.74/22.45 (^[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)))),
% 34.74/22.45 inference(bind,[status(th)],[])).
% 34.74/22.45 tff(9,plain,
% 34.74/22.45 (![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))),
% 34.74/22.45 inference(quant_intro,[status(thm)],[8])).
% 34.74/22.45 tff(10,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 34.74/22.45 tff(11,plain,
% 34.74/22.45 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 34.74/22.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 34.74/22.45 tff(12,plain,
% 34.74/22.45 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 34.74/22.45 inference(modus_ponens,[status(thm)],[11, 7])).
% 34.74/22.45 tff(13,plain,(
% 34.74/22.45 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 34.74/22.45 inference(skolemize,[status(sab)],[12])).
% 34.74/22.45 tff(14,plain,
% 34.74/22.45 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 34.74/22.45 inference(modus_ponens,[status(thm)],[13, 6])).
% 34.74/22.45 tff(15,plain,
% 34.74/22.45 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(intersection(x, z), intersection(y, w)) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z)))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(intersection(x, z), intersection(y, w)) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z)))),
% 34.74/22.45 inference(rewrite,[status(thm)],[])).
% 34.74/22.45 tff(16,plain,
% 34.74/22.45 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(intersection(x, z), intersection(y, w)) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z)))),
% 34.74/22.45 inference(quant_inst,[status(thm)],[])).
% 34.74/22.45 tff(17,plain,
% 34.74/22.45 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(intersection(x, z), intersection(y, w)) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))),
% 34.74/22.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 34.74/22.45 tff(18,plain,
% 34.74/22.45 (member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))),
% 34.74/22.45 inference(unit_resolution,[status(thm)],[17, 14, 4])).
% 34.74/22.46 tff(19,plain,
% 34.74/22.46 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ((~member(Z, intersection(X, Y))) | member(Z, X)))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(20,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[19])).
% 34.74/22.46 tff(21,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(22,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection1')).
% 34.74/22.46 tff(23,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[22, 21])).
% 34.74/22.46 tff(24,plain,(
% 34.74/22.46 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 34.74/22.46 inference(skolemize,[status(sab)],[23])).
% 34.74/22.46 tff(25,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[24, 20])).
% 34.74/22.46 tff(26,plain,
% 34.74/22.46 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), x))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), x))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(27,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), x))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(28,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), x)),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[27, 26])).
% 34.74/22.46 tff(29,plain,
% 34.74/22.46 (member(not_subclass_element(intersection(x, z), intersection(y, w)), x)),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 34.74/22.46 tff(30,plain,
% 34.74/22.46 (subclass(x, y) <=> subclass(x, y)),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(31,axiom,(subclass(x, y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_is_monotonic_1')).
% 34.74/22.46 tff(32,plain,
% 34.74/22.46 (subclass(x, y)),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[31, 30])).
% 34.74/22.46 tff(33,plain,
% 34.74/22.46 (^[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))))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(34,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[33])).
% 34.74/22.46 tff(35,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(36,plain,
% 34.74/22.46 (^[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)))))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(37,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[36])).
% 34.74/22.46 tff(38,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 34.74/22.46 tff(39,plain,
% 34.74/22.46 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 34.74/22.46 tff(40,plain,
% 34.74/22.46 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[39, 35])).
% 34.74/22.46 tff(41,plain,(
% 34.74/22.46 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 34.74/22.46 inference(skolemize,[status(sab)],[40])).
% 34.74/22.46 tff(42,plain,
% 34.74/22.46 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[41, 34])).
% 34.74/22.46 tff(43,plain,
% 34.74/22.46 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), y) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), x)) | (~subclass(x, y)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), y) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), x)) | (~subclass(x, y)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(44,plain,
% 34.74/22.46 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), y) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), x)) | (~subclass(x, y)))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(45,plain,
% 34.74/22.46 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), y) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), x)) | (~subclass(x, y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 34.74/22.46 tff(46,plain,
% 34.74/22.46 ($false),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[45, 42, 32, 29, 1])).
% 34.74/22.46 tff(47,plain,(member(not_subclass_element(intersection(x, z), intersection(y, w)), y)), inference(lemma,lemma(discharge,[]))).
% 34.74/22.46 tff(48,plain,
% 34.74/22.46 (^[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)))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(49,plain,
% 34.74/22.46 (![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))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[48])).
% 34.74/22.46 tff(50,plain,
% 34.74/22.46 (![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))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(51,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 34.74/22.46 tff(52,plain,
% 34.74/22.46 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[51, 50])).
% 34.74/22.46 tff(53,plain,(
% 34.74/22.46 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 34.74/22.46 inference(skolemize,[status(sab)],[52])).
% 34.74/22.46 tff(54,plain,
% 34.74/22.46 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[53, 49])).
% 34.74/22.46 tff(55,plain,
% 34.74/22.46 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w))) | subclass(intersection(x, z), intersection(y, w)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w))) | subclass(intersection(x, z), intersection(y, w)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(56,plain,
% 34.74/22.46 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w))) | subclass(intersection(x, z), intersection(y, w)))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(57,plain,
% 34.74/22.46 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w))) | subclass(intersection(x, z), intersection(y, w))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 34.74/22.46 tff(58,plain,
% 34.74/22.46 (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w))),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[57, 54, 4])).
% 34.74/22.46 tff(59,plain,
% 34.74/22.46 (^[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))))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(60,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[59])).
% 34.74/22.46 tff(61,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(62,plain,
% 34.74/22.46 (^[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))))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(63,plain,
% 34.74/22.46 (![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)))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[62])).
% 34.74/22.46 tff(64,axiom,(![Z: $i, Y: $i, X: $i] : (((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection3')).
% 34.74/22.46 tff(65,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[64, 63])).
% 34.74/22.46 tff(66,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[65, 61])).
% 34.74/22.46 tff(67,plain,(
% 34.74/22.46 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 34.74/22.46 inference(skolemize,[status(sab)],[66])).
% 34.74/22.46 tff(68,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[67, 60])).
% 34.74/22.46 tff(69,plain,
% 34.74/22.46 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), y)))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), y)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(70,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), y)))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(71,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(y, w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 34.74/22.46 tff(72,plain,
% 34.74/22.46 ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), y))),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 34.74/22.46 tff(73,plain,
% 34.74/22.46 (~member(not_subclass_element(intersection(x, z), intersection(y, w)), w)),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[72, 47])).
% 34.74/22.46 tff(74,plain,
% 34.74/22.46 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ((~member(Z, intersection(X, Y))) | member(Z, Y)))),
% 34.74/22.46 inference(bind,[status(th)],[])).
% 34.74/22.46 tff(75,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 34.74/22.46 inference(quant_intro,[status(thm)],[74])).
% 34.74/22.46 tff(76,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(77,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection2')).
% 34.74/22.46 tff(78,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 34.74/22.46 tff(79,plain,(
% 34.74/22.46 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 34.74/22.46 inference(skolemize,[status(sab)],[78])).
% 34.74/22.46 tff(80,plain,
% 34.74/22.46 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[79, 75])).
% 34.74/22.46 tff(81,plain,
% 34.74/22.46 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), z))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), z))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(82,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), z))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(83,plain,
% 34.74/22.46 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), intersection(x, z))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), z)),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 34.74/22.46 tff(84,plain,
% 34.74/22.46 (member(not_subclass_element(intersection(x, z), intersection(y, w)), z)),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[83, 80, 18])).
% 34.74/22.46 tff(85,plain,
% 34.74/22.46 (subclass(z, w) <=> subclass(z, w)),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(86,axiom,(subclass(z, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_is_monotonic_2')).
% 34.74/22.46 tff(87,plain,
% 34.74/22.46 (subclass(z, w)),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[86, 85])).
% 34.74/22.46 tff(88,plain,
% 34.74/22.46 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), w) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), z)) | (~subclass(z, w)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), w) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), z)) | (~subclass(z, w)))),
% 34.74/22.46 inference(rewrite,[status(thm)],[])).
% 34.74/22.46 tff(89,plain,
% 34.74/22.46 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(intersection(x, z), intersection(y, w)), w) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), z)) | (~subclass(z, w)))),
% 34.74/22.46 inference(quant_inst,[status(thm)],[])).
% 34.74/22.46 tff(90,plain,
% 34.74/22.46 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(intersection(x, z), intersection(y, w)), w) | (~member(not_subclass_element(intersection(x, z), intersection(y, w)), z)) | (~subclass(z, w))),
% 34.74/22.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 34.74/22.46 tff(91,plain,
% 34.74/22.46 ($false),
% 34.74/22.46 inference(unit_resolution,[status(thm)],[90, 42, 87, 84, 73])).
% 34.74/22.46 % SZS output end Proof
%------------------------------------------------------------------------------