TSTP Solution File: SET203-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET203-6 : 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 05:06:09 EDT 2022
% Result : Unsatisfiable 21.95s 14.27s
% Output : Proof 21.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET203-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 03:45:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 21.95/14.27 % SZS status Unsatisfiable
% 21.95/14.27 % SZS output start Proof
% 21.95/14.27 tff(subclass_type, type, (
% 21.95/14.27 subclass: ( $i * $i ) > $o)).
% 21.95/14.27 tff(universal_class_type, type, (
% 21.95/14.27 universal_class: $i)).
% 21.95/14.27 tff(y_type, type, (
% 21.95/14.27 y: $i)).
% 21.95/14.27 tff(member_type, type, (
% 21.95/14.27 member: ( $i * $i ) > $o)).
% 21.95/14.27 tff(v_type, type, (
% 21.95/14.27 v: $i)).
% 21.95/14.27 tff(u_type, type, (
% 21.95/14.27 u: $i)).
% 21.95/14.27 tff(x_type, type, (
% 21.95/14.27 x: $i)).
% 21.95/14.27 tff(cross_product_type, type, (
% 21.95/14.27 cross_product: ( $i * $i ) > $i)).
% 21.95/14.27 tff(ordered_pair_type, type, (
% 21.95/14.27 ordered_pair: ( $i * $i ) > $i)).
% 21.95/14.27 tff(1,assumption,(~subclass(y, universal_class)), introduced(assumption)).
% 21.95/14.27 tff(2,plain,
% 21.95/14.27 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 21.95/14.27 inference(bind,[status(th)],[])).
% 21.95/14.27 tff(3,plain,
% 21.95/14.27 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 21.95/14.27 inference(quant_intro,[status(thm)],[2])).
% 21.95/14.27 tff(4,plain,
% 21.95/14.27 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 21.95/14.27 inference(rewrite,[status(thm)],[])).
% 21.95/14.27 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 21.95/14.27 tff(6,plain,
% 21.95/14.27 (![X: $i] : subclass(X, universal_class)),
% 21.95/14.27 inference(modus_ponens,[status(thm)],[5, 4])).
% 21.95/14.27 tff(7,plain,(
% 21.95/14.27 ![X: $i] : subclass(X, universal_class)),
% 21.95/14.27 inference(skolemize,[status(sab)],[6])).
% 21.95/14.27 tff(8,plain,
% 21.95/14.27 (![X: $i] : subclass(X, universal_class)),
% 21.95/14.27 inference(modus_ponens,[status(thm)],[7, 3])).
% 21.95/14.27 tff(9,plain,
% 21.95/14.27 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 21.95/14.27 inference(quant_inst,[status(thm)],[])).
% 21.95/14.27 tff(10,plain,
% 21.95/14.27 ($false),
% 21.95/14.27 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 21.95/14.27 tff(11,plain,(subclass(y, universal_class)), inference(lemma,lemma(discharge,[]))).
% 21.95/14.27 tff(12,assumption,(~subclass(x, universal_class)), introduced(assumption)).
% 21.95/14.27 tff(13,plain,
% 21.95/14.27 ((~![X: $i] : subclass(X, universal_class)) | subclass(x, universal_class)),
% 21.95/14.27 inference(quant_inst,[status(thm)],[])).
% 21.95/14.27 tff(14,plain,
% 21.95/14.27 ($false),
% 21.95/14.27 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 21.95/14.27 tff(15,plain,(subclass(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 21.95/14.27 tff(16,assumption,(~member(u, universal_class)), introduced(assumption)).
% 21.95/14.27 tff(17,plain,
% 21.95/14.27 (member(u, x) <=> member(u, x)),
% 21.95/14.27 inference(rewrite,[status(thm)],[])).
% 21.95/14.27 tff(18,axiom,(member(u, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_1')).
% 21.95/14.27 tff(19,plain,
% 21.95/14.27 (member(u, x)),
% 21.95/14.27 inference(modus_ponens,[status(thm)],[18, 17])).
% 21.95/14.27 tff(20,plain,
% 21.95/14.27 (^[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))))),
% 21.95/14.27 inference(bind,[status(th)],[])).
% 21.95/14.27 tff(21,plain,
% 21.95/14.27 (![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)))),
% 21.95/14.27 inference(quant_intro,[status(thm)],[20])).
% 21.95/14.27 tff(22,plain,
% 21.95/14.27 (![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)))),
% 21.95/14.27 inference(rewrite,[status(thm)],[])).
% 21.95/14.27 tff(23,plain,
% 21.95/14.27 (^[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)))))),
% 21.95/14.27 inference(bind,[status(th)],[])).
% 21.95/14.27 tff(24,plain,
% 21.95/14.27 (![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)))),
% 21.95/14.27 inference(quant_intro,[status(thm)],[23])).
% 21.95/14.27 tff(25,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')).
% 21.95/14.28 tff(26,plain,
% 21.95/14.28 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[25, 24])).
% 21.95/14.28 tff(27,plain,
% 21.95/14.28 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[26, 22])).
% 21.95/14.28 tff(28,plain,(
% 21.95/14.28 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 21.95/14.28 inference(skolemize,[status(sab)],[27])).
% 21.95/14.28 tff(29,plain,
% 21.95/14.28 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[28, 21])).
% 21.95/14.28 tff(30,plain,
% 21.95/14.28 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(31,plain,
% 21.95/14.28 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))),
% 21.95/14.28 inference(quant_inst,[status(thm)],[])).
% 21.95/14.28 tff(32,plain,
% 21.95/14.28 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[31, 30])).
% 21.95/14.28 tff(33,plain,
% 21.95/14.28 ($false),
% 21.95/14.28 inference(unit_resolution,[status(thm)],[32, 29, 19, 16, 15])).
% 21.95/14.28 tff(34,plain,(member(u, universal_class)), inference(lemma,lemma(discharge,[]))).
% 21.95/14.28 tff(35,plain,
% 21.95/14.28 ((~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) <=> (~member(ordered_pair(u, v), cross_product(universal_class, universal_class)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(36,axiom,(~member(ordered_pair(u, v), cross_product(universal_class, universal_class))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_3')).
% 21.95/14.28 tff(37,plain,
% 21.95/14.28 (~member(ordered_pair(u, v), cross_product(universal_class, universal_class))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[36, 35])).
% 21.95/14.28 tff(38,plain,
% 21.95/14.28 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 21.95/14.28 inference(bind,[status(th)],[])).
% 21.95/14.28 tff(39,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(quant_intro,[status(thm)],[38])).
% 21.95/14.28 tff(40,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(41,plain,
% 21.95/14.28 (^[V: $i, Y: $i, U: $i, X: $i] : rewrite((((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 21.95/14.28 inference(bind,[status(th)],[])).
% 21.95/14.28 tff(42,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(quant_intro,[status(thm)],[41])).
% 21.95/14.28 tff(43,axiom,(![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product3')).
% 21.95/14.28 tff(44,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[43, 42])).
% 21.95/14.28 tff(45,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[44, 40])).
% 21.95/14.28 tff(46,plain,(
% 21.95/14.28 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(skolemize,[status(sab)],[45])).
% 21.95/14.28 tff(47,plain,
% 21.95/14.28 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[46, 39])).
% 21.95/14.28 tff(48,plain,
% 21.95/14.28 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(49,plain,
% 21.95/14.28 (((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class))) <=> (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(50,plain,
% 21.95/14.28 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class))))),
% 21.95/14.28 inference(monotonicity,[status(thm)],[49])).
% 21.95/14.28 tff(51,plain,
% 21.95/14.28 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 21.95/14.28 inference(transitivity,[status(thm)],[50, 48])).
% 21.95/14.28 tff(52,plain,
% 21.95/14.28 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class)))),
% 21.95/14.28 inference(quant_inst,[status(thm)],[])).
% 21.95/14.28 tff(53,plain,
% 21.95/14.28 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[52, 51])).
% 21.95/14.28 tff(54,plain,
% 21.95/14.28 ((~member(u, universal_class)) | (~member(v, universal_class))),
% 21.95/14.28 inference(unit_resolution,[status(thm)],[53, 47, 37])).
% 21.95/14.28 tff(55,plain,
% 21.95/14.28 (~member(v, universal_class)),
% 21.95/14.28 inference(unit_resolution,[status(thm)],[54, 34])).
% 21.95/14.28 tff(56,plain,
% 21.95/14.28 (member(v, y) <=> member(v, y)),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(57,axiom,(member(v, y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_2')).
% 21.95/14.28 tff(58,plain,
% 21.95/14.28 (member(v, y)),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[57, 56])).
% 21.95/14.28 tff(59,plain,
% 21.95/14.28 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))),
% 21.95/14.28 inference(rewrite,[status(thm)],[])).
% 21.95/14.28 tff(60,plain,
% 21.95/14.28 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))),
% 21.95/14.28 inference(quant_inst,[status(thm)],[])).
% 21.95/14.28 tff(61,plain,
% 21.95/14.28 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class))),
% 21.95/14.28 inference(modus_ponens,[status(thm)],[60, 59])).
% 21.95/14.28 tff(62,plain,
% 21.95/14.28 ($false),
% 21.95/14.28 inference(unit_resolution,[status(thm)],[61, 29, 58, 55, 11])).
% 21.95/14.28 % SZS output end Proof
%------------------------------------------------------------------------------