TSTP Solution File: NUM397+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM397+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 May 21 01:57:19 EDT 2024
% Result : Theorem 4.43s 1.05s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of formulae : 135 ( 26 unt; 0 def)
% Number of atoms : 408 ( 21 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 429 ( 156 ~; 166 |; 77 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 190 ( 169 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28311,plain,
$false,
inference(subsumption_resolution,[],[f28290,f27470]) ).
fof(f27470,plain,
in(sK6(union(sK3)),sK9(sK3,sK6(union(sK3)))),
inference(unit_resulting_resolution,[],[f27433,f1267]) ).
fof(f1267,plain,
! [X0] :
( in(sK6(union(X0)),sK9(X0,sK6(union(X0))))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1223,f196]) ).
fof(f196,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| in(X1,sK9(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK9(X0,X1),X0)
& in(X1,sK9(X0,X1)) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f114,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK9(X0,X1),X0)
& in(X1,sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f113]) ).
fof(f113,plain,
! [X0,X2] :
( ( sP1(X0,X2)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ sP1(X0,X2) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X2] :
( sP1(X0,X2)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1223,plain,
! [X0] :
( sP1(X0,sK6(union(X0)))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f930,f174]) ).
fof(f174,plain,
! [X0] :
( in(sK6(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK6(X0),sK5(X0))
& sK5(X0) != sK6(X0)
& ~ in(sK5(X0),sK6(X0))
& in(sK6(X0),X0)
& in(sK5(X0),X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f101,f102]) ).
fof(f102,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK6(X0),sK5(X0))
& sK5(X0) != sK6(X0)
& ~ in(sK5(X0),sK6(X0))
& in(sK6(X0),X0)
& in(sK5(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f930,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| sP1(X1,X0) ),
inference(resolution,[],[f192,f234]) ).
fof(f234,plain,
! [X0] : sP2(X0,union(X0)),
inference(equality_resolution,[],[f199]) ).
fof(f199,plain,
! [X0,X1] :
( sP2(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP2(X0,X1) ),
inference(definition_folding,[],[f12,f91,f90]) ).
fof(f91,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP1(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f12,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f192,plain,
! [X3,X0,X1] :
( ~ sP2(X0,X1)
| ~ in(X3,X1)
| sP1(X0,X3) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ sP1(X0,sK8(X0,X1))
| ~ in(sK8(X0,X1),X1) )
& ( sP1(X0,sK8(X0,X1))
| in(sK8(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP1(X0,X3) )
& ( sP1(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f110,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) )
=> ( ( ~ sP1(X0,sK8(X0,X1))
| ~ in(sK8(X0,X1),X1) )
& ( sP1(X0,sK8(X0,X1))
| in(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP1(X0,X3) )
& ( sP1(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP1(X0,X2) )
& ( sP1(X0,X2)
| ~ in(X2,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f27433,plain,
~ epsilon_connected(union(sK3)),
inference(unit_resulting_resolution,[],[f144,f27424,f166]) ).
fof(f166,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f27424,plain,
epsilon_transitive(union(sK3)),
inference(subsumption_resolution,[],[f27412,f171]) ).
fof(f171,plain,
! [X0] :
( ~ subset(sK4(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK4(X0),X0)
& in(sK4(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f97,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK4(X0),X0)
& in(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f27412,plain,
( epsilon_transitive(union(sK3))
| subset(sK4(union(sK3)),union(sK3)) ),
inference(resolution,[],[f27400,f187]) ).
fof(f187,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f27400,plain,
( in(sK4(union(sK3)),sK3)
| epsilon_transitive(union(sK3)) ),
inference(subsumption_resolution,[],[f27399,f1099]) ).
fof(f1099,plain,
~ empty(sK3),
inference(unit_resulting_resolution,[],[f1047,f204]) ).
fof(f204,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f1047,plain,
in(sK9(sK3,sK7(union(sK3))),sK3),
inference(unit_resulting_resolution,[],[f929,f197]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f929,plain,
sP1(sK3,sK7(union(sK3))),
inference(unit_resulting_resolution,[],[f518,f234,f192]) ).
fof(f518,plain,
in(sK7(union(sK3)),union(sK3)),
inference(unit_resulting_resolution,[],[f262,f181,f184]) ).
fof(f184,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f181,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f13,f106]) ).
fof(f106,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f262,plain,
~ empty(union(sK3)),
inference(unit_resulting_resolution,[],[f261,f165]) ).
fof(f165,plain,
! [X0] :
( ~ empty(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( sP0(X0)
| ~ empty(X0) ),
inference(definition_folding,[],[f63,f88]) ).
fof(f88,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f63,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f261,plain,
~ sP0(union(sK3)),
inference(unit_resulting_resolution,[],[f144,f164]) ).
fof(f164,plain,
! [X0] :
( ~ sP0(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f27399,plain,
( epsilon_transitive(union(sK3))
| empty(sK3)
| in(sK4(union(sK3)),sK3) ),
inference(resolution,[],[f27392,f184]) ).
fof(f27392,plain,
( element(sK4(union(sK3)),sK3)
| epsilon_transitive(union(sK3)) ),
inference(duplicate_literal_removal,[],[f27356]) ).
fof(f27356,plain,
( element(sK4(union(sK3)),sK3)
| epsilon_transitive(union(sK3))
| epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f27348,f1247]) ).
fof(f1247,plain,
! [X0] :
( in(sK4(union(X0)),sK9(X0,sK4(union(X0))))
| epsilon_transitive(union(X0)) ),
inference(resolution,[],[f1221,f196]) ).
fof(f1221,plain,
! [X0] :
( sP1(X0,sK4(union(X0)))
| epsilon_transitive(union(X0)) ),
inference(resolution,[],[f930,f170]) ).
fof(f170,plain,
! [X0] :
( in(sK4(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f27348,plain,
! [X0] :
( ~ in(X0,sK9(sK3,sK4(union(sK3))))
| element(X0,sK3)
| epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f27346,f205]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f27346,plain,
( element(sK9(sK3,sK4(union(sK3))),powerset(sK3))
| epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f27216,f202]) ).
fof(f202,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f27216,plain,
( subset(sK9(sK3,sK4(union(sK3))),sK3)
| epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f4108,f246]) ).
fof(f246,plain,
epsilon_transitive(sK3),
inference(unit_resulting_resolution,[],[f143,f156]) ).
fof(f156,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f143,plain,
ordinal(sK3),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ~ ordinal(union(sK3))
& ordinal(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f56,f93]) ).
fof(f93,plain,
( ? [X0] :
( ~ ordinal(union(X0))
& ordinal(X0) )
=> ( ~ ordinal(union(sK3))
& ordinal(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
? [X0] :
( ~ ordinal(union(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
inference(negated_conjecture,[],[f37]) ).
fof(f37,conjecture,
! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_ordinal1) ).
fof(f4108,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| subset(sK9(X0,sK4(union(X0))),X0)
| epsilon_transitive(union(X0)) ),
inference(resolution,[],[f1246,f169]) ).
fof(f169,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f1246,plain,
! [X0] :
( in(sK9(X0,sK4(union(X0))),X0)
| epsilon_transitive(union(X0)) ),
inference(resolution,[],[f1221,f197]) ).
fof(f144,plain,
~ ordinal(union(sK3)),
inference(cnf_transformation,[],[f94]) ).
fof(f28290,plain,
~ in(sK6(union(sK3)),sK9(sK3,sK6(union(sK3)))),
inference(unit_resulting_resolution,[],[f27432,f28231,f183]) ).
fof(f183,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f28231,plain,
~ ordinal(sK6(union(sK3))),
inference(unit_resulting_resolution,[],[f27493,f27495,f27494,f28194,f158]) ).
fof(f158,plain,
! [X0,X1] :
( ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f28194,plain,
ordinal(sK5(union(sK3))),
inference(unit_resulting_resolution,[],[f27431,f27468,f183]) ).
fof(f27468,plain,
in(sK5(union(sK3)),sK9(sK3,sK5(union(sK3)))),
inference(unit_resulting_resolution,[],[f27433,f1257]) ).
fof(f1257,plain,
! [X0] :
( in(sK5(union(X0)),sK9(X0,sK5(union(X0))))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1222,f196]) ).
fof(f1222,plain,
! [X0] :
( sP1(X0,sK5(union(X0)))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f930,f173]) ).
fof(f173,plain,
! [X0] :
( in(sK5(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f27431,plain,
ordinal(sK9(sK3,sK5(union(sK3)))),
inference(unit_resulting_resolution,[],[f27424,f13739]) ).
fof(f13739,plain,
( ~ epsilon_transitive(union(sK3))
| ordinal(sK9(sK3,sK5(union(sK3)))) ),
inference(subsumption_resolution,[],[f13738,f144]) ).
fof(f13738,plain,
( ordinal(sK9(sK3,sK5(union(sK3))))
| ordinal(union(sK3))
| ~ epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f13648,f166]) ).
fof(f13648,plain,
( epsilon_connected(union(sK3))
| ordinal(sK9(sK3,sK5(union(sK3)))) ),
inference(resolution,[],[f4224,f143]) ).
fof(f4224,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK9(X0,sK5(union(X0))))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1256,f183]) ).
fof(f1256,plain,
! [X0] :
( in(sK9(X0,sK5(union(X0))),X0)
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1222,f197]) ).
fof(f27494,plain,
sK5(union(sK3)) != sK6(union(sK3)),
inference(unit_resulting_resolution,[],[f27433,f176]) ).
fof(f176,plain,
! [X0] :
( sK5(X0) != sK6(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f27495,plain,
~ in(sK6(union(sK3)),sK5(union(sK3))),
inference(unit_resulting_resolution,[],[f27433,f177]) ).
fof(f177,plain,
! [X0] :
( ~ in(sK6(X0),sK5(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f27493,plain,
~ in(sK5(union(sK3)),sK6(union(sK3))),
inference(unit_resulting_resolution,[],[f27433,f175]) ).
fof(f175,plain,
! [X0] :
( ~ in(sK5(X0),sK6(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f27432,plain,
ordinal(sK9(sK3,sK6(union(sK3)))),
inference(unit_resulting_resolution,[],[f27424,f13878]) ).
fof(f13878,plain,
( ~ epsilon_transitive(union(sK3))
| ordinal(sK9(sK3,sK6(union(sK3)))) ),
inference(subsumption_resolution,[],[f13877,f144]) ).
fof(f13877,plain,
( ordinal(sK9(sK3,sK6(union(sK3))))
| ordinal(union(sK3))
| ~ epsilon_transitive(union(sK3)) ),
inference(resolution,[],[f13786,f166]) ).
fof(f13786,plain,
( epsilon_connected(union(sK3))
| ordinal(sK9(sK3,sK6(union(sK3)))) ),
inference(resolution,[],[f4346,f143]) ).
fof(f4346,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK9(X0,sK6(union(X0))))
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1266,f183]) ).
fof(f1266,plain,
! [X0] :
( in(sK9(X0,sK6(union(X0))),X0)
| epsilon_connected(union(X0)) ),
inference(resolution,[],[f1223,f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM397+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 04:15:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (19824)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (19827)WARNING: value z3 for option sas not known
% 0.21/0.38 % (19825)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (19826)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (19828)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (19827)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (19829)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (19830)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (19831)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.40 TRYING [5]
% 0.21/0.42 TRYING [6]
% 0.21/0.43 TRYING [4]
% 0.21/0.46 TRYING [7]
% 0.21/0.49 TRYING [5]
% 1.26/0.54 TRYING [8]
% 1.99/0.64 TRYING [6]
% 3.51/0.88 TRYING [1]
% 3.51/0.88 TRYING [2]
% 3.51/0.88 TRYING [3]
% 3.51/0.89 TRYING [4]
% 3.51/0.90 TRYING [5]
% 3.51/0.92 TRYING [6]
% 4.08/0.95 TRYING [7]
% 4.43/1.00 TRYING [9]
% 4.43/1.04 % (19831)First to succeed.
% 4.43/1.04 % (19831)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19824"
% 4.43/1.05 % (19831)Refutation found. Thanks to Tanya!
% 4.43/1.05 % SZS status Theorem for theBenchmark
% 4.43/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 4.43/1.05 % (19831)------------------------------
% 4.43/1.05 % (19831)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.43/1.05 % (19831)Termination reason: Refutation
% 4.43/1.05
% 4.43/1.05 % (19831)Memory used [KB]: 8836
% 4.43/1.05 % (19831)Time elapsed: 0.664 s
% 4.43/1.05 % (19831)Instructions burned: 1714 (million)
% 4.43/1.05 % (19824)Success in time 0.672 s
%------------------------------------------------------------------------------