TSTP Solution File: SET587+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 Apr 30 15:08:38 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 126 ( 15 unt; 0 def)
% Number of atoms : 370 ( 67 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 397 ( 153 ~; 186 |; 37 &)
% ( 13 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 209 ( 194 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f217,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f80,f166,f168,f171,f173,f216]) ).
fof(f216,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f215]) ).
fof(f215,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[],[f214,f61]) ).
fof(f61,plain,
( ~ subset(sK0,sK1)
| spl5_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl5_2
<=> subset(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f214,plain,
( subset(sK0,sK1)
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f211]) ).
fof(f211,plain,
( subset(sK0,sK1)
| subset(sK0,sK1)
| ~ spl5_1 ),
inference(resolution,[],[f186,f46]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f186,plain,
( ! [X0] :
( ~ member(sK4(X0,sK1),sK0)
| subset(X0,sK1) )
| ~ spl5_1 ),
inference(resolution,[],[f182,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f182,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f177,f34]) ).
fof(f34,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f177,plain,
( ! [X0] :
( member(X0,empty_set)
| member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl5_1 ),
inference(superposition,[],[f50,f58]) ).
fof(f58,plain,
( empty_set = difference(sK0,sK1)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f56,plain,
( spl5_1
<=> empty_set = difference(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f50,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f173,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f172,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(global_subsumption,[],[f58,f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163,f169]) ).
fof(f169,plain,
( empty_set != difference(sK0,sK1)
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f33,f62]) ).
fof(f163,plain,
( empty_set = difference(sK0,sK1)
| ~ spl5_2 ),
inference(resolution,[],[f159,f71]) ).
fof(f164,plain,
( ! [X0] : difference(sK0,sK1) = difference(difference(sK0,sK1),X0)
| ~ spl5_2 ),
inference(resolution,[],[f159,f112]) ).
fof(f162,plain,
( ! [X0] :
( difference(sK0,sK1) = X0
| ~ subset(X0,difference(sK0,sK1)) )
| ~ spl5_2 ),
inference(resolution,[],[f159,f40]) ).
fof(f161,plain,
( ! [X0,X1] :
( ~ member(X0,difference(sK0,sK1))
| member(X0,X1) )
| ~ spl5_2 ),
inference(resolution,[],[f159,f45]) ).
fof(f159,plain,
( ! [X0] : subset(difference(sK0,sK1),X0)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f155,plain,
( ! [X0] :
( subset(difference(sK0,sK1),X0)
| subset(difference(sK0,sK1),X0) )
| ~ spl5_2 ),
inference(resolution,[],[f68,f120]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( subset(difference(X0,difference(X1,X2)),X3)
| member(sK4(difference(X0,difference(X1,X2)),X3),X2)
| ~ member(sK4(difference(X0,difference(X1,X2)),X3),X1) ),
inference(resolution,[],[f68,f50]) ).
fof(f156,plain,
( ! [X0,X1] :
( subset(difference(X0,sK1),X1)
| ~ member(sK4(difference(X0,sK1),X1),sK0) )
| ~ spl5_2 ),
inference(resolution,[],[f68,f84]) ).
fof(f160,plain,
! [X0,X1] : subset(difference(X0,X0),X1),
inference(duplicate_literal_removal,[],[f154]) ).
fof(f154,plain,
! [X0,X1] :
( subset(difference(X0,X0),X1)
| subset(difference(X0,X0),X1) ),
inference(resolution,[],[f68,f67]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ member(sK4(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f49,f46]) ).
fof(f112,plain,
! [X0,X1] :
( ~ subset(X0,difference(X0,X1))
| difference(X0,X1) = X0 ),
inference(resolution,[],[f98,f40]) ).
fof(f140,plain,
( ! [X0] :
( ~ member(sK2(X0,sK1),sK0)
| ~ member(sK2(X0,sK1),X0)
| sK1 = X0 )
| ~ spl5_2 ),
inference(resolution,[],[f37,f84]) ).
fof(f141,plain,
! [X2,X0,X1] :
( difference(X1,X2) = X0
| ~ member(sK2(X0,difference(X1,X2)),X0)
| member(sK2(X0,difference(X1,X2)),X2)
| ~ member(sK2(X0,difference(X1,X2)),X1) ),
inference(resolution,[],[f37,f50]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
<~> member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(f132,plain,
( ! [X0] :
( member(sK2(empty_set,difference(sK0,X0)),sK1)
| empty_set = difference(sK0,X0) )
| ~ spl5_2 ),
inference(resolution,[],[f107,f99]) ).
fof(f128,plain,
( ! [X0] :
( member(sK2(difference(sK0,X0),empty_set),sK1)
| empty_set = difference(sK0,X0) )
| ~ spl5_2 ),
inference(resolution,[],[f104,f99]) ).
fof(f120,plain,
( ! [X0,X1] :
( member(sK4(difference(sK0,X0),X1),sK1)
| subset(difference(sK0,X0),X1) )
| ~ spl5_2 ),
inference(resolution,[],[f99,f46]) ).
fof(f131,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| member(sK2(empty_set,difference(X0,X1)),X0) ),
inference(resolution,[],[f107,f48]) ).
fof(f130,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| ~ member(sK2(empty_set,difference(X0,X1)),X1) ),
inference(resolution,[],[f107,f49]) ).
fof(f107,plain,
! [X0] :
( member(sK2(empty_set,X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f36,f34]) ).
fof(f127,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| member(sK2(difference(X0,X1),empty_set),X0) ),
inference(resolution,[],[f104,f48]) ).
fof(f126,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| ~ member(sK2(difference(X0,X1),empty_set),X1) ),
inference(resolution,[],[f104,f49]) ).
fof(f104,plain,
! [X0] :
( member(sK2(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f36,f34]) ).
fof(f100,plain,
( ! [X0] :
( ~ subset(sK1,difference(sK0,X0))
| sK1 = difference(sK0,X0) )
| ~ spl5_2 ),
inference(resolution,[],[f97,f40]) ).
fof(f124,plain,
( ! [X0,X1] :
( member(sK2(difference(sK0,X0),X1),sK1)
| member(sK2(difference(sK0,X0),X1),X1)
| difference(sK0,X0) = X1 )
| ~ spl5_2 ),
inference(resolution,[],[f99,f36]) ).
fof(f123,plain,
( ! [X0,X1] :
( member(sK2(X0,difference(sK0,X1)),sK1)
| member(sK2(X0,difference(sK0,X1)),X0)
| difference(sK0,X1) = X0 )
| ~ spl5_2 ),
inference(resolution,[],[f99,f36]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( member(sK4(difference(difference(sK0,X0),X1),X2),sK1)
| subset(difference(difference(sK0,X0),X1),X2) )
| ~ spl5_2 ),
inference(resolution,[],[f99,f67]) ).
fof(f99,plain,
( ! [X0,X1] :
( ~ member(X0,difference(sK0,X1))
| member(X0,sK1) )
| ~ spl5_2 ),
inference(resolution,[],[f97,f45]) ).
fof(f103,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(resolution,[],[f94,f71]) ).
fof(f113,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(resolution,[],[f98,f71]) ).
fof(f98,plain,
! [X0,X1] : subset(difference(X0,X1),X0),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[],[f67,f47]) ).
fof(f109,plain,
! [X2,X0,X1] :
( member(sK2(difference(X0,X1),X2),X2)
| difference(X0,X1) = X2
| member(sK2(difference(X0,X1),X2),X0) ),
inference(resolution,[],[f36,f48]) ).
fof(f108,plain,
! [X2,X0,X1] :
( member(sK2(difference(X0,X1),X2),X2)
| difference(X0,X1) = X2
| ~ member(sK2(difference(X0,X1),X2),X1) ),
inference(resolution,[],[f36,f49]) ).
fof(f106,plain,
! [X2,X0,X1] :
( member(sK2(X0,difference(X1,X2)),X0)
| difference(X1,X2) = X0
| member(sK2(X0,difference(X1,X2)),X1) ),
inference(resolution,[],[f36,f48]) ).
fof(f105,plain,
! [X2,X0,X1] :
( member(sK2(X0,difference(X1,X2)),X0)
| difference(X1,X2) = X0
| ~ member(sK2(X0,difference(X1,X2)),X2) ),
inference(resolution,[],[f36,f49]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f102,plain,
! [X0,X1] :
( difference(empty_set,X1) = X0
| ~ subset(X0,difference(empty_set,X1)) ),
inference(resolution,[],[f94,f40]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(empty_set,X1))
| member(X0,X2) ),
inference(resolution,[],[f94,f45]) ).
fof(f94,plain,
! [X0,X1] : subset(difference(empty_set,X0),X1),
inference(resolution,[],[f67,f34]) ).
fof(f97,plain,
( ! [X0] : subset(difference(sK0,X0),sK1)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f93]) ).
fof(f93,plain,
( ! [X0] :
( subset(difference(sK0,X0),sK1)
| subset(difference(sK0,X0),sK1) )
| ~ spl5_2 ),
inference(resolution,[],[f67,f86]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| member(sK4(difference(difference(X0,X1),X2),X3),X0) ),
inference(resolution,[],[f67,f48]) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( subset(difference(difference(X0,X1),X2),X3)
| ~ member(sK4(difference(difference(X0,X1),X2),X3),X1) ),
inference(resolution,[],[f67,f49]) ).
fof(f67,plain,
! [X2,X0,X1] :
( member(sK4(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f48,f46]) ).
fof(f91,plain,
! [X2,X0,X1] :
( member(sK4(X0,difference(X1,X2)),X2)
| ~ member(sK4(X0,difference(X1,X2)),X1)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f50,f47]) ).
fof(f86,plain,
( ! [X0] :
( ~ member(sK4(X0,sK1),sK0)
| subset(X0,sK1) )
| ~ spl5_2 ),
inference(resolution,[],[f84,f47]) ).
fof(f84,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl5_2 ),
inference(resolution,[],[f45,f62]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f71,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f40,f64]) ).
fof(f70,plain,
( sK0 = sK1
| ~ subset(sK1,sK0)
| ~ spl5_2 ),
inference(resolution,[],[f40,f62]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f46,f34]) ).
fof(f62,plain,
( subset(sK0,sK1)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f32,plain,
( subset(sK0,sK1)
| empty_set = difference(sK0,sK1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( ~ subset(sK0,sK1)
| empty_set != difference(sK0,sK1) )
& ( subset(sK0,sK1)
| empty_set = difference(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15]) ).
fof(f15,plain,
( ? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) )
=> ( ( ~ subset(sK0,sK1)
| empty_set != difference(sK0,sK1) )
& ( subset(sK0,sK1)
| empty_set = difference(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f43,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) )
& ( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) )
& ( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
( ~ subset(sK0,sK1)
| empty_set != difference(sK0,sK1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f171,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f170,plain,
( $false
| ~ spl5_2 ),
inference(global_subsumption,[],[f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163,f169]) ).
fof(f168,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f167,plain,
( $false
| ~ spl5_2 ),
inference(global_subsumption,[],[f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163]) ).
fof(f166,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f165,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f163,f57]) ).
fof(f57,plain,
( empty_set != difference(sK0,sK1)
| spl5_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f80,plain,
( ~ spl5_3
| spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f70,f60,f77,f73]) ).
fof(f73,plain,
( spl5_3
<=> subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f77,plain,
( spl5_4
<=> sK0 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f63,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f32,f60,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 00:56:17 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (30018)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (30021)WARNING: value z3 for option sas not known
% 0.15/0.38 % (30025)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)
% 0.15/0.38 % (30023)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)
% 0.15/0.38 % (30021)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)
% 0.15/0.38 % (30020)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (30022)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (30024)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 % (30021)First to succeed.
% 0.15/0.39 % (30019)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (30021)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (30021)------------------------------
% 0.15/0.39 % (30021)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (30021)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (30021)Memory used [KB]: 885
% 0.15/0.39 % (30021)Time elapsed: 0.009 s
% 0.15/0.39 % (30021)Instructions burned: 13 (million)
% 0.15/0.39 % (30021)------------------------------
% 0.15/0.39 % (30021)------------------------------
% 0.15/0.39 % (30018)Success in time 0.023 s
%------------------------------------------------------------------------------