%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:53:16 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 134 ( 25 unt; 11 def)
% Number of atoms : 347 ( 83 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 352 ( 139 ~; 155 |; 35 &)
% ( 16 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 89 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ( k5_setfam_1(X0,X1) = k1_xboole_0
<=> ! [X2] :
( r2_hidden(X2,X1)
=> X2 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ( k5_setfam_1(X0,X1) = k1_xboole_0
<=> ! [X2] :
( r2_hidden(X2,X1)
=> X2 = k1_xboole_0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( X0 = k1_xboole_0
<=> ! [X1] : ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = k3_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f15,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f16,axiom,
? [X0] :
( v1_xboole_0(X0)
& v1_relat_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f21,axiom,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> k5_setfam_1(X0,X1) = k3_tarski(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f28,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f29,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f36,plain,
? [X0] : v1_xboole_0(X0),
inference(pure_predicate_removal,[],[f16]) ).
fof(f38,plain,
v1_xboole_0(k1_xboole_0),
inference(pure_predicate_removal,[],[f15]) ).
fof(f41,plain,
? [X0,X1] :
( ( k5_setfam_1(X0,X1) = k1_xboole_0
<~> ! [X2] :
( X2 = k1_xboole_0
| ~ r2_hidden(X2,X1) ) )
& m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1] :
( k5_setfam_1(X0,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
? [X0,X1] :
( ( ? [X2] :
( k1_xboole_0 != X2
& r2_hidden(X2,X1) )
| k5_setfam_1(X0,X1) != k1_xboole_0 )
& ( ! [X2] :
( X2 = k1_xboole_0
| ~ r2_hidden(X2,X1) )
| k5_setfam_1(X0,X1) = k1_xboole_0 )
& m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(nnf_transformation,[],[f41]) ).
fof(f57,plain,
? [X0,X1] :
( ( ? [X2] :
( k1_xboole_0 != X2
& r2_hidden(X2,X1) )
| k5_setfam_1(X0,X1) != k1_xboole_0 )
& ( ! [X2] :
( X2 = k1_xboole_0
| ~ r2_hidden(X2,X1) )
| k5_setfam_1(X0,X1) = k1_xboole_0 )
& m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
? [X0,X1] :
( ( ? [X2] :
( k1_xboole_0 != X2
& r2_hidden(X2,X1) )
| k5_setfam_1(X0,X1) != k1_xboole_0 )
& ( ! [X3] :
( k1_xboole_0 = X3
| ~ r2_hidden(X3,X1) )
| k5_setfam_1(X0,X1) = k1_xboole_0 )
& m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
( ( ( k1_xboole_0 != sK2
& r2_hidden(sK2,sK1) )
| k1_xboole_0 != k5_setfam_1(sK0,sK1) )
& ( ! [X3] :
( k1_xboole_0 = X3
| ~ r2_hidden(X3,sK1) )
| k1_xboole_0 = k5_setfam_1(sK0,sK1) )
& m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f58]) ).
fof(f60,plain,
! [X0] :
( ( X0 = k1_xboole_0
| ? [X1] : r2_hidden(X1,X0) )
& ( ! [X1] : ~ r2_hidden(X1,X0)
| k1_xboole_0 != X0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0] :
( ( X0 = k1_xboole_0
| ? [X1] : r2_hidden(X1,X0) )
& ( ! [X2] : ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ( X0 = k1_xboole_0
| r2_hidden(sK3(X0),X0) )
& ( ! [X2] : ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ? [X2] :
( ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) )
& ( ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) )
| r2_hidden(X2,X1) ) ) )
& ( ! [X2] :
( ( r2_hidden(X2,X1)
| ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) ) )
& ( ? [X3] :
( r2_hidden(X2,X3)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f64,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ? [X2] :
( ( ! [X3] :
( ~ r2_hidden(X2,X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(X2,X1) )
& ( ? [X4] :
( r2_hidden(X2,X4)
& r2_hidden(X4,X0) )
| r2_hidden(X2,X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] :
( ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0) ) )
& ( ? [X7] :
( r2_hidden(X5,X7)
& r2_hidden(X7,X0) )
| ~ r2_hidden(X5,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( X1 = k3_tarski(X0)
| ( ( ! [X3] :
( ~ r2_hidden(sK4(X0,X1),X3)
| ~ r2_hidden(X3,X0) )
| ~ r2_hidden(sK4(X0,X1),X1) )
& ( ( r2_hidden(sK4(X0,X1),sK5(X0,X1))
& r2_hidden(sK5(X0,X1),X0) )
| r2_hidden(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( r2_hidden(X5,X1)
| ! [X6] :
( ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0) ) )
& ( ( r2_hidden(X5,sK6(X0,X5))
& r2_hidden(sK6(X0,X5),X0) )
| ~ r2_hidden(X5,X1) ) )
| k3_tarski(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f64]) ).
fof(f67,plain,
v1_xboole_0(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f36]) ).
fof(f71,plain,
m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X3] :
( k1_xboole_0 = X3
| ~ r2_hidden(X3,sK1)
| k1_xboole_0 = k5_setfam_1(sK0,sK1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
( r2_hidden(sK2,sK1)
| k1_xboole_0 != k5_setfam_1(sK0,sK1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
( k1_xboole_0 != sK2
| k1_xboole_0 != k5_setfam_1(sK0,sK1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f76,plain,
! [X2,X0] :
( ~ r2_hidden(X2,X0)
| k1_xboole_0 != X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X0] :
( k1_xboole_0 = X0
| r2_hidden(sK3(X0),X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f80,plain,
! [X0,X1,X6,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0)
| k3_tarski(X0) != X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f81,plain,
! [X0,X1] :
( k3_tarski(X0) = X1
| r2_hidden(sK5(X0,X1),X0)
| r2_hidden(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f82,plain,
! [X0,X1] :
( k3_tarski(X0) = X1
| r2_hidden(sK4(X0,X1),sK5(X0,X1))
| r2_hidden(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f88,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f38]) ).
fof(f89,plain,
v1_xboole_0(sK8),
inference(cnf_transformation,[],[f67]) ).
fof(f95,plain,
! [X0,X1] :
( k5_setfam_1(X0,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(cnf_transformation,[],[f45]) ).
fof(f102,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f103,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f105,plain,
! [X2] : ~ r2_hidden(X2,k1_xboole_0),
inference(equality_resolution,[],[f76]) ).
fof(f106,plain,
! [X0,X6,X5] :
( r2_hidden(X5,k3_tarski(X0))
| ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f109,plain,
( ~ r2_hidden(sK2,sK1)
| k1_xboole_0 != k5_setfam_1(sK0,sK1) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f110,plain,
! [X3] :
( k1_xboole_0 = X3
| r2_hidden(X3,sK1)
| k1_xboole_0 = k5_setfam_1(sK0,sK1) ),
inference(consistent_polarity_flipping,[],[f72]) ).
fof(f111,plain,
~ m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(consistent_polarity_flipping,[],[f71]) ).
fof(f113,plain,
! [X0] :
( ~ r2_hidden(sK3(X0),X0)
| k1_xboole_0 = X0 ),
inference(consistent_polarity_flipping,[],[f77]) ).
fof(f114,plain,
! [X2] : r2_hidden(X2,k1_xboole_0),
inference(consistent_polarity_flipping,[],[f105]) ).
fof(f116,plain,
! [X0,X1] :
( ~ r2_hidden(sK4(X0,X1),sK5(X0,X1))
| k3_tarski(X0) = X1
| ~ r2_hidden(sK4(X0,X1),X1) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f117,plain,
! [X0,X1] :
( ~ r2_hidden(sK5(X0,X1),X0)
| k3_tarski(X0) = X1
| ~ r2_hidden(sK4(X0,X1),X1) ),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f118,plain,
! [X0,X6,X5] :
( r2_hidden(X6,X0)
| r2_hidden(X5,X6)
| ~ r2_hidden(X5,k3_tarski(X0)) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f125,plain,
~ v1_xboole_0(k1_xboole_0),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f126,plain,
~ v1_xboole_0(sK8),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f132,plain,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| k5_setfam_1(X0,X1) = k3_tarski(X1) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f139,plain,
! [X0] :
( v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f140,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1) ),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f143,definition,
( spl12_1
<=> k1_xboole_0 = k5_setfam_1(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f144,plain,
( k1_xboole_0 != k5_setfam_1(sK0,sK1)
| spl12_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( k1_xboole_0 = k5_setfam_1(sK0,sK1)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f147,definition,
( spl12_2
<=> ! [X3] :
( k1_xboole_0 = X3
| r2_hidden(X3,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f148,plain,
( ! [X3] :
( r2_hidden(X3,sK1)
| k1_xboole_0 = X3 )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f110,f147,f143]) ).
fof(f151,definition,
( spl12_3
<=> r2_hidden(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f153,plain,
( ~ r2_hidden(sK2,sK1)
| spl12_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( ~ spl12_1
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f109,f151,f143]) ).
fof(f156,definition,
( spl12_4
<=> k1_xboole_0 = sK2 ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f159,plain,
( ~ spl12_1
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f74,f156,f143]) ).
fof(f168,plain,
! [X0] : r2_hidden(X0,sK8),
inference(resolution,[],[f140,f126]) ).
fof(f439,plain,
( ! [X0] :
( r2_hidden(X0,sK2)
| ~ r2_hidden(X0,k3_tarski(sK1)) )
| spl12_3 ),
inference(resolution,[],[f118,f153]) ).
fof(f442,plain,
( ~ r2_hidden(sK3(sK2),k3_tarski(sK1))
| k1_xboole_0 = sK2
| spl12_3 ),
inference(resolution,[],[f439,f113]) ).
fof(f444,definition,
( spl12_20
<=> r2_hidden(sK3(sK2),k3_tarski(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
fof(f446,plain,
( ~ r2_hidden(sK3(sK2),k3_tarski(sK1))
| spl12_20 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f447,plain,
( spl12_4
| ~ spl12_20
| spl12_3 ),
inference(avatar_split_clause,[],[f442,f151,f444,f156]) ).
fof(f855,plain,
k5_setfam_1(sK0,sK1) = k3_tarski(sK1),
inference(resolution,[],[f132,f111]) ).
fof(f875,plain,
( k1_xboole_0 != k3_tarski(sK1)
| spl12_1 ),
inference(superposition,[],[f144,f855]) ).
fof(f961,plain,
( ! [X0] :
( ~ r2_hidden(sK4(sK1,X0),X0)
| k3_tarski(sK1) = X0
| k1_xboole_0 = sK5(sK1,X0) )
| ~ spl12_2 ),
inference(resolution,[],[f117,f148]) ).
fof(f1040,definition,
( spl12_35
<=> v1_xboole_0(k3_tarski(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_35])],[avatar_definition]) ).
fof(f1041,plain,
( v1_xboole_0(k3_tarski(sK1))
| ~ spl12_35 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1042,plain,
( ~ v1_xboole_0(k3_tarski(sK1))
| spl12_35 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1045,plain,
( k1_xboole_0 = k3_tarski(sK1)
| spl12_35 ),
inference(resolution,[],[f1042,f139]) ).
fof(f1057,plain,
( k1_xboole_0 != k1_xboole_0
| spl12_1
| spl12_35 ),
inference(superposition,[],[f875,f1045]) ).
fof(f1062,plain,
( $false
| spl12_1
| spl12_35 ),
inference(trivial_inequality_removal,[],[f1057]) ).
fof(f1063,plain,
( spl12_1
| spl12_35 ),
inference(avatar_contradiction_clause,[],[f1062]) ).
fof(f1292,plain,
( sK8 = k3_tarski(sK1)
| k1_xboole_0 = sK5(sK1,sK8)
| ~ spl12_2 ),
inference(resolution,[],[f961,f168]) ).
fof(f1296,definition,
( spl12_40
<=> k1_xboole_0 = sK5(sK1,sK8) ),
introduced(definition,[new_symbols(definition,[spl12_40])],[avatar_definition]) ).
fof(f1298,plain,
( k1_xboole_0 = sK5(sK1,sK8)
| ~ spl12_40 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f1300,definition,
( spl12_41
<=> sK8 = k3_tarski(sK1) ),
introduced(definition,[new_symbols(definition,[spl12_41])],[avatar_definition]) ).
fof(f1302,plain,
( sK8 = k3_tarski(sK1)
| ~ spl12_41 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f1303,plain,
( spl12_40
| spl12_41
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f1292,f147,f1300,f1296]) ).
fof(f1381,definition,
( spl12_59
<=> k1_xboole_0 = k3_tarski(sK1) ),
introduced(definition,[new_symbols(definition,[spl12_59])],[avatar_definition]) ).
fof(f1383,plain,
( k1_xboole_0 = k3_tarski(sK1)
| ~ spl12_59 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f1420,plain,
( v1_xboole_0(k1_xboole_0)
| ~ spl12_35
| ~ spl12_59 ),
inference(superposition,[],[f1041,f1383]) ).
fof(f1471,plain,
( ~ r2_hidden(sK4(sK1,sK8),k1_xboole_0)
| sK8 = k3_tarski(sK1)
| ~ r2_hidden(sK4(sK1,sK8),sK8)
| ~ spl12_40 ),
inference(superposition,[],[f116,f1298]) ).
fof(f1474,definition,
( spl12_62
<=> r2_hidden(sK4(sK1,sK8),sK8) ),
introduced(definition,[new_symbols(definition,[spl12_62])],[avatar_definition]) ).
fof(f1476,plain,
( ~ r2_hidden(sK4(sK1,sK8),sK8)
| spl12_62 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f1478,definition,
( spl12_63
<=> r2_hidden(sK4(sK1,sK8),k1_xboole_0) ),
introduced(definition,[new_symbols(definition,[spl12_63])],[avatar_definition]) ).
fof(f1480,plain,
( ~ r2_hidden(sK4(sK1,sK8),k1_xboole_0)
| spl12_63 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f1481,plain,
( ~ spl12_62
| spl12_41
| ~ spl12_63
| ~ spl12_40 ),
inference(avatar_split_clause,[],[f1471,f1296,f1478,f1300,f1474]) ).
fof(f1520,plain,
( $false
| spl12_62 ),
inference(resolution,[],[f1476,f168]) ).
fof(f1527,plain,
spl12_62,
inference(avatar_contradiction_clause,[],[f1520]) ).
fof(f1557,plain,
( $false
| spl12_63 ),
inference(resolution,[],[f1480,f114]) ).
fof(f1564,plain,
spl12_63,
inference(avatar_contradiction_clause,[],[f1557]) ).
fof(f1575,plain,
( v1_xboole_0(sK8)
| ~ spl12_35
| ~ spl12_41 ),
inference(superposition,[],[f1041,f1302]) ).
fof(f1581,plain,
( $false
| ~ spl12_35
| ~ spl12_41 ),
inference(resolution,[],[f1575,f126]) ).
fof(f1584,plain,
( ~ spl12_35
| ~ spl12_41 ),
inference(avatar_contradiction_clause,[],[f1581]) ).
fof(f1589,plain,
( ! [X0] : r2_hidden(X0,k3_tarski(sK1))
| spl12_35 ),
inference(resolution,[],[f1042,f140]) ).
fof(f1599,plain,
( k1_xboole_0 = k3_tarski(sK1)
| ~ spl12_1 ),
inference(superposition,[],[f855,f145]) ).
fof(f1615,plain,
( $false
| spl12_20
| spl12_35 ),
inference(resolution,[],[f1589,f446]) ).
fof(f1621,plain,
( spl12_20
| spl12_35 ),
inference(avatar_contradiction_clause,[],[f1615]) ).
fof(f1623,plain,
( $false
| ~ spl12_35
| ~ spl12_59 ),
inference(resolution,[],[f1420,f125]) ).
fof(f1624,plain,
( ~ spl12_35
| ~ spl12_59 ),
inference(avatar_contradiction_clause,[],[f1623]) ).
fof(f1625,plain,
( spl12_59
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f1599,f143,f1381]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f149]) ).
cnf(s2,plain,
( ~ spl12_1
| ~ spl12_3 ),
inference(sat_conversion,[],[f154]) ).
cnf(s3,plain,
( ~ spl12_1
| ~ spl12_4 ),
inference(sat_conversion,[],[f159]) ).
cnf(s25,plain,
( spl12_3
| spl12_4
| ~ spl12_20 ),
inference(sat_conversion,[],[f447]) ).
cnf(s43,plain,
( spl12_1
| spl12_35 ),
inference(sat_conversion,[],[f1063]) ).
cnf(s46,plain,
( ~ spl12_2
| spl12_40
| spl12_41 ),
inference(sat_conversion,[],[f1303]) ).
cnf(s62,plain,
( ~ spl12_40
| spl12_41
| ~ spl12_62
| ~ spl12_63 ),
inference(sat_conversion,[],[f1481]) ).
cnf(s65,plain,
spl12_62,
inference(sat_conversion,[],[f1527]) ).
cnf(s68,plain,
spl12_63,
inference(sat_conversion,[],[f1564]) ).
cnf(s69,plain,
( ~ spl12_35
| ~ spl12_41 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s74,plain,
( spl12_20
| spl12_35 ),
inference(sat_conversion,[],[f1621]) ).
cnf(s75,plain,
( ~ spl12_35
| ~ spl12_59 ),
inference(sat_conversion,[],[f1624]) ).
cnf(s76,plain,
( ~ spl12_1
| spl12_59 ),
inference(sat_conversion,[],[f1625]) ).
cnf(s78,plain,
( ~ spl12_40
| spl12_41 ),
inference(rat,[],[s62,s68,s65]) ).
cnf(s80,plain,
( ~ spl12_2
| spl12_41 ),
inference(rat,[],[s78,s46]) ).
cnf(s81,plain,
spl12_1,
inference(rat,[],[s80,s69,s1,s43]) ).
cnf(s82,plain,
spl12_59,
inference(rat,[],[s76,s81]) ).
cnf(s83,plain,
~ spl12_4,
inference(rat,[],[s3,s81]) ).
cnf(s84,plain,
~ spl12_3,
inference(rat,[],[s2,s81]) ).
cnf(s85,plain,
~ spl12_35,
inference(rat,[],[s75,s82]) ).
cnf(s87,plain,
~ spl12_20,
inference(rat,[],[s25,s83,s84]) ).
cnf(s93,plain,
$false,
inference(rat,[],[s74,s85,s87]) ).
fof(f1626,plain,
$false,
inference(avatar_sat_refutation,[],[s93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n020.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 05:24:35 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % (4056318)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (4056329)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2093809148:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (4056324)% WARNING: option uhcvi not known.
% 0.18/0.48 % (4056324)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1403824824:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (4056323)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=971125205_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (4056325)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3987216129:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (4056326)dis+10_1_sil=32000:sp=arity:random_seed=51228765:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (4056328)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=141205636:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (4056327)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3479097103:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % TRYING [4]
% 0.18/0.48 % (4056329) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4056318-4056329"...
% 0.18/0.48 % TRYING [5]
% 0.18/0.48 % (4056329)...printing done.
% 0.18/0.48 % (4056326) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4056318-4056326"...
% 0.18/0.48 % (4056329)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (4056329)------------------------------
% 0.18/0.48 % (4056329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (4056329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (4056329)CaDiCaL version: 2.1.3
% 0.18/0.48 % (4056329)Termination reason: Refutation
% 0.18/0.48 % (4056329)Time elapsed: 0.016 s
% 0.18/0.48 % (4056329)Peak memory usage: 13 MB
% 0.18/0.48 % (4056329)Instructions burned: 37 (million)
% 0.18/0.48 % (4056318)Success in time 0.045 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------