%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU425+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 : n010.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 12:53:15 PM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 95 ( 20 unt; 5 def)
% Number of atoms : 299 ( 80 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 339 ( 135 ~; 136 |; 38 &)
% ( 15 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 6 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 1 sgn 125 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( v1_funct_1(k5_relset_2(X0,X2))
& v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( v1_funct_1(k5_relset_2(X0,X2))
& v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
& m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( ( ( X1 = k1_xboole_0
=> X0 = k1_xboole_0 )
=> ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) ) )
& ( X1 = k1_xboole_0
=> ( X0 = k1_xboole_0
| ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f7,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( ( v1_relat_1(X2)
& v1_funct_1(X2) )
=> ( X2 = k5_relset_2(X0,X1)
<=> ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X3] :
( r1_tarski(X3,X0)
=> k1_funct_1(X2,X3) = k9_relat_1(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
fof(f15,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( v1_relat_1(k5_relset_2(X0,X1))
& v1_funct_1(k5_relset_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(f23,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f24,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f38,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f39,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f40,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f41,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( ( r1_tarski(k1_relat_1(X2),X0)
& r1_tarski(k2_relat_1(X2),X1) )
=> m2_relset_1(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
fof(f51,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f40]) ).
fof(f53,plain,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0) ),
inference(pure_predicate_removal,[],[f23]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ( ~ v1_funct_1(k5_relset_2(X0,X2))
| ~ v1_funct_2(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2)))
| ~ m2_relset_1(k5_relset_2(X0,X2),k1_zfmisc_1(X0),k1_zfmisc_1(k2_relat_1(X2))) )
& m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ( ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) )
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 ) )
& ( X0 = k1_xboole_0
| ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 )
| k1_xboole_0 != X1 ) )
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ( ( v1_funct_2(X2,X0,X1)
<=> X0 = k4_relset_1(X0,X1,X2) )
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 ) )
& ( X0 = k1_xboole_0
| ( v1_funct_2(X2,X0,X1)
<=> X2 = k1_xboole_0 )
| k1_xboole_0 != X1 ) )
| ~ m2_relset_1(X2,X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = k5_relset_2(X0,X1)
<=> ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X3] :
( k1_funct_1(X2,X3) = k9_relat_1(X1,X3)
| ~ r1_tarski(X3,X0) ) ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = k5_relset_2(X0,X1)
<=> ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X3] :
( k1_funct_1(X2,X3) = k9_relat_1(X1,X3)
| ~ r1_tarski(X3,X0) ) ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ( v1_relat_1(k5_relset_2(X0,X1))
& v1_funct_1(k5_relset_2(X0,X1)) )
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f74,plain,
! [X0,X1,X2] :
( k4_relset_1(X0,X1,X2) = k1_relat_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f75,plain,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,plain,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f75]) ).
fof(f78,plain,
! [X0,X1,X2] :
( r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f43]) ).
fof(f87,plain,
( ( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) )
& m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f54]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ( ( ( v1_funct_2(X2,X0,X1)
| k4_relset_1(X0,X1,X2) != X0 )
& ( X0 = k4_relset_1(X0,X1,X2)
| ~ v1_funct_2(X2,X0,X1) ) )
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 ) )
& ( X0 = k1_xboole_0
| ( ( v1_funct_2(X2,X0,X1)
| k1_xboole_0 != X2 )
& ( X2 = k1_xboole_0
| ~ v1_funct_2(X2,X0,X1) ) )
| k1_xboole_0 != X1 ) )
| ~ m2_relset_1(X2,X0,X1) ),
inference(nnf_transformation,[],[f59]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = k5_relset_2(X0,X1)
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| ? [X3] :
( k1_funct_1(X2,X3) != k9_relat_1(X1,X3)
& r1_tarski(X3,X0) ) )
& ( ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X3] :
( k1_funct_1(X2,X3) = k9_relat_1(X1,X3)
| ~ r1_tarski(X3,X0) ) )
| k5_relset_2(X0,X1) != X2 ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(nnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = k5_relset_2(X0,X1)
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| ? [X3] :
( k1_funct_1(X2,X3) != k9_relat_1(X1,X3)
& r1_tarski(X3,X0) ) )
& ( ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X3] :
( k1_funct_1(X2,X3) = k9_relat_1(X1,X3)
| ~ r1_tarski(X3,X0) ) )
| k5_relset_2(X0,X1) != X2 ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = k5_relset_2(X0,X1)
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| ? [X3] :
( k1_funct_1(X2,X3) != k9_relat_1(X1,X3)
& r1_tarski(X3,X0) ) )
& ( ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X4] :
( k1_funct_1(X2,X4) = k9_relat_1(X1,X4)
| ~ r1_tarski(X4,X0) ) )
| k5_relset_2(X0,X1) != X2 ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = k5_relset_2(X0,X1)
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| ( k1_funct_1(X2,sK3(X0,X1,X2)) != k9_relat_1(X1,sK3(X0,X1,X2))
& r1_tarski(sK3(X0,X1,X2),X0) ) )
& ( ( k1_relat_1(X2) = k1_zfmisc_1(X0)
& ! [X4] :
( k1_funct_1(X2,X4) = k9_relat_1(X1,X4)
| ~ r1_tarski(X4,X0) ) )
| k5_relset_2(X0,X1) != X2 ) )
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) )
| ~ v1_relat_1(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f91]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f104,plain,
m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f87]) ).
fof(f105,plain,
( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f113,plain,
! [X2,X0,X1] :
( k4_relset_1(X0,X1,X2) != X0
| v1_funct_2(X2,X0,X1)
| k1_xboole_0 = X1
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f116,plain,
! [X2,X0,X1] :
( k1_zfmisc_1(X0) = k1_relat_1(X2)
| k5_relset_2(X0,X1) != X2
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f120,plain,
! [X0,X1] :
( v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f121,plain,
! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f127,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f53]) ).
fof(f128,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f51]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ r1_tarski(k1_relat_1(X2),X0)
| m2_relset_1(X2,X0,X1)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2))) ),
inference(cnf_transformation,[],[f78]) ).
fof(f171,plain,
! [X0,X1] :
( k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(equality_resolution,[],[f116]) ).
fof(f174,definition,
( spl13_1
<=> m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f175,plain,
( m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| spl13_1 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f178,definition,
( spl13_2
<=> v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f182,definition,
( spl13_3
<=> v1_funct_1(k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f184,plain,
( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| spl13_3 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f105,f182,f178,f174]) ).
fof(f229,plain,
v1_relat_1(sK2),
inference(resolution,[],[f108,f104]) ).
fof(f312,plain,
! [X0,X1] :
( m2_relset_1(X0,k1_relat_1(X0),X1)
| ~ r1_tarski(k2_relat_1(X0),X1)
| ~ v1_relat_1(X0) ),
inference(resolution,[],[f155,f154]) ).
fof(f330,plain,
r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2))),
inference(resolution,[],[f157,f104]) ).
fof(f343,plain,
! [X0,X1] :
( k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,X1))
| ~ v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(forward_subsumption_resolution,[],[f171,f121]) ).
fof(f344,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f343,f120]) ).
fof(f355,plain,
! [X0] : k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,sK2)),
inference(resolution,[],[f344,f229]) ).
fof(f745,plain,
! [X0,X1] :
( m2_relset_1(k5_relset_2(X0,sK2),k1_zfmisc_1(X0),X1)
| ~ r1_tarski(k2_relat_1(k5_relset_2(X0,sK2)),X1)
| ~ v1_relat_1(k5_relset_2(X0,sK2)) ),
inference(superposition,[],[f312,f355]) ).
fof(f979,plain,
( ~ r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(k5_relset_2(sK0,sK2))
| spl13_1 ),
inference(resolution,[],[f745,f176]) ).
fof(f986,plain,
( ~ v1_relat_1(k5_relset_2(sK0,sK2))
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f979,f330]) ).
fof(f990,plain,
( ~ v1_relat_1(sK2)
| spl13_1 ),
inference(resolution,[],[f986,f121]) ).
fof(f991,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f990,f229]) ).
fof(f992,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f997,plain,
( m1_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl13_1 ),
inference(resolution,[],[f175,f152]) ).
fof(f999,definition,
( spl13_16
<=> k1_zfmisc_1(sK0) = k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f1001,plain,
( k1_zfmisc_1(sK0) = k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2))
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f1003,definition,
( spl13_17
<=> k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
fof(f1005,plain,
( k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1013,plain,
( k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2)) = k1_relat_1(k5_relset_2(sK0,sK2))
| ~ spl13_1 ),
inference(resolution,[],[f997,f151]) ).
fof(f1015,plain,
( k1_zfmisc_1(sK0) = k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f1013,f355]) ).
fof(f1016,plain,
( spl13_16
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f1015,f174,f999]) ).
fof(f1021,plain,
( k1_zfmisc_1(sK0) != k1_zfmisc_1(sK0)
| v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl13_16 ),
inference(superposition,[],[f113,f1001]) ).
fof(f1023,plain,
( v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl13_16 ),
inference(trivial_inequality_removal,[],[f1021]) ).
fof(f1043,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ spl13_17 ),
inference(superposition,[],[f128,f1005]) ).
fof(f1078,plain,
( $false
| ~ spl13_17 ),
inference(forward_subsumption_resolution,[],[f1043,f127]) ).
fof(f1079,plain,
~ spl13_17,
inference(avatar_contradiction_clause,[],[f1078]) ).
fof(f1086,plain,
( v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ spl13_1
| ~ spl13_16 ),
inference(forward_subsumption_resolution,[],[f1023,f175]) ).
fof(f1087,plain,
( spl13_17
| spl13_2
| ~ spl13_1
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f1086,f999,f174,f178,f1003]) ).
fof(f1088,plain,
( ~ v1_relat_1(sK2)
| spl13_3 ),
inference(resolution,[],[f184,f120]) ).
fof(f1089,plain,
( $false
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f1088,f229]) ).
fof(f1090,plain,
spl13_3,
inference(avatar_contradiction_clause,[],[f1089]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s13,plain,
spl13_1,
inference(sat_conversion,[],[f992]) ).
cnf(s15,plain,
( ~ spl13_1
| spl13_16 ),
inference(sat_conversion,[],[f1016]) ).
cnf(s19,plain,
~ spl13_17,
inference(sat_conversion,[],[f1079]) ).
cnf(s22,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_16
| spl13_17 ),
inference(sat_conversion,[],[f1087]) ).
cnf(s23,plain,
spl13_3,
inference(sat_conversion,[],[f1090]) ).
cnf(s26,plain,
spl13_16,
inference(rat,[],[s15,s13]) ).
cnf(s27,plain,
spl13_2,
inference(rat,[],[s22,s19,s13,s26]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s23,s27,s13]) ).
fof(f1091,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 05:21:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 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
% 0.08/0.45 % (1582467)Will run a generic schedule for satisfiability detection.
% 0.08/0.45 % (1582475)dis+10_1_sil=32000:sp=arity:random_seed=1447383930:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.45 % (1582472)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3733137658_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.45 % (1582477)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3842274502:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.45 % (1582474)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2994597951:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.45 % (1582476)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1219948418:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.45 % (1582478)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=987428507:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.45 % (1582473)% WARNING: option uhcvi not known.
% 0.08/0.45 % TRYING [1]
% 0.08/0.45 % (1582473)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2437859033:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.45 % TRYING [2]
% 0.08/0.45 % (1582475) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1582467-1582475"...
% 0.08/0.45 % TRYING [3]
% 0.08/0.45 % (1582475)...printing done.
% 0.08/0.45 % (1582475)Refutation found. Thanks to Tanya!
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.45 % (1582475)------------------------------
% 0.08/0.45 % (1582475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.45 % (1582475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.45 % (1582475)CaDiCaL version: 2.1.3
% 0.08/0.45 % (1582475)Termination reason: Refutation
% 0.08/0.45 % (1582475)Time elapsed: 0.015 s
% 0.08/0.45 % (1582475)Peak memory usage: 13 MB
% 0.08/0.45 % (1582475)Instructions burned: 39 (million)
% 0.08/0.45 % (1582467)Success in time 0.043 s
% 0.08/0.45 % Vampire exiting
%------------------------------------------------------------------------------