%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU425+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:48:56 PM UTC 2026
% Result : Theorem 1.41s 1.47s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 10 unt; 4 def)
% Number of atoms : 279 ( 36 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 341 ( 145 ~; 143 |; 33 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 97 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1120,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(f1131,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( r1_tarski(k2_relat_1(X1),X0)
=> m2_relset_1(X1,k1_relat_1(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
fof(f1133,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( r1_tarski(k1_relat_1(X2),X0)
& r1_tarski(k2_relat_1(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f1567,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ( r1_tarski(k2_relat_1(X1),X0)
=> ( v1_funct_1(X1)
& v1_funct_2(X1,k1_relat_1(X1),X0)
& m2_relset_1(X1,k1_relat_1(X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
fof(f4461,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(f4489,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(f4491,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(f4492,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(f4493,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)],[f4492]) ).
fof(f4496,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,[],[f4493]) ).
fof(f4501,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f1120]) ).
fof(f4552,plain,
! [X0,X1] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k1_relat_1(X1),X0)
& m2_relset_1(X1,k1_relat_1(X1),X0) )
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f1567]) ).
fof(f4553,plain,
! [X0,X1] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k1_relat_1(X1),X0)
& m2_relset_1(X1,k1_relat_1(X1),X0) )
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f4552]) ).
fof(f4566,plain,
! [X0,X1,X2] :
( ( r1_tarski(k1_relat_1(X2),X0)
& r1_tarski(k2_relat_1(X2),X1) )
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f1133]) ).
fof(f4569,plain,
! [X0,X1] :
( m2_relset_1(X1,k1_relat_1(X1),X0)
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f1131]) ).
fof(f4570,plain,
! [X0,X1] :
( m2_relset_1(X1,k1_relat_1(X1),X0)
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f4569]) ).
fof(f4614,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,[],[f4491]) ).
fof(f4617,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,[],[f4489]) ).
fof(f4618,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,[],[f4617]) ).
fof(f4619,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,[],[f4461]) ).
fof(f4620,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)],[f4496]) ).
fof(f4654,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,[],[f4618]) ).
fof(f4655,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,[],[f4654]) ).
fof(f4656,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,[],[f4655]) ).
fof(f4657,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = k5_relset_2(X0,X1)
| k1_zfmisc_1(X0) != k1_relat_1(X2)
| ( k1_funct_1(X2,sK26(X0,X1,X2)) != k9_relat_1(X1,sK26(X0,X1,X2))
& r1_tarski(sK26(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,[sK26]),skolemize(X3,sK26(X0,X1,X2))],[f4656]) ).
fof(f4658,plain,
m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f4620]) ).
fof(f4659,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,[],[f4620]) ).
fof(f4668,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f4501]) ).
fof(f4743,plain,
! [X0,X1] :
( v1_funct_2(X1,k1_relat_1(X1),X0)
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f4553]) ).
fof(f4758,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| r1_tarski(k2_relat_1(X2),X1) ),
inference(cnf_transformation,[],[f4566]) ).
fof(f4761,plain,
! [X0,X1] :
( m2_relset_1(X1,k1_relat_1(X1),X0)
| ~ r1_tarski(k2_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f4570]) ).
fof(f4816,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f4614]) ).
fof(f4819,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,[],[f4657]) ).
fof(f4822,plain,
! [X0,X1] :
( v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f4619]) ).
fof(f4823,plain,
! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f4619]) ).
fof(f4878,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,[],[f4819]) ).
fof(f4923,definition,
( spl70_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,[spl70_1])],[avatar_definition]) ).
fof(f4924,plain,
( m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl70_1 ),
inference(avatar_component_clause,[],[f4923]) ).
fof(f4925,plain,
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| spl70_1 ),
inference(avatar_component_clause,[],[f4923]) ).
fof(f4927,definition,
( spl70_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,[spl70_2])],[avatar_definition]) ).
fof(f4929,plain,
( ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)))
| spl70_2 ),
inference(avatar_component_clause,[],[f4927]) ).
fof(f4931,definition,
( spl70_3
<=> v1_funct_1(k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl70_3])],[avatar_definition]) ).
fof(f4932,plain,
( v1_funct_1(k5_relset_2(sK0,sK2))
| ~ spl70_3 ),
inference(avatar_component_clause,[],[f4931]) ).
fof(f4933,plain,
( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| spl70_3 ),
inference(avatar_component_clause,[],[f4931]) ).
fof(f4934,plain,
( ~ spl70_1
| ~ spl70_2
| ~ spl70_3 ),
inference(avatar_split_clause,[],[f4659,f4931,f4927,f4923]) ).
fof(f4935,plain,
v1_relat_1(sK2),
inference(resolution,[],[f4658,f4668]) ).
fof(f4970,plain,
( ! [X0] :
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(k5_relset_2(sK0,X0))
| ~ v1_funct_1(k5_relset_2(sK0,X0))
| ~ v1_relat_1(X0) )
| spl70_1 ),
inference(superposition,[],[f4925,f4878]) ).
fof(f4975,plain,
( ! [X0] :
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_1(k5_relset_2(sK0,X0))
| ~ v1_relat_1(X0) )
| spl70_1 ),
inference(forward_subsumption_resolution,[],[f4970,f4823]) ).
fof(f4977,definition,
( spl70_9
<=> v1_relat_1(k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl70_9])],[avatar_definition]) ).
fof(f4978,plain,
( v1_relat_1(k5_relset_2(sK0,sK2))
| ~ spl70_9 ),
inference(avatar_component_clause,[],[f4977]) ).
fof(f4979,plain,
( ~ v1_relat_1(k5_relset_2(sK0,sK2))
| spl70_9 ),
inference(avatar_component_clause,[],[f4977]) ).
fof(f4995,plain,
( ! [X0] :
( ~ m2_relset_1(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(X0) )
| spl70_1 ),
inference(forward_subsumption_resolution,[],[f4975,f4822]) ).
fof(f4996,plain,
( ~ v1_relat_1(sK2)
| spl70_3 ),
inference(resolution,[],[f4933,f4822]) ).
fof(f4997,plain,
( $false
| spl70_3 ),
inference(forward_subsumption_resolution,[],[f4996,f4935]) ).
fof(f4998,plain,
spl70_3,
inference(avatar_contradiction_clause,[],[f4997]) ).
fof(f5013,plain,
( ~ v1_relat_1(sK2)
| spl70_9 ),
inference(resolution,[],[f4979,f4823]) ).
fof(f5014,plain,
( $false
| spl70_9 ),
inference(forward_subsumption_resolution,[],[f5013,f4935]) ).
fof(f5015,plain,
spl70_9,
inference(avatar_contradiction_clause,[],[f5014]) ).
fof(f5131,plain,
( ~ v1_relat_1(sK2)
| ~ 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))
| spl70_1 ),
inference(resolution,[],[f4995,f4761]) ).
fof(f5143,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))
| spl70_1 ),
inference(forward_subsumption_resolution,[],[f5131,f4935]) ).
fof(f5154,plain,
( ~ r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2)))
| spl70_1
| ~ spl70_9 ),
inference(forward_subsumption_resolution,[],[f5143,f4978]) ).
fof(f5249,plain,
( ! [X0] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,X0)))
| spl70_1
| ~ spl70_9 ),
inference(resolution,[],[f5154,f4816]) ).
fof(f5263,plain,
( $false
| spl70_1
| ~ spl70_9 ),
inference(resolution,[],[f5249,f4658]) ).
fof(f5269,plain,
( spl70_1
| ~ spl70_9 ),
inference(avatar_contradiction_clause,[],[f5263]) ).
fof(f5272,plain,
( r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ spl70_1 ),
inference(resolution,[],[f4924,f4758]) ).
fof(f5294,plain,
( ! [X0] :
( ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(k5_relset_2(sK0,X0))
| ~ v1_funct_1(k5_relset_2(sK0,X0))
| ~ v1_relat_1(X0) )
| spl70_2 ),
inference(superposition,[],[f4929,f4878]) ).
fof(f5298,plain,
( ! [X0] :
( ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_funct_1(k5_relset_2(sK0,X0))
| ~ v1_relat_1(X0) )
| spl70_2 ),
inference(forward_subsumption_resolution,[],[f5294,f4823]) ).
fof(f5300,plain,
( ! [X0] :
( ~ v1_funct_2(k5_relset_2(sK0,sK2),k1_relat_1(k5_relset_2(sK0,X0)),k1_zfmisc_1(k2_relat_1(sK2)))
| ~ v1_relat_1(X0) )
| spl70_2 ),
inference(forward_subsumption_resolution,[],[f5298,f4822]) ).
fof(f5469,plain,
( ~ v1_relat_1(sK2)
| ~ 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))
| ~ v1_funct_1(k5_relset_2(sK0,sK2))
| spl70_2 ),
inference(resolution,[],[f5300,f4743]) ).
fof(f5475,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))
| ~ v1_funct_1(k5_relset_2(sK0,sK2))
| spl70_2 ),
inference(forward_subsumption_resolution,[],[f5469,f4935]) ).
fof(f5476,plain,
( ~ v1_relat_1(k5_relset_2(sK0,sK2))
| ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ spl70_1
| spl70_2 ),
inference(forward_subsumption_resolution,[],[f5475,f5272]) ).
fof(f5477,plain,
( ~ v1_funct_1(k5_relset_2(sK0,sK2))
| ~ spl70_1
| spl70_2
| ~ spl70_9 ),
inference(forward_subsumption_resolution,[],[f5476,f4978]) ).
fof(f5478,plain,
( $false
| ~ spl70_1
| spl70_2
| ~ spl70_3
| ~ spl70_9 ),
inference(forward_subsumption_resolution,[],[f5477,f4932]) ).
fof(f5479,plain,
( ~ spl70_1
| spl70_2
| ~ spl70_3
| ~ spl70_9 ),
inference(avatar_contradiction_clause,[],[f5478]) ).
cnf(s1,plain,
( ~ spl70_1
| ~ spl70_2
| ~ spl70_3 ),
inference(sat_conversion,[],[f4934]) ).
cnf(s7,plain,
spl70_3,
inference(sat_conversion,[],[f4998]) ).
cnf(s9,plain,
spl70_9,
inference(sat_conversion,[],[f5015]) ).
cnf(s26,plain,
( spl70_1
| ~ spl70_9 ),
inference(sat_conversion,[],[f5269]) ).
cnf(s29,plain,
( ~ spl70_1
| spl70_2
| ~ spl70_3
| ~ spl70_9 ),
inference(sat_conversion,[],[f5479]) ).
cnf(s30,plain,
spl70_1,
inference(rat,[],[s26,s9]) ).
cnf(s31,plain,
spl70_2,
inference(rat,[],[s29,s9,s30,s7]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s7,s31,s30]) ).
fof(f5480,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU425+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 05:21:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.41/1.47 % (3690275)Detected formulas, will run a generic FOF schedule.
% 1.41/1.47 % (3690285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3585968836:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 1.41/1.47 % (3690280)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3640570875:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 1.41/1.47 % (3690282)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1049417639:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 1.41/1.47 % (3690281)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=569599458:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 1.41/1.47 % (3690283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1271164576:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 1.41/1.47 % (3690285)Instruction limit reached!
% 1.41/1.47 % (3690285)------------------------------
% 1.41/1.47 % (3690285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.41/1.47 % (3690285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/1.47 % (3690285)CaDiCaL version: 2.1.3
% 1.41/1.47 % (3690285)Termination reason: Instruction limit
% 1.41/1.47 % (3690285)Termination phase: Preprocessing 3
% 1.41/1.47 % (3690285)Time elapsed: 0.052 s
% 1.41/1.47 % (3690285)Peak memory usage: 95 MB
% 1.41/1.47 % (3690285)Instructions burned: 141 (million)
% 1.41/1.47 % (3690284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3710635472:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 1.41/1.47 % (3690286)dis-21_1_sil=8000:lcm=predicate:random_seed=1103662899:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 1.41/1.47 % (3690283)First to succeed.
% 1.41/1.47 % (3690283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3690275"
% 1.41/1.47 % (3690284)Instruction limit reached!
% 1.41/1.47 % (3690284)------------------------------
% 1.41/1.47 % (3690284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.41/1.47 % (3690284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/1.47 % (3690284)CaDiCaL version: 2.1.3
% 1.41/1.47 % (3690284)Termination reason: Instruction limit
% 1.41/1.47 % (3690284)Termination phase: Saturation
% 1.41/1.47 % (3690284)Time elapsed: 0.080 s
% 1.41/1.47 % (3690284)Peak memory usage: 94 MB
% 1.41/1.47 % (3690284)Instructions burned: 119 (million)
% 1.41/1.47 % (3690286)Instruction limit reached!
% 1.41/1.47 % (3690286)------------------------------
% 1.41/1.47 % (3690286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.41/1.47 % (3690286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/1.47 % (3690286)CaDiCaL version: 2.1.3
% 1.41/1.47 % (3690286)Termination reason: Instruction limit
% 1.41/1.47 % (3690286)Termination phase: Clausification
% 1.41/1.47 % (3690286)Time elapsed: 0.092 s
% 1.41/1.47 % (3690286)Peak memory usage: 95 MB
% 1.41/1.47 % (3690286)Instructions burned: 129 (million)
% 1.41/1.47 % (3690294)lrs+10_1_sil=8000:sp=occurrence:random_seed=3529448996:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 1.41/1.47 % (3690294)Instruction limit reached!
% 1.41/1.47 % (3690294)------------------------------
% 1.41/1.47 % (3690294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.41/1.47 % (3690294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/1.47 % (3690294)CaDiCaL version: 2.1.3
% 1.41/1.47 % (3690294)Termination reason: Instruction limit
% 1.41/1.47 % (3690294)Termination phase: Saturation
% 1.41/1.47 % (3690294)Time elapsed: 0.106 s
% 1.41/1.47 % (3690294)Peak memory usage: 97 MB
% 1.41/1.47 % (3690294)Instructions burned: 285 (million)
% 1.41/1.47 % (3690295)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3384393262:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 1.41/1.47 % (3690296)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1372089849:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 1.41/1.47 % (3690283)Refutation found. Thanks to Tanya!
% 1.41/1.47 % SZS status Theorem for theBenchmark
% 1.41/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.67 % (3690283)------------------------------
% 4.01/1.67 % (3690283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.67 % (3690283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.67 % (3690283)CaDiCaL version: 2.1.3
% 4.01/1.67 % (3690283)Termination reason: Refutation
% 4.01/1.67 % (3690283)Time elapsed: 0.038 s
% 4.01/1.67 % (3690283)Peak memory usage: 95 MB
% 4.01/1.67 % (3690283)Instructions burned: 50 (million)
% 4.01/1.67 % (3690283)------------------------------
% 4.01/1.67 % (3690283)------------------------------
% 4.01/1.67 % (3690275)Success in time 0.629 s
% 4.01/1.67 % Vampire exiting
%------------------------------------------------------------------------------