%------------------------------------------------------------------------------
% File : Vampire---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 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 2.49s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 111 ( 23 unt; 8 def)
% Number of atoms : 331 ( 80 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 366 ( 146 ~; 149 |; 38 &)
% ( 18 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 138 ( 1 sgn 132 !; 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] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
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] :
( m1_relset_1(X2,X0,X1)
| ~ m2_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] :
( 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(cnf_transformation,[],[f76]) ).
fof(f157,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,[],[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(f242,plain,
( ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(sK0))
| ~ 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,[],[f155,f176]) ).
fof(f244,definition,
( spl13_6
<=> v1_relat_1(k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f246,plain,
( ~ v1_relat_1(k5_relset_2(sK0,sK2))
| spl13_6 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl13_7
<=> r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f250,plain,
( ~ r1_tarski(k2_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(k2_relat_1(sK2)))
| spl13_7 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f252,definition,
( spl13_8
<=> r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f254,plain,
( ~ r1_tarski(k1_relat_1(k5_relset_2(sK0,sK2)),k1_zfmisc_1(sK0))
| spl13_8 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,plain,
( ~ spl13_6
| ~ spl13_7
| ~ spl13_8
| spl13_1 ),
inference(avatar_split_clause,[],[f242,f174,f252,f248,f244]) ).
fof(f256,plain,
( ~ v1_relat_1(sK2)
| spl13_6 ),
inference(resolution,[],[f246,f121]) ).
fof(f261,plain,
( ! [X0,X1] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| spl13_6 ),
inference(resolution,[],[f256,f108]) ).
fof(f265,plain,
( $false
| spl13_6 ),
inference(resolution,[],[f261,f104]) ).
fof(f268,plain,
spl13_6,
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f273,plain,
( ! [X0] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(sK0,X0)))
| spl13_7 ),
inference(resolution,[],[f250,f157]) ).
fof(f286,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(f287,plain,
! [X0,X1] :
( k1_zfmisc_1(X0) = k1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(forward_subsumption_resolution,[],[f286,f120]) ).
fof(f288,plain,
( $false
| spl13_7 ),
inference(resolution,[],[f273,f104]) ).
fof(f291,plain,
spl13_7,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f299,plain,
( ~ r1_tarski(k1_zfmisc_1(sK0),k1_zfmisc_1(sK0))
| ~ v1_relat_1(sK2)
| spl13_8 ),
inference(superposition,[],[f254,f287]) ).
fof(f301,plain,
( ~ v1_relat_1(sK2)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f299,f154]) ).
fof(f302,plain,
( ! [X0,X1] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| spl13_8 ),
inference(resolution,[],[f301,f108]) ).
fof(f306,plain,
( $false
| spl13_8 ),
inference(resolution,[],[f302,f104]) ).
fof(f309,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f306]) ).
fof(f323,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k4_relset_1(X0,X1,X2) = k1_relat_1(X2) ),
inference(resolution,[],[f151,f152]) ).
fof(f404,plain,
( k1_relat_1(k5_relset_2(sK0,sK2)) = k4_relset_1(k1_zfmisc_1(sK0),k1_zfmisc_1(k2_relat_1(sK2)),k5_relset_2(sK0,sK2))
| ~ spl13_1 ),
inference(resolution,[],[f323,f175]) ).
fof(f406,plain,
( k1_zfmisc_1(sK0) != k1_relat_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)))
| 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_1 ),
inference(superposition,[],[f113,f404]) ).
fof(f420,definition,
( spl13_15
<=> k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f422,plain,
( k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f424,definition,
( spl13_16
<=> k1_zfmisc_1(sK0) = k1_relat_1(k5_relset_2(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f426,plain,
( k1_zfmisc_1(sK0) != k1_relat_1(k5_relset_2(sK0,sK2))
| spl13_16 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f441,plain,
( k1_zfmisc_1(sK0) != k1_zfmisc_1(sK0)
| ~ v1_relat_1(sK2)
| spl13_16 ),
inference(superposition,[],[f426,f287]) ).
fof(f443,plain,
( ~ v1_relat_1(sK2)
| spl13_16 ),
inference(trivial_inequality_removal,[],[f441]) ).
fof(f453,plain,
( ! [X0,X1] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| spl13_16 ),
inference(resolution,[],[f443,f108]) ).
fof(f458,plain,
( $false
| spl13_16 ),
inference(resolution,[],[f453,f104]) ).
fof(f462,plain,
spl13_16,
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f479,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ spl13_15 ),
inference(superposition,[],[f128,f422]) ).
fof(f496,plain,
( $false
| ~ spl13_15 ),
inference(forward_subsumption_resolution,[],[f479,f127]) ).
fof(f497,plain,
~ spl13_15,
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f498,plain,
( k1_zfmisc_1(sK0) != k1_relat_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)))
| k1_xboole_0 = k1_zfmisc_1(k2_relat_1(sK2))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f406,f175]) ).
fof(f499,plain,
( spl13_15
| spl13_2
| ~ spl13_16
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f498,f174,f424,f178,f420]) ).
fof(f500,plain,
( ~ v1_relat_1(sK2)
| spl13_3 ),
inference(resolution,[],[f184,f120]) ).
fof(f501,plain,
( ! [X0,X1] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| spl13_3 ),
inference(resolution,[],[f500,f108]) ).
fof(f509,plain,
( $false
| spl13_3 ),
inference(resolution,[],[f501,f104]) ).
fof(f513,plain,
spl13_3,
inference(avatar_contradiction_clause,[],[f509]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s3,plain,
( spl13_1
| ~ spl13_6
| ~ spl13_7
| ~ spl13_8 ),
inference(sat_conversion,[],[f255]) ).
cnf(s4,plain,
spl13_6,
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
spl13_7,
inference(sat_conversion,[],[f291]) ).
cnf(s7,plain,
spl13_8,
inference(sat_conversion,[],[f309]) ).
cnf(s12,plain,
spl13_16,
inference(sat_conversion,[],[f462]) ).
cnf(s14,plain,
~ spl13_15,
inference(sat_conversion,[],[f497]) ).
cnf(s15,plain,
( ~ spl13_1
| spl13_2
| spl13_15
| ~ spl13_16 ),
inference(sat_conversion,[],[f499]) ).
cnf(s17,plain,
spl13_3,
inference(sat_conversion,[],[f513]) ).
cnf(s20,plain,
spl13_1,
inference(rat,[],[s3,s7,s6,s4]) ).
cnf(s21,plain,
spl13_2,
inference(rat,[],[s15,s12,s14,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s17,s21,s20]) ).
fof(f514,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:21:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.49/1.31 % (3689604)Detected formulas, will run a generic FOF schedule.
% 2.49/1.31 % (3689610)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=3060166381:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.49/1.31 % (3689612)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2721863744:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.49/1.31 % (3689615)dis-21_1_sil=8000:lcm=predicate:random_seed=3750164163:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.49/1.31 % (3689611)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=3919307195:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.49/1.31 % (3689614)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4262584889:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.49/1.31 % (3689613)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3186672689:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.49/1.31 % (3689609)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=4024088357:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.49/1.31 % (3689612)Refutation not found, incomplete strategy
% 2.49/1.31 % (3689612)------------------------------
% 2.49/1.31 % (3689612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.31 % (3689612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.31 % (3689612)CaDiCaL version: 2.1.3
% 2.49/1.31 % (3689612)Termination reason: Refutation not found, incomplete strategy
% 2.49/1.31 % (3689612)Time elapsed: 0.002 s
% 2.49/1.31 % (3689612)Peak memory usage: 88 MB
% 2.49/1.31 % (3689612)Instructions burned: 2 (million)
% 2.49/1.31 % (3689614)First to succeed.
% 2.49/1.31 % (3689614)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3689604"
% 2.49/1.31 % (3689613)Refutation not found, incomplete strategy
% 2.49/1.31 % (3689613)------------------------------
% 2.49/1.31 % (3689613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.31 % (3689613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.31 % (3689613)CaDiCaL version: 2.1.3
% 2.49/1.31 % (3689613)Termination reason: Refutation not found, incomplete strategy
% 2.49/1.31 % (3689613)Time elapsed: 0.015 s
% 2.49/1.31 % (3689613)Peak memory usage: 88 MB
% 2.49/1.31 % (3689613)Instructions burned: 21 (million)
% 2.49/1.31 % (3689615)Instruction limit reached!
% 2.49/1.31 % (3689615)------------------------------
% 2.49/1.31 % (3689615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.31 % (3689615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.31 % (3689615)CaDiCaL version: 2.1.3
% 2.49/1.31 % (3689615)Termination reason: Instruction limit
% 2.49/1.31 % (3689615)Termination phase: Saturation
% 2.49/1.31 % (3689615)Time elapsed: 0.082 s
% 2.49/1.31 % (3689615)Peak memory usage: 90 MB
% 2.49/1.31 % (3689615)Instructions burned: 130 (million)
% 2.49/1.31 % (3689612)------------------------------
% 2.49/1.31 % (3689612)------------------------------
% 2.49/1.31 % (3689613)------------------------------
% 2.49/1.31 % (3689613)------------------------------
% 2.49/1.31 % (3689623)lrs+10_1_sil=8000:sp=occurrence:random_seed=2737763955:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.49/1.31 % (3689614)Refutation found. Thanks to Tanya!
% 2.49/1.31 % SZS status Theorem for theBenchmark
% 2.49/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.51 % (3689614)------------------------------
% 0.17/1.51 % (3689614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (3689614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (3689614)CaDiCaL version: 2.1.3
% 0.17/1.51 % (3689614)Termination reason: Refutation
% 0.17/1.51 % (3689614)Time elapsed: 0.014 s
% 0.17/1.51 % (3689614)Peak memory usage: 90 MB
% 0.17/1.51 % (3689614)Instructions burned: 17 (million)
% 0.17/1.51 % (3689614)------------------------------
% 0.17/1.51 % (3689614)------------------------------
% 0.17/1.51 % (3689604)Success in time 0.441 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------