%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU011+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:47:03 PM UTC 2026
% Result : Theorem 6.69s 1.93s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 24
% Syntax : Number of formulae : 181 ( 42 unt; 15 def)
% Number of atoms : 769 ( 149 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1095 ( 507 ~; 507 |; 54 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 152 ( 0 sgn 142 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f15,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).
fof(f37,conjecture,
! [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) = identity_relation(set_intersection2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) = identity_relation(set_intersection2(X0,X1)),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f44,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f57]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f75,plain,
! [X0,X1] :
( relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f74]) ).
fof(f77,plain,
? [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) != identity_relation(set_intersection2(X0,X1)),
inference(ennf_transformation,[],[f38]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f88]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK10(X0,X1) != apply(X1,sK10(X0,X1))
& in(sK10(X0,X1),X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f101]) ).
fof(f103,plain,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK11,sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f77]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ( apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
& in(sK13(X0,X1),relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f85]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f115,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f122,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f127,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f155,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f161,plain,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK11,sK12)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
! [X0,X1] :
( relation_dom(X0) != relation_dom(X1)
| X0 = X1
| in(sK13(X0,X1),relation_dom(X0))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f168,plain,
! [X0,X1] :
( apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f170,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f171,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f174,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f156]) ).
fof(f175,plain,
! [X3,X0] :
( ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f155]) ).
fof(f176,definition,
sF14 = identity_relation(sK12),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f177,plain,
identity_relation(sK12) = sF14,
inference(reorient_equations,[],[f176]) ).
fof(f178,definition,
sF15 = identity_relation(sK11),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f179,plain,
identity_relation(sK11) = sF15,
inference(reorient_equations,[],[f178]) ).
fof(f180,definition,
sF16 = relation_composition(sF14,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f181,plain,
relation_composition(sF14,sF15) = sF16,
inference(reorient_equations,[],[f180]) ).
fof(f182,definition,
sF17 = set_intersection2(sK11,sK12),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f183,plain,
set_intersection2(sK11,sK12) = sF17,
inference(reorient_equations,[],[f182]) ).
fof(f184,definition,
sF18 = identity_relation(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f185,plain,
identity_relation(sF17) = sF18,
inference(reorient_equations,[],[f184]) ).
fof(f186,plain,
sF16 != sF18,
inference(definition_folding,[],[f161,f185,f183,f181,f179,f177]) ).
fof(f187,plain,
! [X0] :
( ~ relation(sF15)
| ~ in(X0,sK11)
| apply(sF15,X0) = X0
| ~ function(sF15) ),
inference(superposition,[],[f175,f179]) ).
fof(f188,plain,
! [X0] :
( ~ relation(sF14)
| ~ in(X0,sK12)
| apply(sF14,X0) = X0
| ~ function(sF14) ),
inference(superposition,[],[f175,f177]) ).
fof(f190,definition,
( spl19_1
<=> function(sF14) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f191,plain,
( function(sF14)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( ~ function(sF14)
| spl19_1 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f194,definition,
( spl19_2
<=> ! [X0] :
( ~ in(X0,sK12)
| apply(sF14,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f195,plain,
( ! [X0] :
( ~ in(X0,sK12)
| apply(sF14,X0) = X0 )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,definition,
( spl19_3
<=> relation(sF14) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f198,plain,
( relation(sF14)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( ~ spl19_1
| spl19_2
| ~ spl19_3 ),
inference(avatar_split_clause,[],[f188,f197,f194,f190]) ).
fof(f202,definition,
( spl19_4
<=> function(sF15) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f203,plain,
( function(sF15)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( ~ function(sF15)
| spl19_4 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f206,definition,
( spl19_5
<=> ! [X0] :
( ~ in(X0,sK11)
| apply(sF15,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f207,plain,
( ! [X0] :
( ~ in(X0,sK11)
| apply(sF15,X0) = X0 )
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f209,definition,
( spl19_6
<=> relation(sF15) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f210,plain,
( relation(sF15)
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( ~ relation(sF15)
| spl19_6 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( ~ spl19_4
| spl19_5
| ~ spl19_6 ),
inference(avatar_split_clause,[],[f187,f209,f206,f202]) ).
fof(f213,plain,
! [X0] :
( ~ relation(sF18)
| ~ in(X0,sF17)
| apply(sF18,X0) = X0
| ~ function(sF18) ),
inference(superposition,[],[f175,f185]) ).
fof(f215,definition,
( spl19_7
<=> function(sF18) ),
introduced(definition,[new_symbols(definition,[spl19_7])],[avatar_definition]) ).
fof(f216,plain,
( function(sF18)
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f217,plain,
( ~ function(sF18)
| spl19_7 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f219,definition,
( spl19_8
<=> ! [X0] :
( ~ in(X0,sF17)
| apply(sF18,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl19_8])],[avatar_definition]) ).
fof(f220,plain,
( ! [X0] :
( ~ in(X0,sF17)
| apply(sF18,X0) = X0 )
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,definition,
( spl19_9
<=> relation(sF18) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
fof(f223,plain,
( relation(sF18)
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,plain,
( ~ spl19_7
| spl19_8
| ~ spl19_9 ),
inference(avatar_split_clause,[],[f213,f222,f219,f215]) ).
fof(f227,plain,
relation(sF15),
inference(superposition,[],[f128,f179]) ).
fof(f228,plain,
relation(sF14),
inference(superposition,[],[f128,f177]) ).
fof(f229,plain,
relation(sF18),
inference(superposition,[],[f128,f185]) ).
fof(f230,plain,
spl19_9,
inference(avatar_split_clause,[],[f229,f222]) ).
fof(f231,plain,
spl19_3,
inference(avatar_split_clause,[],[f228,f197]) ).
fof(f232,plain,
( $false
| spl19_6 ),
inference(forward_subsumption_resolution,[],[f227,f211]) ).
fof(f233,plain,
spl19_6,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f235,plain,
! [X0] :
( ~ in(X0,sF17)
| in(X0,sK11) ),
inference(superposition,[],[f170,f183]) ).
fof(f236,plain,
! [X0] :
( ~ in(X0,sF17)
| in(X0,sK12) ),
inference(superposition,[],[f171,f183]) ).
fof(f237,plain,
function(sF15),
inference(superposition,[],[f127,f179]) ).
fof(f238,plain,
function(sF14),
inference(superposition,[],[f127,f177]) ).
fof(f239,plain,
function(sF18),
inference(superposition,[],[f127,f185]) ).
fof(f240,plain,
( $false
| spl19_7 ),
inference(forward_subsumption_resolution,[],[f239,f217]) ).
fof(f241,plain,
spl19_7,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f242,plain,
( $false
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f238,f192]) ).
fof(f243,plain,
spl19_1,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f244,plain,
( $false
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f237,f204]) ).
fof(f245,plain,
spl19_4,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f247,plain,
( ~ relation(sF15)
| sK11 = relation_dom(sF15)
| ~ function(sF15) ),
inference(superposition,[],[f174,f179]) ).
fof(f249,plain,
( ~ relation(sF18)
| sF17 = relation_dom(sF18)
| ~ function(sF18) ),
inference(superposition,[],[f174,f185]) ).
fof(f250,plain,
( sF17 = relation_dom(sF18)
| ~ function(sF18)
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f249,f223]) ).
fof(f252,plain,
( sK11 = relation_dom(sF15)
| ~ function(sF15)
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f247,f210]) ).
fof(f254,plain,
( sF17 = relation_dom(sF18)
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f250,f216]) ).
fof(f256,plain,
( sK11 = relation_dom(sF15)
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f252,f203]) ).
fof(f267,plain,
( ! [X0] :
( relation_dom(relation_composition(identity_relation(X0),sF15)) = set_intersection2(relation_dom(sF15),X0)
| ~ function(sF15) )
| ~ spl19_6 ),
inference(resolution,[],[f210,f159]) ).
fof(f268,plain,
( ! [X0] : relation_dom(relation_composition(identity_relation(X0),sF15)) = set_intersection2(relation_dom(sF15),X0)
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f267,f203]) ).
fof(f269,plain,
( ! [X0] : relation_dom(relation_composition(identity_relation(X0),sF15)) = set_intersection2(sK11,X0)
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_demodulation,[],[f268,f256]) ).
fof(f276,plain,
! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0)
| ~ relation(sF14)
| ~ function(sF14)
| ~ relation(sF15)
| ~ function(sF15) ),
inference(superposition,[],[f152,f181]) ).
fof(f277,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0)
| ~ function(sF14)
| ~ relation(sF15)
| ~ function(sF15) )
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f276,f198]) ).
fof(f278,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0)
| ~ relation(sF15)
| ~ function(sF15) )
| ~ spl19_1
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f277,f191]) ).
fof(f279,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0)
| ~ function(sF15) )
| ~ spl19_1
| ~ spl19_3
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f278,f210]) ).
fof(f280,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sF16))
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0) )
| ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f279,f203]) ).
fof(f291,plain,
( set_intersection2(sK11,sK12) = relation_dom(relation_composition(sF14,sF15))
| ~ spl19_4
| ~ spl19_6 ),
inference(superposition,[],[f269,f177]) ).
fof(f295,plain,
( set_intersection2(sK11,sK12) = relation_dom(sF16)
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_demodulation,[],[f291,f181]) ).
fof(f298,plain,
( sF17 = relation_dom(sF16)
| ~ spl19_4
| ~ spl19_6 ),
inference(forward_demodulation,[],[f295,f183]) ).
fof(f301,plain,
( ! [X0] :
( ~ in(X0,sF17)
| apply(sF15,apply(sF14,X0)) = apply(sF16,X0) )
| ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6 ),
inference(superposition,[],[f280,f298]) ).
fof(f336,plain,
( relation(sF16)
| ~ relation(sF14)
| ~ relation(sF15) ),
inference(superposition,[],[f115,f181]) ).
fof(f337,plain,
( relation(sF16)
| ~ relation(sF15)
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f336,f198]) ).
fof(f338,plain,
( relation(sF16)
| ~ spl19_3
| ~ spl19_6 ),
inference(forward_subsumption_resolution,[],[f337,f210]) ).
fof(f342,definition,
( spl19_10
<=> function(sF16) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f343,plain,
( function(sF16)
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f344,plain,
( ~ function(sF16)
| spl19_10 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f357,plain,
( ! [X0] :
( relation_dom(X0) != sF17
| sF18 = X0
| in(sK13(sF18,X0),sF17)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sF18)
| ~ function(sF18) )
| ~ spl19_7
| ~ spl19_9 ),
inference(superposition,[],[f167,f254]) ).
fof(f373,plain,
( ! [X0] :
( relation_dom(X0) != sF17
| sF18 = X0
| in(sK13(sF18,X0),sF17)
| ~ relation(X0)
| ~ function(X0)
| ~ function(sF18) )
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f357,f223]) ).
fof(f381,plain,
( ! [X0] :
( relation_dom(X0) != sF17
| sF18 = X0
| in(sK13(sF18,X0),sF17)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f373,f216]) ).
fof(f433,plain,
( sF17 != sF17
| sF16 = sF18
| in(sK13(sF18,sF16),sF17)
| ~ relation(sF16)
| ~ function(sF16)
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9 ),
inference(superposition,[],[f381,f298]) ).
fof(f434,plain,
( sF16 = sF18
| in(sK13(sF18,sF16),sF17)
| ~ relation(sF16)
| ~ function(sF16)
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9 ),
inference(trivial_inequality_removal,[],[f433]) ).
fof(f479,plain,
( function(sF16)
| ~ relation(sF14)
| ~ function(sF14)
| ~ relation(sF15)
| ~ function(sF15) ),
inference(superposition,[],[f122,f181]) ).
fof(f480,plain,
( ~ relation(sF14)
| ~ function(sF14)
| ~ relation(sF15)
| ~ function(sF15)
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f479,f344]) ).
fof(f481,plain,
( ~ function(sF14)
| ~ relation(sF15)
| ~ function(sF15)
| ~ spl19_3
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f480,f198]) ).
fof(f482,plain,
( ~ relation(sF15)
| ~ function(sF15)
| ~ spl19_1
| ~ spl19_3
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f481,f191]) ).
fof(f483,plain,
( ~ function(sF15)
| ~ spl19_1
| ~ spl19_3
| ~ spl19_6
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f482,f210]) ).
fof(f484,plain,
( $false
| ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f483,f203]) ).
fof(f485,plain,
( ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| spl19_10 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f489,plain,
( in(sK13(sF18,sF16),sF17)
| ~ relation(sF16)
| ~ function(sF16)
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f434,f186]) ).
fof(f493,plain,
( in(sK13(sF18,sF16),sF17)
| ~ function(sF16)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f489,f338]) ).
fof(f495,plain,
( in(sK13(sF18,sF16),sF17)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f493,f343]) ).
fof(f504,plain,
( apply(sF15,apply(sF14,sK13(sF18,sF16))) = apply(sF16,sK13(sF18,sF16))
| ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f495,f301]) ).
fof(f505,plain,
( sK13(sF18,sF16) = apply(sF18,sK13(sF18,sF16))
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f495,f220]) ).
fof(f506,plain,
( in(sK13(sF18,sF16),sK12)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f495,f236]) ).
fof(f507,plain,
( in(sK13(sF18,sF16),sK11)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f495,f235]) ).
fof(f511,plain,
( sK13(sF18,sF16) = apply(sF14,sK13(sF18,sF16))
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f506,f195]) ).
fof(f518,plain,
( sK13(sF18,sF16) = apply(sF15,sK13(sF18,sF16))
| ~ spl19_3
| ~ spl19_4
| ~ spl19_5
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(resolution,[],[f507,f207]) ).
fof(f524,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| sF16 = sF18
| ~ relation(sF16)
| ~ function(sF16)
| ~ relation(sF18)
| ~ function(sF18)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(superposition,[],[f168,f505]) ).
fof(f525,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| ~ relation(sF16)
| ~ function(sF16)
| ~ relation(sF18)
| ~ function(sF18)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f524,f186]) ).
fof(f526,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| ~ function(sF16)
| ~ relation(sF18)
| ~ function(sF18)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f525,f338]) ).
fof(f527,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| ~ relation(sF18)
| ~ function(sF18)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f526,f343]) ).
fof(f528,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| ~ function(sF18)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f527,f223]) ).
fof(f529,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| relation_dom(sF18) != relation_dom(sF16)
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f528,f216]) ).
fof(f530,plain,
( sF17 != relation_dom(sF18)
| sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_demodulation,[],[f529,f298]) ).
fof(f531,plain,
( sK13(sF18,sF16) != apply(sF16,sK13(sF18,sF16))
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f530,f254]) ).
fof(f540,plain,
( apply(sF15,sK13(sF18,sF16)) = apply(sF16,sK13(sF18,sF16))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(superposition,[],[f504,f511]) ).
fof(f541,plain,
( sK13(sF18,sF16) = apply(sF16,sK13(sF18,sF16))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_5
| ~ spl19_6
| ~ spl19_7
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_demodulation,[],[f540,f518]) ).
fof(f542,plain,
( $false
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_5
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(forward_subsumption_resolution,[],[f541,f531]) ).
fof(f543,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_5
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(avatar_contradiction_clause,[],[f542]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2
| ~ spl19_3 ),
inference(sat_conversion,[],[f200]) ).
cnf(s2,plain,
( ~ spl19_4
| spl19_5
| ~ spl19_6 ),
inference(sat_conversion,[],[f212]) ).
cnf(s3,plain,
( ~ spl19_7
| spl19_8
| ~ spl19_9 ),
inference(sat_conversion,[],[f225]) ).
cnf(s4,plain,
spl19_9,
inference(sat_conversion,[],[f230]) ).
cnf(s5,plain,
spl19_3,
inference(sat_conversion,[],[f231]) ).
cnf(s6,plain,
spl19_6,
inference(sat_conversion,[],[f233]) ).
cnf(s7,plain,
spl19_7,
inference(sat_conversion,[],[f241]) ).
cnf(s8,plain,
spl19_1,
inference(sat_conversion,[],[f243]) ).
cnf(s9,plain,
spl19_4,
inference(sat_conversion,[],[f245]) ).
cnf(s14,plain,
( ~ spl19_1
| ~ spl19_3
| ~ spl19_4
| ~ spl19_6
| spl19_10 ),
inference(sat_conversion,[],[f485]) ).
cnf(s15,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| ~ spl19_5
| ~ spl19_6
| ~ spl19_7
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10 ),
inference(sat_conversion,[],[f543]) ).
cnf(s16,plain,
spl19_10,
inference(rat,[],[s14,s6,s8,s9,s5]) ).
cnf(s18,plain,
spl19_8,
inference(rat,[],[s3,s4,s7]) ).
cnf(s19,plain,
spl19_5,
inference(rat,[],[s2,s6,s9]) ).
cnf(s20,plain,
~ spl19_2,
inference(rat,[],[s15,s16,s4,s18,s7,s6,s5,s9,s8,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s5,s20,s8]) ).
fof(f544,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU011+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:22:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.69/1.93 % (3995202)Detected formulas, will run a generic FOF schedule.
% 6.69/1.93 % (3995274)dis-21_1_sil=8000:lcm=predicate:random_seed=1763426020: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)
% 6.69/1.93 % (3995268)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=3367144261:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.69/1.93 % (3995271)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2792338931:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.69/1.93 % (3995269)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=674449771:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.69/1.93 % (3995270)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=789520548:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.69/1.93 % (3995274)Instruction limit reached!
% 6.69/1.93 % (3995274)------------------------------
% 6.69/1.93 % (3995274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995274)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995274)Termination reason: Instruction limit
% 6.69/1.93 % (3995274)Termination phase: Saturation
% 6.69/1.93 % (3995274)Time elapsed: 0.042 s
% 6.69/1.93 % (3995274)Peak memory usage: 90 MB
% 6.69/1.93 % (3995274)Instructions burned: 130 (million)
% 6.69/1.93 % (3995271)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995271)------------------------------
% 6.69/1.93 % (3995271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995271)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995271)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995271)Time elapsed: 0.002 s
% 6.69/1.93 % (3995271)Peak memory usage: 88 MB
% 6.69/1.93 % (3995271)Instructions burned: 1 (million)
% 6.69/1.93 % (3995272)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4166338881:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.69/1.93 % (3995273)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=288568819:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.69/1.93 % (3995272)Instruction limit reached!
% 6.69/1.93 % (3995272)------------------------------
% 6.69/1.93 % (3995272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995272)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995272)Termination reason: Instruction limit
% 6.69/1.93 % (3995272)Termination phase: Saturation
% 6.69/1.93 % (3995272)Time elapsed: 0.066 s
% 6.69/1.93 % (3995272)Peak memory usage: 88 MB
% 6.69/1.93 % (3995272)Instructions burned: 121 (million)
% 6.69/1.93 % (3995280)lrs+10_1_sil=8000:sp=occurrence:random_seed=585894169:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.69/1.93 % (3995273)Instruction limit reached!
% 6.69/1.93 % (3995273)------------------------------
% 6.69/1.93 % (3995273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995273)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995273)Termination reason: Instruction limit
% 6.69/1.93 % (3995273)Termination phase: Saturation
% 6.69/1.93 % (3995273)Time elapsed: 0.096 s
% 6.69/1.93 % (3995273)Peak memory usage: 89 MB
% 6.69/1.93 % (3995273)Instructions burned: 139 (million)
% 6.69/1.93 % (3995280)Instruction limit reached!
% 6.69/1.93 % (3995280)------------------------------
% 6.69/1.93 % (3995280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995280)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995280)Termination reason: Instruction limit
% 6.69/1.93 % (3995280)Termination phase: Saturation
% 6.69/1.93 % (3995280)Time elapsed: 0.088 s
% 6.69/1.93 % (3995280)Peak memory usage: 91 MB
% 6.69/1.93 % (3995280)Instructions burned: 289 (million)
% 6.69/1.93 % (3995283)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3883392258:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.69/1.93 % (3995285)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1889163475:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.69/1.93 % (3995271)------------------------------
% 6.69/1.93 % (3995271)------------------------------
% 6.69/1.93 % (3995286)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=472036941:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.69/1.93 % (3995283)Instruction limit reached!
% 6.69/1.93 % (3995283)------------------------------
% 6.69/1.93 % (3995283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995283)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995283)Termination reason: Instruction limit
% 6.69/1.93 % (3995283)Termination phase: Saturation
% 6.69/1.93 % (3995283)Time elapsed: 0.079 s
% 6.69/1.93 % (3995283)Peak memory usage: 90 MB
% 6.69/1.93 % (3995283)Instructions burned: 157 (million)
% 6.69/1.93 % (3995286)Instruction limit reached!
% 6.69/1.93 % (3995286)------------------------------
% 6.69/1.93 % (3995286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995286)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995286)Termination reason: Instruction limit
% 6.69/1.93 % (3995286)Termination phase: Saturation
% 6.69/1.93 % (3995286)Time elapsed: 0.067 s
% 6.69/1.93 % (3995286)Peak memory usage: 93 MB
% 6.69/1.93 % (3995286)Instructions burned: 250 (million)
% 6.69/1.93 % (3995289)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1691868694:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.69/1.93 % (3995289)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995289)------------------------------
% 6.69/1.93 % (3995289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995289)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995289)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995289)Time elapsed: 0.002 s
% 6.69/1.93 % (3995289)Peak memory usage: 88 MB
% 6.69/1.93 % (3995289)Instructions burned: 2 (million)
% 6.69/1.93 % (3995291)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3912489965:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.69/1.93 % (3995285)Instruction limit reached!
% 6.69/1.93 % (3995285)------------------------------
% 6.69/1.93 % (3995285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995285)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995285)Termination reason: Instruction limit
% 6.69/1.93 % (3995285)Termination phase: Saturation
% 6.69/1.93 % (3995285)Time elapsed: 0.205 s
% 6.69/1.93 % (3995285)Peak memory usage: 90 MB
% 6.69/1.93 % (3995285)Instructions burned: 326 (million)
% 6.69/1.93 % (3995292)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3435380931:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.69/1.93 % (3995292)Instruction limit reached!
% 6.69/1.93 % (3995292)------------------------------
% 6.69/1.93 % (3995292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995292)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995292)Termination reason: Instruction limit
% 6.69/1.93 % (3995292)Termination phase: Saturation
% 6.69/1.93 % (3995292)Time elapsed: 0.037 s
% 6.69/1.93 % (3995292)Peak memory usage: 88 MB
% 6.69/1.93 % (3995292)Instructions burned: 115 (million)
% 6.69/1.93 % (3995295)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3930317307:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.69/1.93 % (3995295)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995295)------------------------------
% 6.69/1.93 % (3995295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995295)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995295)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995295)Time elapsed: 0.002 s
% 6.69/1.93 % (3995295)Peak memory usage: 88 MB
% 6.69/1.93 % (3995295)Instructions burned: 2 (million)
% 6.69/1.93 % (3995297)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2943818203:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.69/1.93 % (3995297)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995297)------------------------------
% 6.69/1.93 % (3995297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995297)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995297)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995297)Time elapsed: 0.001 s
% 6.69/1.93 % (3995297)Peak memory usage: 88 MB
% 6.69/1.93 % (3995297)Instructions burned: 1 (million)
% 6.69/1.93 % (3995270)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995270)------------------------------
% 6.69/1.93 % (3995270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995270)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995270)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995270)Time elapsed: 0.602 s
% 6.69/1.93 % (3995270)Peak memory usage: 128 MB
% 6.69/1.93 % (3995270)Instructions burned: 896 (million)
% 6.69/1.93 % (3995289)------------------------------
% 6.69/1.93 % (3995289)------------------------------
% 6.69/1.93 % (3995268)First to succeed.
% 6.69/1.93 % (3995268)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3995202"
% 6.69/1.93 % (3995269)Also succeeded, but the first one will report.
% 6.69/1.93 % (3995297)------------------------------
% 6.69/1.93 % (3995297)------------------------------
% 6.69/1.93 % (3995300)lrs+10_1_sil=8000:sp=occurrence:random_seed=3931049506:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.69/1.93 % (3995295)------------------------------
% 6.69/1.93 % (3995295)------------------------------
% 6.69/1.93 % (3995270)------------------------------
% 6.69/1.93 % (3995270)------------------------------
% 6.69/1.93 % (3995301)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3574577453:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.69/1.93 % (3995301)Refutation not found, incomplete strategy
% 6.69/1.93 % (3995301)------------------------------
% 6.69/1.93 % (3995301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.93 % (3995301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.93 % (3995301)CaDiCaL version: 2.1.3
% 6.69/1.93 % (3995301)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.93 % (3995301)Time elapsed: 0.002 s
% 6.69/1.93 % (3995301)Peak memory usage: 88 MB
% 6.69/1.93 % (3995301)Instructions burned: 2 (million)
% 6.69/1.93 % (3995268)Refutation found. Thanks to Tanya!
% 6.69/1.93 % SZS status Theorem for theBenchmark
% 6.69/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.03 % (3995268)------------------------------
% 0.17/2.03 % (3995268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.03 % (3995268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.03 % (3995268)CaDiCaL version: 2.1.3
% 0.17/2.03 % (3995268)Termination reason: Refutation
% 0.17/2.03 % (3995268)Time elapsed: 0.678 s
% 0.17/2.03 % (3995268)Peak memory usage: 130 MB
% 0.17/2.03 % (3995268)Instructions burned: 1002 (million)
% 0.17/2.03 % (3995268)------------------------------
% 0.17/2.03 % (3995268)------------------------------
% 0.17/2.03 % (3995202)Success in time 1.079 s
% 0.17/2.03 % Vampire exiting
%------------------------------------------------------------------------------