%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU081+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:47:12 PM UTC 2026
% Result : Theorem 6.81s 1.70s
% Output : Refutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 157 ( 19 unt; 15 def)
% Number of atoms : 578 ( 105 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 746 ( 325 ~; 340 |; 50 &)
% ( 24 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 145 ( 0 sgn 131 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f11,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f26,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> relation_image(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f30,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f33,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f54,plain,
? [X0,X1] :
( relation_image(identity_relation(X0),X1) != X1
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f56,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f58,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,[],[f30]) ).
fof(f59,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,[],[f58]) ).
fof(f61,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),relation_dom(X0))
& in(sK1(X0,X1,X2),X1)
& sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK2(X0,X1,X6),relation_dom(X0))
& in(sK2(X0,X1,X6),X1)
& apply(X0,sK2(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f68]) ).
fof(f81,plain,
( sK15 != relation_image(identity_relation(sK14),sK15)
& element(sK15,powerset(sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f54]) ).
fof(f82,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,[],[f59]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK16(X0,X1) != apply(X1,sK16(X0,X1))
& in(sK16(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,[sK16]),skolemize(X2,sK16(X0,X1))],[f84]) ).
fof(f95,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f96,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f99,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f105,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f131,plain,
element(sK15,powerset(sK14)),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
sK15 != relation_image(identity_relation(sK14),sK15),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f135,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f140,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f152,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f136]) ).
fof(f153,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f135]) ).
fof(f154,plain,
! [X2,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| sP17(X1) ),
inference(cnf_transformation,[],[f154_D]) ).
fof(f154_D,definition,
! [X1] :
( ! [X2] :
( ~ element(X1,powerset(X2))
| ~ empty(X2) )
<=> ~ sP17(X1) ),
introduced(definition,[new_symbols(definition,[sP17])],[general_splitting_component_introduction]) ).
fof(f155,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP17(X1) ),
inference(general_splitting,[],[f141,f154_D]) ).
fof(f157,definition,
( spl18_1
<=> sK15 = relation_image(identity_relation(sK14),sK15) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f159,plain,
( sK15 != relation_image(identity_relation(sK14),sK15)
| spl18_1 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
~ spl18_1,
inference(avatar_split_clause,[],[f132,f157]) ).
fof(f162,plain,
( ! [X0] :
( sK15 != X0
| in(sK1(identity_relation(sK14),sK15,X0),sK15)
| in(sK0(identity_relation(sK14),sK15,X0),X0)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14)) )
| spl18_1 ),
inference(superposition,[],[f159,f96]) ).
fof(f167,plain,
( ! [X0] :
( sK15 != X0
| in(sK1(identity_relation(sK14),sK15,X0),sK15)
| in(sK0(identity_relation(sK14),sK15,X0),X0)
| ~ function(identity_relation(sK14)) )
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f162,f99]) ).
fof(f171,plain,
( ! [X0] :
( sK15 != X0
| in(sK1(identity_relation(sK14),sK15,X0),sK15)
| in(sK0(identity_relation(sK14),sK15,X0),X0) )
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f167,f105]) ).
fof(f174,definition,
( spl18_2
<=> element(sK15,powerset(sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f176,plain,
( element(sK15,powerset(sK14))
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
spl18_2,
inference(avatar_split_clause,[],[f131,f174]) ).
fof(f178,plain,
( ! [X0] :
( element(X0,sK14)
| ~ in(X0,sK15) )
| ~ spl18_2 ),
inference(resolution,[],[f176,f140]) ).
fof(f179,plain,
( ~ empty(sK14)
| sP17(sK15)
| ~ spl18_2 ),
inference(resolution,[],[f176,f154]) ).
fof(f183,definition,
( spl18_3
<=> ! [X0] :
( element(X0,sK14)
| ~ in(X0,sK15) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f184,plain,
( ! [X0] :
( ~ in(X0,sK15)
| element(X0,sK14) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f185,plain,
( spl18_3
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f178,f174,f183]) ).
fof(f193,definition,
( spl18_4
<=> ! [X0] :
( sK15 != X0
| in(sK1(identity_relation(sK14),sK15,X0),sK15)
| in(sK0(identity_relation(sK14),sK15,X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f194,plain,
( ! [X0] :
( sK15 != X0
| in(sK1(identity_relation(sK14),sK15,X0),sK15)
| in(sK0(identity_relation(sK14),sK15,X0),X0) )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
( spl18_4
| spl18_1 ),
inference(avatar_split_clause,[],[f171,f157,f193]) ).
fof(f196,plain,
( in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ spl18_4 ),
inference(equality_resolution,[],[f194]) ).
fof(f198,definition,
( spl18_5
<=> in(sK0(identity_relation(sK14),sK15,sK15),sK15) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f199,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| spl18_5 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f202,definition,
( spl18_6
<=> in(sK1(identity_relation(sK14),sK15,sK15),sK15) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f204,plain,
( in(sK1(identity_relation(sK14),sK15,sK15),sK15)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
( spl18_5
| spl18_6
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f196,f193,f202,f198]) ).
fof(f206,plain,
( element(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_3
| ~ spl18_6 ),
inference(resolution,[],[f204,f184]) ).
fof(f215,plain,
( ~ sP17(sK15)
| ~ spl18_6 ),
inference(resolution,[],[f204,f155]) ).
fof(f216,plain,
( ~ empty(sK14)
| ~ spl18_2
| ~ spl18_6 ),
inference(backward_subsumption_resolution,[],[f179,f215]) ).
fof(f232,definition,
( spl18_8
<=> element(sK1(identity_relation(sK14),sK15,sK15),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f234,plain,
( element(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( spl18_8
| ~ spl18_3
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f206,f202,f183,f232]) ).
fof(f236,plain,
( empty(sK14)
| in(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_8 ),
inference(resolution,[],[f234,f134]) ).
fof(f237,plain,
( in(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_2
| ~ spl18_6
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f236,f216]) ).
fof(f244,plain,
( element(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_3
| ~ spl18_5 ),
inference(resolution,[],[f200,f184]) ).
fof(f253,plain,
( ~ sP17(sK15)
| ~ spl18_5 ),
inference(resolution,[],[f200,f155]) ).
fof(f254,plain,
( ~ empty(sK14)
| ~ spl18_2
| ~ spl18_5 ),
inference(backward_subsumption_resolution,[],[f179,f253]) ).
fof(f280,plain,
( sK15 = relation_image(identity_relation(sK14),sK15)
| sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| spl18_5 ),
inference(resolution,[],[f199,f95]) ).
fof(f286,plain,
( sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| spl18_1
| spl18_5 ),
inference(forward_subsumption_resolution,[],[f280,f159]) ).
fof(f288,plain,
( sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| ~ function(identity_relation(sK14))
| spl18_1
| spl18_5 ),
inference(forward_subsumption_resolution,[],[f286,f99]) ).
fof(f290,plain,
( sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| spl18_1
| spl18_5 ),
inference(forward_subsumption_resolution,[],[f288,f105]) ).
fof(f292,definition,
( spl18_11
<=> sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
fof(f294,plain,
( sK0(identity_relation(sK14),sK15,sK15) = apply(identity_relation(sK14),sK1(identity_relation(sK14),sK15,sK15))
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,plain,
( spl18_11
| spl18_1
| spl18_5 ),
inference(avatar_split_clause,[],[f290,f198,f157,f292]) ).
fof(f317,definition,
( spl18_12
<=> element(sK0(identity_relation(sK14),sK15,sK15),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_12])],[avatar_definition]) ).
fof(f319,plain,
( element(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f320,plain,
( spl18_12
| ~ spl18_3
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f244,f198,f183,f317]) ).
fof(f322,plain,
( sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15)
| ~ in(sK1(identity_relation(sK14),sK15,sK15),sK14)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| ~ spl18_11 ),
inference(superposition,[],[f153,f294]) ).
fof(f327,plain,
( sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| ~ spl18_2
| ~ spl18_6
| ~ spl18_8
| ~ spl18_11 ),
inference(forward_subsumption_resolution,[],[f322,f237]) ).
fof(f331,plain,
( sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15)
| ~ function(identity_relation(sK14))
| ~ spl18_2
| ~ spl18_6
| ~ spl18_8
| ~ spl18_11 ),
inference(forward_subsumption_resolution,[],[f327,f99]) ).
fof(f333,plain,
( sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15)
| ~ spl18_2
| ~ spl18_6
| ~ spl18_8
| ~ spl18_11 ),
inference(forward_subsumption_resolution,[],[f331,f105]) ).
fof(f344,definition,
( spl18_13
<=> in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_13])],[avatar_definition]) ).
fof(f345,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| spl18_13 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f346,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f348,plain,
( ! [X0] :
( sK15 = relation_image(identity_relation(sK14),sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14)) )
| ~ spl18_5 ),
inference(resolution,[],[f200,f98]) ).
fof(f359,plain,
( ! [X0] :
( ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14)) )
| spl18_1
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f348,f159]) ).
fof(f360,plain,
( ! [X0] :
( ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0)
| ~ function(identity_relation(sK14)) )
| spl18_1
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f359,f99]) ).
fof(f361,plain,
( ! [X0] :
( ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0) )
| spl18_1
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f360,f105]) ).
fof(f362,plain,
( empty(sK14)
| in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_12 ),
inference(resolution,[],[f319,f134]) ).
fof(f365,definition,
( spl18_14
<=> sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
fof(f367,plain,
( sK1(identity_relation(sK14),sK15,sK15) = sK0(identity_relation(sK14),sK15,sK15)
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f368,plain,
( spl18_14
| ~ spl18_2
| ~ spl18_6
| ~ spl18_8
| ~ spl18_11 ),
inference(avatar_split_clause,[],[f333,f292,f232,f202,f174,f365]) ).
fof(f370,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ spl18_6
| ~ spl18_14 ),
inference(superposition,[],[f204,f367]) ).
fof(f379,definition,
( spl18_15
<=> in(sK0(identity_relation(sK14),sK15,sK15),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_15])],[avatar_definition]) ).
fof(f380,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| spl18_15 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f381,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f393,definition,
( spl18_16
<=> ! [X0] :
( ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK15)
| sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_16])],[avatar_definition]) ).
fof(f394,plain,
( ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != apply(identity_relation(sK14),X0)
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14))) )
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f395,plain,
( spl18_16
| spl18_1
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f361,f198,f157,f393]) ).
fof(f396,plain,
( ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != X0
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK14)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14)) )
| ~ spl18_16 ),
inference(superposition,[],[f394,f153]) ).
fof(f404,plain,
( ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != X0
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK14)
| ~ function(identity_relation(sK14)) )
| ~ spl18_16 ),
inference(forward_subsumption_resolution,[],[f396,f99]) ).
fof(f408,plain,
( ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != X0
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK14) )
| ~ spl18_16 ),
inference(forward_subsumption_resolution,[],[f404,f105]) ).
fof(f412,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| spl18_13 ),
inference(superposition,[],[f345,f152]) ).
fof(f413,plain,
( ~ relation(identity_relation(sK14))
| ~ function(identity_relation(sK14))
| spl18_13
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f412,f381]) ).
fof(f414,plain,
( ~ function(identity_relation(sK14))
| spl18_13
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f413,f99]) ).
fof(f415,plain,
( $false
| spl18_13
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f414,f105]) ).
fof(f416,plain,
( spl18_13
| ~ spl18_15 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f423,plain,
( in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_2
| ~ spl18_5
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f362,f254]) ).
fof(f434,plain,
( $false
| ~ spl18_2
| ~ spl18_5
| ~ spl18_12
| spl18_15 ),
inference(forward_subsumption_resolution,[],[f423,f380]) ).
fof(f435,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_12
| spl18_15 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f516,definition,
( spl18_20
<=> ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != X0
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK14) ) ),
introduced(definition,[new_symbols(definition,[spl18_20])],[avatar_definition]) ).
fof(f517,plain,
( ! [X0] :
( sK0(identity_relation(sK14),sK15,sK15) != X0
| ~ in(X0,sK15)
| ~ in(X0,relation_dom(identity_relation(sK14)))
| ~ in(X0,sK14) )
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( spl18_20
| ~ spl18_16 ),
inference(avatar_split_clause,[],[f408,f393,f516]) ).
fof(f519,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK15)
| ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_20 ),
inference(equality_resolution,[],[f517]) ).
fof(f520,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),relation_dom(identity_relation(sK14)))
| ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_5
| ~ spl18_20 ),
inference(forward_subsumption_resolution,[],[f519,f200]) ).
fof(f521,plain,
( ~ in(sK0(identity_relation(sK14),sK15,sK15),sK14)
| ~ spl18_5
| ~ spl18_13
| ~ spl18_20 ),
inference(forward_subsumption_resolution,[],[f520,f346]) ).
fof(f522,plain,
( $false
| ~ spl18_5
| ~ spl18_13
| ~ spl18_15
| ~ spl18_20 ),
inference(forward_subsumption_resolution,[],[f521,f381]) ).
fof(f523,plain,
( ~ spl18_5
| ~ spl18_13
| ~ spl18_15
| ~ spl18_20 ),
inference(avatar_contradiction_clause,[],[f522]) ).
fof(f526,plain,
( $false
| spl18_5
| ~ spl18_6
| ~ spl18_14 ),
inference(forward_subsumption_resolution,[],[f370,f199]) ).
fof(f527,plain,
( spl18_5
| ~ spl18_6
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f526]) ).
cnf(s1,plain,
~ spl18_1,
inference(sat_conversion,[],[f160]) ).
cnf(s2,plain,
spl18_2,
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
( ~ spl18_2
| spl18_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s4,plain,
( spl18_1
| spl18_4 ),
inference(sat_conversion,[],[f195]) ).
cnf(s5,plain,
( ~ spl18_4
| spl18_5
| spl18_6 ),
inference(sat_conversion,[],[f205]) ).
cnf(s7,plain,
( ~ spl18_3
| ~ spl18_6
| spl18_8 ),
inference(sat_conversion,[],[f235]) ).
cnf(s10,plain,
( spl18_1
| spl18_5
| spl18_11 ),
inference(sat_conversion,[],[f295]) ).
cnf(s11,plain,
( ~ spl18_3
| ~ spl18_5
| spl18_12 ),
inference(sat_conversion,[],[f320]) ).
cnf(s14,plain,
( ~ spl18_2
| ~ spl18_6
| ~ spl18_8
| ~ spl18_11
| spl18_14 ),
inference(sat_conversion,[],[f368]) ).
cnf(s17,plain,
( spl18_1
| ~ spl18_5
| spl18_16 ),
inference(sat_conversion,[],[f395]) ).
cnf(s19,plain,
( spl18_13
| ~ spl18_15 ),
inference(sat_conversion,[],[f416]) ).
cnf(s24,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_12
| spl18_15 ),
inference(sat_conversion,[],[f435]) ).
cnf(s33,plain,
( ~ spl18_16
| spl18_20 ),
inference(sat_conversion,[],[f518]) ).
cnf(s34,plain,
( ~ spl18_5
| ~ spl18_13
| ~ spl18_15
| ~ spl18_20 ),
inference(sat_conversion,[],[f523]) ).
cnf(s36,plain,
( spl18_5
| ~ spl18_6
| ~ spl18_14 ),
inference(sat_conversion,[],[f527]) ).
cnf(s38,plain,
spl18_3,
inference(rat,[],[s3,s2]) ).
cnf(s40,plain,
spl18_4,
inference(rat,[],[s4,s1]) ).
cnf(s41,plain,
spl18_5,
inference(rat,[],[s14,s7,s36,s5,s10,s2,s38,s40,s1]) ).
cnf(s42,plain,
spl18_16,
inference(rat,[],[s17,s1,s41]) ).
cnf(s43,plain,
spl18_12,
inference(rat,[],[s11,s38,s41]) ).
cnf(s45,plain,
spl18_20,
inference(rat,[],[s33,s42]) ).
cnf(s46,plain,
spl18_15,
inference(rat,[],[s24,s41,s2,s43]) ).
cnf(s47,plain,
spl18_13,
inference(rat,[],[s19,s46]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s34,s45,s41,s46,s47]) ).
fof(f532,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU081+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.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 03:26:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.81/1.70 % (3181615)Detected formulas, will run a generic FOF schedule.
% 6.81/1.70 % (3181620)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=1697411054:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.81/1.70 % (3181623)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2004239813:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.81/1.70 % (3181622)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=441093251:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.81/1.70 % (3181625)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=941882556:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.81/1.70 % (3181626)dis-21_1_sil=8000:lcm=predicate:random_seed=1022265297: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)
% 6.81/1.70 % (3181624)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=894240126:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.81/1.70 % (3181621)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=236215647:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.81/1.70 % (3181623)Refutation not found, incomplete strategy
% 6.81/1.70 % (3181623)------------------------------
% 6.81/1.70 % (3181623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181623)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181623)Termination reason: Refutation not found, incomplete strategy
% 6.81/1.70 % (3181623)Time elapsed: 0.002 s
% 6.81/1.70 % (3181623)Peak memory usage: 88 MB
% 6.81/1.70 % (3181623)Instructions burned: 2 (million)
% 6.81/1.70 % (3181624)Instruction limit reached!
% 6.81/1.70 % (3181624)------------------------------
% 6.81/1.70 % (3181624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181624)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181624)Termination reason: Instruction limit
% 6.81/1.70 % (3181624)Termination phase: Saturation
% 6.81/1.70 % (3181624)Time elapsed: 0.069 s
% 6.81/1.70 % (3181624)Peak memory usage: 88 MB
% 6.81/1.70 % (3181624)Instructions burned: 119 (million)
% 6.81/1.70 % (3181626)Instruction limit reached!
% 6.81/1.70 % (3181626)------------------------------
% 6.81/1.70 % (3181626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181626)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181626)Termination reason: Instruction limit
% 6.81/1.70 % (3181626)Termination phase: Saturation
% 6.81/1.70 % (3181626)Time elapsed: 0.080 s
% 6.81/1.70 % (3181626)Peak memory usage: 90 MB
% 6.81/1.70 % (3181626)Instructions burned: 129 (million)
% 6.81/1.70 % (3181625)Instruction limit reached!
% 6.81/1.70 % (3181625)------------------------------
% 6.81/1.70 % (3181625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181625)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181625)Termination reason: Instruction limit
% 6.81/1.70 % (3181625)Termination phase: Saturation
% 6.81/1.70 % (3181625)Time elapsed: 0.096 s
% 6.81/1.70 % (3181625)Peak memory usage: 89 MB
% 6.81/1.70 % (3181625)Instructions burned: 140 (million)
% 6.81/1.70 % (3181634)lrs+10_1_sil=8000:sp=occurrence:random_seed=780517824:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.81/1.70 % (3181635)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2236774001:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.81/1.70 % (3181623)------------------------------
% 6.81/1.70 % (3181623)------------------------------
% 6.81/1.70 % (3181636)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2475647339:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.81/1.70 % (3181635)Instruction limit reached!
% 6.81/1.70 % (3181635)------------------------------
% 6.81/1.70 % (3181635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181635)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181635)Termination reason: Instruction limit
% 6.81/1.70 % (3181635)Termination phase: Saturation
% 6.81/1.70 % (3181635)Time elapsed: 0.067 s
% 6.81/1.70 % (3181635)Peak memory usage: 88 MB
% 6.81/1.70 % (3181635)Instructions burned: 160 (million)
% 6.81/1.70 % (3181636)Instruction limit reached!
% 6.81/1.70 % (3181636)------------------------------
% 6.81/1.70 % (3181636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181636)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181636)Termination reason: Instruction limit
% 6.81/1.70 % (3181636)Termination phase: Saturation
% 6.81/1.70 % (3181636)Time elapsed: 0.110 s
% 6.81/1.70 % (3181636)Peak memory usage: 91 MB
% 6.81/1.70 % (3181636)Instructions burned: 325 (million)
% 6.81/1.70 % (3181634)Instruction limit reached!
% 6.81/1.70 % (3181634)------------------------------
% 6.81/1.70 % (3181634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181634)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181634)Termination reason: Instruction limit
% 6.81/1.70 % (3181634)Termination phase: Saturation
% 6.81/1.70 % (3181634)Time elapsed: 0.173 s
% 6.81/1.70 % (3181634)Peak memory usage: 91 MB
% 6.81/1.70 % (3181634)Instructions burned: 285 (million)
% 6.81/1.70 % (3181640)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=4173679067:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.81/1.70 % (3181641)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1517325078:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.81/1.70 % (3181641)Refutation not found, incomplete strategy
% 6.81/1.70 % (3181641)------------------------------
% 6.81/1.70 % (3181641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181641)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181641)Termination reason: Refutation not found, incomplete strategy
% 6.81/1.70 % (3181641)Time elapsed: 0.003 s
% 6.81/1.70 % (3181641)Peak memory usage: 88 MB
% 6.81/1.70 % (3181641)Instructions burned: 2 (million)
% 6.81/1.70 % (3181642)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2616132396:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.81/1.70 % (3181640)Instruction limit reached!
% 6.81/1.70 % (3181640)------------------------------
% 6.81/1.70 % (3181640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181640)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181640)Termination reason: Instruction limit
% 6.81/1.70 % (3181640)Termination phase: Saturation
% 6.81/1.70 % (3181640)Time elapsed: 0.129 s
% 6.81/1.70 % (3181640)Peak memory usage: 91 MB
% 6.81/1.70 % (3181640)Instructions burned: 249 (million)
% 6.81/1.70 % (3181643)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2996007024:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.81/1.70 % (3181622)First to succeed.
% 6.81/1.70 % (3181643)Instruction limit reached!
% 6.81/1.70 % (3181643)------------------------------
% 6.81/1.70 % (3181643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181643)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181643)Termination reason: Instruction limit
% 6.81/1.70 % (3181643)Termination phase: Saturation
% 6.81/1.70 % (3181643)Time elapsed: 0.084 s
% 6.81/1.70 % (3181643)Peak memory usage: 90 MB
% 6.81/1.70 % (3181622)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3181615"
% 6.81/1.70 % (3181643)Instructions burned: 114 (million)
% 6.81/1.70 % (3181641)------------------------------
% 6.81/1.70 % (3181641)------------------------------
% 6.81/1.70 % (3181647)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3082019415:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.81/1.70 % (3181647)Instruction limit reached!
% 6.81/1.70 % (3181647)------------------------------
% 6.81/1.70 % (3181647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181647)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181647)Termination reason: Instruction limit
% 6.81/1.70 % (3181647)Termination phase: Saturation
% 6.81/1.70 % (3181647)Time elapsed: 0.071 s
% 6.81/1.70 % (3181647)Peak memory usage: 89 MB
% 6.81/1.70 % (3181647)Instructions burned: 128 (million)
% 6.81/1.70 % (3181649)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1498980339:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.81/1.70 % (3181651)lrs+10_1_sil=8000:sp=occurrence:random_seed=3823343471:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.81/1.70 % (3181649)Instruction limit reached!
% 6.81/1.70 % (3181649)------------------------------
% 6.81/1.70 % (3181649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.70 % (3181649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.70 % (3181649)CaDiCaL version: 2.1.3
% 6.81/1.70 % (3181649)Termination reason: Instruction limit
% 6.81/1.70 % (3181649)Termination phase: Saturation
% 6.81/1.70 % (3181649)Time elapsed: 0.062 s
% 6.81/1.70 % (3181649)Peak memory usage: 89 MB
% 6.81/1.70 % (3181649)Instructions burned: 115 (million)
% 6.81/1.70 % (3181622)Refutation found. Thanks to Tanya!
% 6.81/1.70 % SZS status Theorem for theBenchmark
% 6.81/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 8.01/1.90 % (3181622)------------------------------
% 8.01/1.90 % (3181622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.01/1.90 % (3181622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.01/1.90 % (3181622)CaDiCaL version: 2.1.3
% 8.01/1.90 % (3181622)Termination reason: Refutation
% 8.01/1.90 % (3181622)Time elapsed: 0.656 s
% 8.01/1.90 % (3181622)Peak memory usage: 127 MB
% 8.01/1.90 % (3181622)Instructions burned: 972 (million)
% 8.01/1.90 % (3181622)------------------------------
% 8.01/1.90 % (3181622)------------------------------
% 8.01/1.90 % (3181615)Success in time 1.089 s
% 8.01/1.90 % Vampire exiting
%------------------------------------------------------------------------------