%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT025+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 : n007.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 09:36:41 AM UTC 2026
% Result : Theorem 2.96s 1.10s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 133 ( 23 unt; 9 def)
% Number of atoms : 494 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 652 ( 291 ~; 277 |; 58 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 10 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( ( v2_cat_1(X2)
& l1_cat_1(X2) )
=> r1_isocat_1(k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_isocat_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( ( v2_cat_1(X2)
& l1_cat_1(X2) )
=> r1_isocat_1(k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ( r1_isocat_1(X0,X1)
<=> ? [X2] :
( m2_cat_1(X2,X0,X1)
& v8_cat_1(X2,X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_isocat_1) ).
fof(f8,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& v2_cat_1(X1)
& l1_cat_1(X1) )
=> ( v2_cat_1(k11_cat_2(X0,X1))
& l1_cat_1(k11_cat_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_cat_2) ).
fof(f9,axiom,
! [X0,X1] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& v2_cat_1(X1)
& l1_cat_1(X1) )
=> ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_nattra_1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( v2_cat_1(X0)
& l1_cat_1(X0)
& v2_cat_1(X1)
& l1_cat_1(X1)
& v2_cat_1(X2)
& l1_cat_1(X2) )
=> m2_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_isocat_2) ).
fof(f44,axiom,
! [X0] :
( ( v2_cat_1(X0)
& l1_cat_1(X0) )
=> ! [X1] :
( ( v2_cat_1(X1)
& l1_cat_1(X1) )
=> ! [X2] :
( ( v2_cat_1(X2)
& l1_cat_1(X2) )
=> v8_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_isocat_2) ).
fof(f54,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_isocat_1(k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
& v2_cat_1(X2)
& l1_cat_1(X2) )
& v2_cat_1(X1)
& l1_cat_1(X1) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f55,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_isocat_1(k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
& v2_cat_1(X2)
& l1_cat_1(X2) )
& v2_cat_1(X1)
& l1_cat_1(X1) )
& v2_cat_1(X0)
& l1_cat_1(X0) ),
inference(flattening,[],[f54]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( r1_isocat_1(X0,X1)
<=> ? [X2] :
( m2_cat_1(X2,X0,X1)
& v8_cat_1(X2,X0,X1) ) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( r1_isocat_1(X0,X1)
<=> ? [X2] :
( m2_cat_1(X2,X0,X1)
& v8_cat_1(X2,X0,X1) ) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f59]) ).
fof(f63,plain,
! [X0,X1] :
( ( v2_cat_1(k11_cat_2(X0,X1))
& l1_cat_1(k11_cat_2(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0,X1] :
( ( v2_cat_1(k11_cat_2(X0,X1))
& l1_cat_1(k11_cat_2(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( ( v1_cat_1(k12_nattra_1(X0,X1))
& v2_cat_1(k12_nattra_1(X0,X1))
& l1_cat_1(k12_nattra_1(X0,X1)) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( m2_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f68,plain,
! [X0,X1,X2] :
( m2_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) ),
inference(flattening,[],[f67]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( v8_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( v8_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(flattening,[],[f92]) ).
fof(f101,plain,
( ~ r1_isocat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
& v2_cat_1(sK2)
& l1_cat_1(sK2)
& v2_cat_1(sK1)
& l1_cat_1(sK1)
& v2_cat_1(sK0)
& l1_cat_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f55]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( r1_isocat_1(X0,X1)
| ! [X2] :
( ~ m2_cat_1(X2,X0,X1)
| ~ v8_cat_1(X2,X0,X1) ) )
& ( ? [X2] :
( m2_cat_1(X2,X0,X1)
& v8_cat_1(X2,X0,X1) )
| ~ r1_isocat_1(X0,X1) ) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( r1_isocat_1(X0,X1)
| ! [X2] :
( ~ m2_cat_1(X2,X0,X1)
| ~ v8_cat_1(X2,X0,X1) ) )
& ( ? [X3] :
( m2_cat_1(X3,X0,X1)
& v8_cat_1(X3,X0,X1) )
| ~ r1_isocat_1(X0,X1) ) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( ( r1_isocat_1(X0,X1)
| ! [X2] :
( ~ m2_cat_1(X2,X0,X1)
| ~ v8_cat_1(X2,X0,X1) ) )
& ( ( m2_cat_1(sK3(X0,X1),X0,X1)
& v8_cat_1(sK3(X0,X1),X0,X1) )
| ~ r1_isocat_1(X0,X1) ) )
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) )
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f103]) ).
fof(f115,plain,
l1_cat_1(sK0),
inference(cnf_transformation,[],[f101]) ).
fof(f116,plain,
v2_cat_1(sK0),
inference(cnf_transformation,[],[f101]) ).
fof(f117,plain,
l1_cat_1(sK1),
inference(cnf_transformation,[],[f101]) ).
fof(f118,plain,
v2_cat_1(sK1),
inference(cnf_transformation,[],[f101]) ).
fof(f119,plain,
l1_cat_1(sK2),
inference(cnf_transformation,[],[f101]) ).
fof(f120,plain,
v2_cat_1(sK2),
inference(cnf_transformation,[],[f101]) ).
fof(f121,plain,
~ r1_isocat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2))),
inference(cnf_transformation,[],[f101]) ).
fof(f126,plain,
! [X2,X0,X1] :
( r1_isocat_1(X0,X1)
| ~ m2_cat_1(X2,X0,X1)
| ~ v8_cat_1(X2,X0,X1)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f129,plain,
! [X0,X1] :
( l1_cat_1(k11_cat_2(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f130,plain,
! [X0,X1] :
( v2_cat_1(k11_cat_2(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f131,plain,
! [X0,X1] :
( l1_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f132,plain,
! [X0,X1] :
( v2_cat_1(k12_nattra_1(X0,X1))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f134,plain,
! [X2,X0,X1] :
( m2_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f179,plain,
! [X2,X0,X1] :
( v8_cat_1(k7_isocat_2(X0,X1,X2),k12_nattra_1(k11_cat_2(X0,X1),X2),k12_nattra_1(X0,k12_nattra_1(X1,X2)))
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X0)
| ~ l1_cat_1(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f208,definition,
( spl13_3
<=> l1_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f209,plain,
( l1_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f210,plain,
( ~ l1_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2))
| spl13_3 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl13_4
<=> v2_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f214,plain,
( ~ v2_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2))
| spl13_4 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f216,definition,
( spl13_5
<=> l1_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f218,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| spl13_5 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f220,definition,
( spl13_6
<=> v2_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f222,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| spl13_6 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f228,plain,
( ~ v2_cat_1(k11_cat_2(sK0,sK1))
| ~ l1_cat_1(k11_cat_2(sK0,sK1))
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_3 ),
inference(resolution,[],[f210,f131]) ).
fof(f229,plain,
( ~ v2_cat_1(k11_cat_2(sK0,sK1))
| ~ l1_cat_1(k11_cat_2(sK0,sK1))
| ~ l1_cat_1(sK2)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f228,f120]) ).
fof(f230,plain,
( ~ v2_cat_1(k11_cat_2(sK0,sK1))
| ~ l1_cat_1(k11_cat_2(sK0,sK1))
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f229,f119]) ).
fof(f232,definition,
( spl13_8
<=> l1_cat_1(k11_cat_2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f233,plain,
( l1_cat_1(k11_cat_2(sK0,sK1))
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( ~ l1_cat_1(k11_cat_2(sK0,sK1))
| spl13_8 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl13_9
<=> v2_cat_1(k11_cat_2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f237,plain,
( v2_cat_1(k11_cat_2(sK0,sK1))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ v2_cat_1(k11_cat_2(sK0,sK1))
| spl13_9 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
( ~ spl13_8
| ~ spl13_9
| spl13_3 ),
inference(avatar_split_clause,[],[f230,f208,f236,f232]) ).
fof(f240,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_8 ),
inference(resolution,[],[f234,f129]) ).
fof(f241,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f240,f116]) ).
fof(f242,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f241,f115]) ).
fof(f243,plain,
( ~ l1_cat_1(sK1)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f242,f118]) ).
fof(f244,plain,
( $false
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f243,f117]) ).
fof(f245,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f246,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_9 ),
inference(resolution,[],[f238,f130]) ).
fof(f247,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f246,f116]) ).
fof(f248,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f247,f115]) ).
fof(f249,plain,
( ~ l1_cat_1(sK1)
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f248,f118]) ).
fof(f250,plain,
( $false
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f249,f117]) ).
fof(f251,plain,
spl13_9,
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f252,plain,
! [X0] :
( ~ m2_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v8_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v2_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2))
| ~ l1_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2)) ),
inference(resolution,[],[f126,f121]) ).
fof(f253,plain,
( ! [X0] :
( ~ m2_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v8_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v2_cat_1(k12_nattra_1(k11_cat_2(sK0,sK1),sK2)) )
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f252,f209]) ).
fof(f255,definition,
( spl13_10
<=> ! [X0] :
( ~ m2_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v8_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2))) ) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f256,plain,
( ! [X0] :
( ~ v8_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ m2_cat_1(X0,k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2))) )
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ spl13_4
| ~ spl13_5
| ~ spl13_6
| spl13_10
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f253,f208,f255,f220,f216,f212]) ).
fof(f258,plain,
( ~ v2_cat_1(k11_cat_2(sK0,sK1))
| ~ l1_cat_1(k11_cat_2(sK0,sK1))
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_4 ),
inference(resolution,[],[f214,f132]) ).
fof(f259,plain,
( ~ l1_cat_1(k11_cat_2(sK0,sK1))
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_4
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f258,f237]) ).
fof(f260,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_4
| ~ spl13_8
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f259,f233]) ).
fof(f261,plain,
( ~ l1_cat_1(sK2)
| spl13_4
| ~ spl13_8
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f260,f120]) ).
fof(f262,plain,
( $false
| spl13_4
| ~ spl13_8
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f261,f119]) ).
fof(f263,plain,
( spl13_4
| ~ spl13_8
| ~ spl13_9 ),
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f264,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_5 ),
inference(resolution,[],[f218,f131]) ).
fof(f265,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f264,f116]) ).
fof(f266,plain,
( ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f265,f115]) ).
fof(f268,definition,
( spl13_11
<=> l1_cat_1(k12_nattra_1(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f269,plain,
( l1_cat_1(k12_nattra_1(sK1,sK2))
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f270,plain,
( ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_11 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,definition,
( spl13_12
<=> v2_cat_1(k12_nattra_1(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f273,plain,
( v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| spl13_12 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ spl13_11
| ~ spl13_12
| spl13_5 ),
inference(avatar_split_clause,[],[f266,f216,f272,f268]) ).
fof(f277,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_11 ),
inference(resolution,[],[f270,f131]) ).
fof(f278,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f277,f118]) ).
fof(f279,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f278,f117]) ).
fof(f280,plain,
( ~ l1_cat_1(sK2)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f279,f120]) ).
fof(f281,plain,
( $false
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f280,f119]) ).
fof(f282,plain,
spl13_11,
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f284,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_12 ),
inference(resolution,[],[f274,f132]) ).
fof(f285,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f284,f118]) ).
fof(f286,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f285,f117]) ).
fof(f287,plain,
( ~ l1_cat_1(sK2)
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f286,f120]) ).
fof(f288,plain,
( $false
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f287,f119]) ).
fof(f289,plain,
spl13_12,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f290,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_6 ),
inference(resolution,[],[f222,f132]) ).
fof(f291,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f290,f116]) ).
fof(f292,plain,
( ~ v2_cat_1(k12_nattra_1(sK1,sK2))
| ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f291,f115]) ).
fof(f293,plain,
( ~ l1_cat_1(k12_nattra_1(sK1,sK2))
| spl13_6
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f292,f273]) ).
fof(f294,plain,
( $false
| spl13_6
| ~ spl13_11
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f293,f269]) ).
fof(f295,plain,
( spl13_6
| ~ spl13_11
| ~ spl13_12 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f303,plain,
( ~ m2_cat_1(k7_isocat_2(sK0,sK1,sK2),k12_nattra_1(k11_cat_2(sK0,sK1),sK2),k12_nattra_1(sK0,k12_nattra_1(sK1,sK2)))
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(resolution,[],[f256,f179]) ).
fof(f304,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f303,f134]) ).
fof(f305,plain,
( ~ l1_cat_1(sK2)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f304,f120]) ).
fof(f306,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f305,f119]) ).
fof(f307,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f306,f118]) ).
fof(f308,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f307,f117]) ).
fof(f309,plain,
( ~ l1_cat_1(sK0)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f308,f116]) ).
fof(f310,plain,
( $false
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f309,f115]) ).
fof(f311,plain,
~ spl13_10,
inference(avatar_contradiction_clause,[],[f310]) ).
cnf(s3,plain,
( spl13_3
| ~ spl13_8
| ~ spl13_9 ),
inference(sat_conversion,[],[f239]) ).
cnf(s4,plain,
spl13_8,
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
spl13_9,
inference(sat_conversion,[],[f251]) ).
cnf(s6,plain,
( ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_6
| spl13_10 ),
inference(sat_conversion,[],[f257]) ).
cnf(s7,plain,
( spl13_4
| ~ spl13_8
| ~ spl13_9 ),
inference(sat_conversion,[],[f263]) ).
cnf(s8,plain,
( spl13_5
| ~ spl13_11
| ~ spl13_12 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
spl13_11,
inference(sat_conversion,[],[f282]) ).
cnf(s10,plain,
spl13_12,
inference(sat_conversion,[],[f289]) ).
cnf(s11,plain,
( spl13_6
| ~ spl13_11
| ~ spl13_12 ),
inference(sat_conversion,[],[f295]) ).
cnf(s12,plain,
~ spl13_10,
inference(sat_conversion,[],[f311]) ).
cnf(s13,plain,
spl13_6,
inference(rat,[],[s11,s10,s9]) ).
cnf(s14,plain,
spl13_5,
inference(rat,[],[s8,s10,s9]) ).
cnf(s15,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(rat,[],[s6,s12,s13,s14]) ).
cnf(s16,plain,
spl13_4,
inference(rat,[],[s7,s5,s4]) ).
cnf(s17,plain,
~ spl13_3,
inference(rat,[],[s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s3,s5,s4,s17]) ).
fof(f312,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT025+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n007.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 21:14:41 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running first-order theorem proving
% 0.06/0.23 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
% 2.96/1.10 % (2835737)Detected formulas, will run a generic FOF schedule.
% 2.96/1.10 % (2835743)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=3712804653:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.96/1.10 % (2835747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1077324021:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.96/1.10 % (2835744)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=329945344:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.96/1.10 % (2835746)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3124409434:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.96/1.10 % (2835745)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3926173863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.96/1.10 % (2835742)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=347267344:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.96/1.10 % (2835748)dis-21_1_sil=8000:lcm=predicate:random_seed=3010063676: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)
% 2.96/1.10 % (2835745)Refutation not found, incomplete strategy
% 2.96/1.10 % (2835745)------------------------------
% 2.96/1.10 % (2835745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.10 % (2835746)Refutation not found, incomplete strategy
% 2.96/1.10 % (2835746)------------------------------
% 2.96/1.10 % (2835746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.10 % (2835746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.10 % (2835745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.10 % (2835745)CaDiCaL version: 2.1.3
% 2.96/1.10 % (2835746)CaDiCaL version: 2.1.3
% 2.96/1.10 % (2835746)Termination reason: Refutation not found, incomplete strategy
% 2.96/1.10 % (2835746)Time elapsed: 0.001 s
% 2.96/1.10 % (2835745)Termination reason: Refutation not found, incomplete strategy
% 2.96/1.10 % (2835745)Time elapsed: 0.001 s
% 2.96/1.10 % (2835746)Peak memory usage: 88 MB
% 2.96/1.10 % (2835745)Peak memory usage: 88 MB
% 2.96/1.10 % (2835747)First to succeed.
% 2.96/1.10 % (2835747)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2835737"
% 2.96/1.10 % (2835748)Instruction limit reached!
% 2.96/1.10 % (2835748)------------------------------
% 2.96/1.10 % (2835748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.10 % (2835748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.10 % (2835748)CaDiCaL version: 2.1.3
% 2.96/1.10 % (2835748)Termination reason: Instruction limit
% 2.96/1.10 % (2835748)Termination phase: Saturation
% 2.96/1.10 % (2835748)Time elapsed: 0.083 s
% 2.96/1.10 % (2835748)Peak memory usage: 90 MB
% 2.96/1.10 % (2835748)Instructions burned: 129 (million)
% 2.96/1.10 % (2835756)lrs+10_1_sil=8000:sp=occurrence:random_seed=1906029747:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.96/1.10 % (2835756)Also succeeded, but the first one will report.
% 2.96/1.10 % (2835746)------------------------------
% 2.96/1.10 % (2835746)------------------------------
% 2.96/1.10 % (2835745)------------------------------
% 2.96/1.10 % (2835745)------------------------------
% 2.96/1.10 % (2835747)Refutation found. Thanks to Tanya!
% 2.96/1.10 % SZS status Theorem for theBenchmark
% 2.96/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.19 % (2835747)------------------------------
% 3.49/1.19 % (2835747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.19 % (2835747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.19 % (2835747)CaDiCaL version: 2.1.3
% 3.49/1.19 % (2835747)Termination reason: Refutation
% 3.49/1.19 % (2835747)Time elapsed: 0.009 s
% 3.49/1.19 % (2835747)Peak memory usage: 89 MB
% 3.49/1.19 % (2835747)Instructions burned: 11 (million)
% 3.49/1.19 % (2835747)------------------------------
% 3.49/1.19 % (2835747)------------------------------
% 3.49/1.19 % (2835737)Success in time 0.418 s
% 3.49/1.19 % Vampire exiting
%------------------------------------------------------------------------------