%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CAT032+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:37:02 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 144 ( 25 unt; 10 def)
% Number of atoms : 555 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 743 ( 332 ~; 326 |; 58 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 74 !; 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(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_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(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_k12_nattra_1) ).
fof(f10,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(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_isocat_2) ).
fof(f45,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(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_isocat_2) ).
fof(f54,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_isocat_1(k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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,[],[f10]) ).
fof(f68,plain,
! [X0,X1,X2] :
( m2_cat_1(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( v8_cat_1(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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,[],[f45]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( v8_cat_1(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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,[],[f93]) ).
fof(f101,plain,
( ~ r1_isocat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)),k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,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(sK0,k11_cat_2(sK1,sK2)),k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2))),
inference(cnf_transformation,[],[f101]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ v8_cat_1(X2,X0,X1)
| ~ m2_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(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(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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(f180,plain,
! [X2,X0,X1] :
( v8_cat_1(k17_isocat_2(X0,X1,X2),k12_nattra_1(X0,k11_cat_2(X1,X2)),k11_cat_2(k12_nattra_1(X0,X1),k12_nattra_1(X0,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,[],[f94]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ 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(k17_isocat_2(X2,X1,X0),k12_nattra_1(X2,k11_cat_2(X1,X0)),k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| r1_isocat_1(k12_nattra_1(X2,k11_cat_2(X1,X0)),k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ v2_cat_1(k12_nattra_1(X2,k11_cat_2(X1,X0)))
| ~ l1_cat_1(k12_nattra_1(X2,k11_cat_2(X1,X0))) ),
inference(resolution,[],[f180,f126]) ).
fof(f303,plain,
! [X2,X0,X1] :
( r1_isocat_1(k12_nattra_1(X2,k11_cat_2(X1,X0)),k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ l1_cat_1(X0)
| ~ v2_cat_1(X1)
| ~ l1_cat_1(X1)
| ~ v2_cat_1(X2)
| ~ l1_cat_1(X2)
| ~ v2_cat_1(X0)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(X2,X1),k12_nattra_1(X2,X0)))
| ~ v2_cat_1(k12_nattra_1(X2,k11_cat_2(X1,X0)))
| ~ l1_cat_1(k12_nattra_1(X2,k11_cat_2(X1,X0))) ),
inference(forward_subsumption_resolution,[],[f302,f134]) ).
fof(f540,plain,
( ~ l1_cat_1(sK2)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(resolution,[],[f303,f121]) ).
fof(f543,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f540,f119]) ).
fof(f544,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f543,f118]) ).
fof(f545,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f544,f117]) ).
fof(f546,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f545,f116]) ).
fof(f547,plain,
( ~ v2_cat_1(sK2)
| ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f546,f115]) ).
fof(f548,plain,
( ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f547,f120]) ).
fof(f550,definition,
( spl13_28
<=> l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_28])],[avatar_definition]) ).
fof(f552,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| spl13_28 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f554,definition,
( spl13_29
<=> v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_29])],[avatar_definition]) ).
fof(f556,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,k11_cat_2(sK1,sK2)))
| spl13_29 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f558,definition,
( spl13_30
<=> l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f560,plain,
( ~ l1_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| spl13_30 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f562,definition,
( spl13_31
<=> v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f564,plain,
( ~ v2_cat_1(k11_cat_2(k12_nattra_1(sK0,sK1),k12_nattra_1(sK0,sK2)))
| spl13_31 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f565,plain,
( ~ spl13_28
| ~ spl13_29
| ~ spl13_30
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f548,f562,f558,f554,f550]) ).
fof(f571,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_28 ),
inference(resolution,[],[f552,f131]) ).
fof(f572,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_28 ),
inference(forward_subsumption_resolution,[],[f571,f116]) ).
fof(f573,plain,
( ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_28 ),
inference(forward_subsumption_resolution,[],[f572,f115]) ).
fof(f575,definition,
( spl13_32
<=> l1_cat_1(k11_cat_2(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_32])],[avatar_definition]) ).
fof(f576,plain,
( l1_cat_1(k11_cat_2(sK1,sK2))
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f577,plain,
( ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_32 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f579,definition,
( spl13_33
<=> v2_cat_1(k11_cat_2(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_33])],[avatar_definition]) ).
fof(f580,plain,
( v2_cat_1(k11_cat_2(sK1,sK2))
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f581,plain,
( ~ v2_cat_1(k11_cat_2(sK1,sK2))
| spl13_33 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f582,plain,
( ~ spl13_32
| ~ spl13_33
| spl13_28 ),
inference(avatar_split_clause,[],[f573,f550,f579,f575]) ).
fof(f583,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_32 ),
inference(resolution,[],[f577,f129]) ).
fof(f584,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f583,f118]) ).
fof(f585,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f584,f117]) ).
fof(f586,plain,
( ~ l1_cat_1(sK2)
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f585,f120]) ).
fof(f587,plain,
( $false
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f586,f119]) ).
fof(f588,plain,
spl13_32,
inference(avatar_contradiction_clause,[],[f587]) ).
fof(f636,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_33 ),
inference(resolution,[],[f581,f130]) ).
fof(f637,plain,
( ~ l1_cat_1(sK1)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_33 ),
inference(forward_subsumption_resolution,[],[f636,f118]) ).
fof(f638,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_33 ),
inference(forward_subsumption_resolution,[],[f637,f117]) ).
fof(f639,plain,
( ~ l1_cat_1(sK2)
| spl13_33 ),
inference(forward_subsumption_resolution,[],[f638,f120]) ).
fof(f640,plain,
( $false
| spl13_33 ),
inference(forward_subsumption_resolution,[],[f639,f119]) ).
fof(f641,plain,
spl13_33,
inference(avatar_contradiction_clause,[],[f640]) ).
fof(f665,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_29 ),
inference(resolution,[],[f556,f132]) ).
fof(f666,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_29 ),
inference(forward_subsumption_resolution,[],[f665,f116]) ).
fof(f667,plain,
( ~ v2_cat_1(k11_cat_2(sK1,sK2))
| ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_29 ),
inference(forward_subsumption_resolution,[],[f666,f115]) ).
fof(f668,plain,
( ~ l1_cat_1(k11_cat_2(sK1,sK2))
| spl13_29
| ~ spl13_33 ),
inference(forward_subsumption_resolution,[],[f667,f580]) ).
fof(f669,plain,
( $false
| spl13_29
| ~ spl13_32
| ~ spl13_33 ),
inference(forward_subsumption_resolution,[],[f668,f576]) ).
fof(f670,plain,
( spl13_29
| ~ spl13_32
| ~ spl13_33 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f671,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,sK1))
| ~ l1_cat_1(k12_nattra_1(sK0,sK1))
| ~ v2_cat_1(k12_nattra_1(sK0,sK2))
| ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_30 ),
inference(resolution,[],[f560,f129]) ).
fof(f673,definition,
( spl13_42
<=> l1_cat_1(k12_nattra_1(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_42])],[avatar_definition]) ).
fof(f674,plain,
( l1_cat_1(k12_nattra_1(sK0,sK2))
| ~ spl13_42 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f675,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_42 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f677,definition,
( spl13_43
<=> v2_cat_1(k12_nattra_1(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_43])],[avatar_definition]) ).
fof(f678,plain,
( v2_cat_1(k12_nattra_1(sK0,sK2))
| ~ spl13_43 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f679,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,sK2))
| spl13_43 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f681,definition,
( spl13_44
<=> l1_cat_1(k12_nattra_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl13_44])],[avatar_definition]) ).
fof(f682,plain,
( l1_cat_1(k12_nattra_1(sK0,sK1))
| ~ spl13_44 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f683,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,sK1))
| spl13_44 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f685,definition,
( spl13_45
<=> v2_cat_1(k12_nattra_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl13_45])],[avatar_definition]) ).
fof(f686,plain,
( v2_cat_1(k12_nattra_1(sK0,sK1))
| ~ spl13_45 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f687,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,sK1))
| spl13_45 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f688,plain,
( ~ spl13_42
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45
| spl13_30 ),
inference(avatar_split_clause,[],[f671,f558,f685,f681,f677,f673]) ).
fof(f689,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_42 ),
inference(resolution,[],[f675,f131]) ).
fof(f690,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_42 ),
inference(forward_subsumption_resolution,[],[f689,f116]) ).
fof(f691,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_42 ),
inference(forward_subsumption_resolution,[],[f690,f115]) ).
fof(f692,plain,
( ~ l1_cat_1(sK2)
| spl13_42 ),
inference(forward_subsumption_resolution,[],[f691,f120]) ).
fof(f693,plain,
( $false
| spl13_42 ),
inference(forward_subsumption_resolution,[],[f692,f119]) ).
fof(f694,plain,
spl13_42,
inference(avatar_contradiction_clause,[],[f693]) ).
fof(f724,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_43 ),
inference(resolution,[],[f679,f132]) ).
fof(f725,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_43 ),
inference(forward_subsumption_resolution,[],[f724,f116]) ).
fof(f726,plain,
( ~ v2_cat_1(sK2)
| ~ l1_cat_1(sK2)
| spl13_43 ),
inference(forward_subsumption_resolution,[],[f725,f115]) ).
fof(f727,plain,
( ~ l1_cat_1(sK2)
| spl13_43 ),
inference(forward_subsumption_resolution,[],[f726,f120]) ).
fof(f728,plain,
( $false
| spl13_43 ),
inference(forward_subsumption_resolution,[],[f727,f119]) ).
fof(f729,plain,
spl13_43,
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f737,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_44 ),
inference(resolution,[],[f683,f131]) ).
fof(f738,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_44 ),
inference(forward_subsumption_resolution,[],[f737,f116]) ).
fof(f739,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_44 ),
inference(forward_subsumption_resolution,[],[f738,f115]) ).
fof(f740,plain,
( ~ l1_cat_1(sK1)
| spl13_44 ),
inference(forward_subsumption_resolution,[],[f739,f118]) ).
fof(f741,plain,
( $false
| spl13_44 ),
inference(forward_subsumption_resolution,[],[f740,f117]) ).
fof(f742,plain,
spl13_44,
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f772,plain,
( ~ v2_cat_1(sK0)
| ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_45 ),
inference(resolution,[],[f687,f132]) ).
fof(f773,plain,
( ~ l1_cat_1(sK0)
| ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_45 ),
inference(forward_subsumption_resolution,[],[f772,f116]) ).
fof(f774,plain,
( ~ v2_cat_1(sK1)
| ~ l1_cat_1(sK1)
| spl13_45 ),
inference(forward_subsumption_resolution,[],[f773,f115]) ).
fof(f775,plain,
( ~ l1_cat_1(sK1)
| spl13_45 ),
inference(forward_subsumption_resolution,[],[f774,f118]) ).
fof(f776,plain,
( $false
| spl13_45 ),
inference(forward_subsumption_resolution,[],[f775,f117]) ).
fof(f777,plain,
spl13_45,
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f815,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,sK1))
| ~ l1_cat_1(k12_nattra_1(sK0,sK1))
| ~ v2_cat_1(k12_nattra_1(sK0,sK2))
| ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_31 ),
inference(resolution,[],[f564,f130]) ).
fof(f816,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,sK1))
| ~ v2_cat_1(k12_nattra_1(sK0,sK2))
| ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_31
| ~ spl13_45 ),
inference(forward_subsumption_resolution,[],[f815,f686]) ).
fof(f817,plain,
( ~ v2_cat_1(k12_nattra_1(sK0,sK2))
| ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_31
| ~ spl13_44
| ~ spl13_45 ),
inference(forward_subsumption_resolution,[],[f816,f682]) ).
fof(f818,plain,
( ~ l1_cat_1(k12_nattra_1(sK0,sK2))
| spl13_31
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45 ),
inference(forward_subsumption_resolution,[],[f817,f678]) ).
fof(f819,plain,
( $false
| spl13_31
| ~ spl13_42
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45 ),
inference(forward_subsumption_resolution,[],[f818,f674]) ).
fof(f820,plain,
( spl13_31
| ~ spl13_42
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45 ),
inference(avatar_contradiction_clause,[],[f819]) ).
cnf(s17,plain,
( ~ spl13_28
| ~ spl13_29
| ~ spl13_30
| ~ spl13_31 ),
inference(sat_conversion,[],[f565]) ).
cnf(s19,plain,
( spl13_28
| ~ spl13_32
| ~ spl13_33 ),
inference(sat_conversion,[],[f582]) ).
cnf(s20,plain,
spl13_32,
inference(sat_conversion,[],[f588]) ).
cnf(s25,plain,
spl13_33,
inference(sat_conversion,[],[f641]) ).
cnf(s30,plain,
( spl13_29
| ~ spl13_32
| ~ spl13_33 ),
inference(sat_conversion,[],[f670]) ).
cnf(s31,plain,
( spl13_30
| ~ spl13_42
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45 ),
inference(sat_conversion,[],[f688]) ).
cnf(s32,plain,
spl13_42,
inference(sat_conversion,[],[f694]) ).
cnf(s37,plain,
spl13_43,
inference(sat_conversion,[],[f729]) ).
cnf(s38,plain,
spl13_44,
inference(sat_conversion,[],[f742]) ).
cnf(s43,plain,
spl13_45,
inference(sat_conversion,[],[f777]) ).
cnf(s49,plain,
( spl13_31
| ~ spl13_42
| ~ spl13_43
| ~ spl13_44
| ~ spl13_45 ),
inference(sat_conversion,[],[f820]) ).
cnf(s62,plain,
spl13_31,
inference(rat,[],[s49,s43,s38,s37,s32]) ).
cnf(s67,plain,
spl13_30,
inference(rat,[],[s31,s43,s38,s37,s32]) ).
cnf(s76,plain,
spl13_29,
inference(rat,[],[s30,s25,s20]) ).
cnf(s81,plain,
spl13_28,
inference(rat,[],[s19,s25,s20]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s17,s62,s67,s76,s81]) ).
fof(f821,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT032+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 21:23:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.27 % (2362178)Will run a generic schedule for satisfiability detection.
% 0.10/0.27 % (2362185)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1093607014:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.27 % (2362183)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1445924322_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.27 % (2362186)dis+10_1_sil=32000:sp=arity:random_seed=3475607649:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.27 % (2362187)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3660613808:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.27 % (2362188)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2214866842:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.27 % (2362189)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1056941224:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.27 % (2362184)% WARNING: option uhcvi not known.
% 0.10/0.27 % TRYING [1]
% 0.10/0.27 % TRYING [2]
% 0.10/0.27 % (2362184)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2971459394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.27 % TRYING [3]
% 0.10/0.27 % (2362186) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2362178-2362186"...
% 0.10/0.27 % (2362186)...printing done.
% 0.10/0.27 % (2362186)Refutation found. Thanks to Tanya!
% 0.10/0.27 % SZS status Theorem for theBenchmark
% 0.10/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.27 % (2362186)------------------------------
% 0.10/0.27 % (2362186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.27 % (2362186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.27 % (2362186)CaDiCaL version: 2.1.3
% 0.10/0.27 % (2362186)Termination reason: Refutation
% 0.10/0.27 % (2362186)Time elapsed: 0.020 s
% 0.10/0.27 % (2362186)Peak memory usage: 12 MB
% 0.10/0.27 % (2362186)Instructions burned: 31 (million)
% 0.10/0.27 % (2362178)Success in time 0.054 s
% 0.10/0.27 % Vampire exiting
%------------------------------------------------------------------------------