%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP645+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:15:15 AM UTC 2026
% Result : Theorem 3.11s 1.32s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 12 unt; 0 def)
% Number of atoms : 388 ( 44 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 568 ( 243 ~; 237 |; 71 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 68 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f11,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
=> ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f15,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0)
& m1_group_2(X2,X0) )
=> ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).
fof(f55,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsubgr) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2))
& v1_group_1(X2)
& m1_group_2(X2,X0) )
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2))
& v1_group_1(X2)
& m1_group_2(X2,X0) )
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2))
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2))
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f78]) ).
fof(f87,plain,
! [X0] :
( ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f88,plain,
! [X0] :
( ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f87]) ).
fof(f91,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),sK2))
& v1_group_1(sK2)
& m1_group_2(sK2,sK0)
& v1_group_1(sK1)
& m1_group_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f70]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ? [X2] :
( k1_funct_1(X1,X2) != u1_struct_0(X2)
& v1_group_1(X2)
& m1_group_2(X2,X0) ) )
& ( ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ? [X2] :
( k1_funct_1(X1,X2) != u1_struct_0(X2)
& v1_group_1(X2)
& m1_group_2(X2,X0) ) )
& ( ! [X3] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ( k1_funct_1(X1,sK3(X0,X1)) != u1_struct_0(sK3(X0,X1))
& v1_group_1(sK3(X0,X1))
& m1_group_2(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f93]) ).
fof(f105,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f106,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f107,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f108,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f109,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f110,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f111,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f112,plain,
v1_group_1(sK2),
inference(cnf_transformation,[],[f91]) ).
fof(f113,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),sK2)),
inference(cnf_transformation,[],[f91]) ).
fof(f115,plain,
! [X2,X0,X1] :
( m1_group_2(k9_group_2(X0,X1,X2),X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
! [X2,X0,X1] :
( v1_group_1(k9_group_2(X0,X1,X2))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
! [X2,X0,X1] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) = u1_struct_0(k9_group_2(X0,X1,X2))
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X3,X0,X1] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| k1_latsubgr(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f136,plain,
! [X0] :
( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f137,plain,
! [X0] :
( v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
! [X0] :
( v1_funct_1(k1_latsubgr(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f215,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ v1_group_1(sK2)
| ~ m1_group_2(sK2,sK0)
| ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f113,f118]) ).
fof(f221,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(sK2,sK0)
| ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f215,f112]) ).
fof(f222,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ v1_group_1(sK1)
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f221,f111]) ).
fof(f223,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f222,f110]) ).
fof(f224,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f223,f109]) ).
fof(f225,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f224,f108]) ).
fof(f226,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f225,f107]) ).
fof(f227,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f226,f106]) ).
fof(f228,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[],[f227,f105]) ).
fof(f238,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f144,f138]) ).
fof(f239,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f238,f137]) ).
fof(f240,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f239,f136]) ).
fof(f243,plain,
( u1_struct_0(k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f228,f240]) ).
fof(f250,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(trivial_inequality_removal,[],[f243]) ).
fof(f252,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f250,f108]) ).
fof(f256,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f252,f107]) ).
fof(f259,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f256,f106]) ).
fof(f262,plain,
( ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| ~ v1_group_1(k9_group_2(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[],[f259,f105]) ).
fof(f275,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(resolution,[],[f262,f115]) ).
fof(f276,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f275,f116]) ).
fof(f277,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f276,f108]) ).
fof(f278,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f277,f107]) ).
fof(f279,plain,
( ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f278,f106]) ).
fof(f280,plain,
( ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f279,f105]) ).
fof(f281,plain,
~ m1_group_2(sK2,sK0),
inference(forward_subsumption_resolution,[],[f280,f109]) ).
fof(f282,plain,
$false,
inference(forward_subsumption_resolution,[],[f281,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP645+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 % Computer : n018.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sun Sep 27 10:25:53 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.46 Running first-order theorem proving
% 0.11/0.46 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.11/1.32 % (2122112)Detected formulas, will run a generic FOF schedule.
% 3.11/1.32 % (2122117)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=2454303693:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.11/1.32 % (2122120)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1997255181:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.11/1.32 % (2122123)dis-21_1_sil=8000:lcm=predicate:random_seed=21872372: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)
% 3.11/1.32 % (2122121)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=585997515:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.11/1.32 % (2122119)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=3168250099:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.11/1.32 % (2122118)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=1059739800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.11/1.32 % (2122122)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=84651147:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.11/1.32 % (2122120)Refutation not found, incomplete strategy
% 3.11/1.32 % (2122120)------------------------------
% 3.11/1.32 % (2122120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (2122120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (2122120)CaDiCaL version: 2.1.3
% 3.11/1.32 % (2122120)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.32 % (2122120)Time elapsed: 0.003 s
% 3.11/1.32 % (2122120)Peak memory usage: 88 MB
% 3.11/1.32 % (2122120)Instructions burned: 2 (million)
% 3.11/1.32 % (2122121)First to succeed.
% 3.11/1.32 % (2122121)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2122112"
% 3.11/1.32 % (2122122)Also succeeded, but the first one will report.
% 3.11/1.32 % (2122123)Instruction limit reached!
% 3.11/1.32 % (2122123)------------------------------
% 3.11/1.32 % (2122123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.32 % (2122123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.32 % (2122123)CaDiCaL version: 2.1.3
% 3.11/1.32 % (2122123)Termination reason: Instruction limit
% 3.11/1.32 % (2122123)Termination phase: Saturation
% 3.11/1.32 % (2122123)Time elapsed: 0.070 s
% 3.11/1.32 % (2122123)Peak memory usage: 91 MB
% 3.11/1.32 % (2122123)Instructions burned: 129 (million)
% 3.11/1.32 % (2122131)lrs+10_1_sil=8000:sp=occurrence:random_seed=1278751104:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.11/1.32 % (2122120)------------------------------
% 3.11/1.32 % (2122120)------------------------------
% 3.11/1.32 % (2122121)Refutation found. Thanks to Tanya!
% 3.11/1.32 % SZS status Theorem for theBenchmark
% 3.11/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.42 % (2122121)------------------------------
% 3.55/1.42 % (2122121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.42 % (2122121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.42 % (2122121)CaDiCaL version: 2.1.3
% 3.55/1.42 % (2122121)Termination reason: Refutation
% 3.55/1.42 % (2122121)Time elapsed: 0.008 s
% 3.55/1.42 % (2122121)Peak memory usage: 88 MB
% 3.55/1.42 % (2122121)Instructions burned: 11 (million)
% 3.55/1.42 % (2122121)------------------------------
% 3.55/1.42 % (2122121)------------------------------
% 3.55/1.42 % (2122112)Success in time 0.429 s
% 3.55/1.42 % Vampire exiting
%------------------------------------------------------------------------------