%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP641+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 : n004.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 10:15:13 AM UTC 2026
% Result : Theorem 2.53s 1.26s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 109 ( 20 unt; 5 def)
% Number of atoms : 438 ( 39 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 561 ( 232 ~; 242 |; 63 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 6 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 86 !; 6 ?)
% 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) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_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) )
=> r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f16,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f18,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f20,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(f33,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f49,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f52,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> k2_group_1(X1) = k2_group_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_group_2) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1))
& 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(f63,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1))
& 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,[],[f62]) ).
fof(f73,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,[],[f9]) ).
fof(f74,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,[],[f73]) ).
fof(f77,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,[],[f13]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f80,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f82]) ).
fof(f90,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f91,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f90]) ).
fof(f100,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f101,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f100]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( k2_group_1(X1) = k2_group_1(X0)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( k2_group_1(X1) = k2_group_1(X0)
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f105]) ).
fof(f111,plain,
( ~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
& 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]),skolemize(X0,sK0),skolemize(X1,sK1)],[f63]) ).
fof(f112,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,[],[f74]) ).
fof(f113,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,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ( k1_funct_1(X1,sK2(X0,X1)) != u1_struct_0(sK2(X0,X1))
& v1_group_1(sK2(X0,X1))
& m1_group_2(sK2(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,[sK2]),skolemize(X2,sK2(X0,X1))],[f113]) ).
fof(f130,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f132,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f133,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f134,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f135,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f111]) ).
fof(f136,plain,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(cnf_transformation,[],[f111]) ).
fof(f148,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,[],[f114]) ).
fof(f154,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,[],[f78]) ).
fof(f155,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,[],[f78]) ).
fof(f156,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,[],[f78]) ).
fof(f157,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f158,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f159,plain,
! [X0,X1] :
( l1_group_1(X1)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f161,plain,
! [X0,X1] :
( ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f173,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f198,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f201,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k2_group_1(X0) = k2_group_1(X1)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f206,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,[],[f148]) ).
fof(f228,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| k2_group_1(X0) = k2_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f201,f131]) ).
fof(f229,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| ~ v3_group_1(sK0)
| k2_group_1(X0) = k2_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f228,f133]) ).
fof(f230,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| k2_group_1(X0) = k2_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f229,f132]) ).
fof(f231,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| k2_group_1(X0) = k2_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f230,f130]) ).
fof(f232,plain,
k2_group_1(sK0) = k2_group_1(sK1),
inference(resolution,[],[f231,f134]) ).
fof(f238,plain,
( m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ l1_group_1(sK1) ),
inference(superposition,[],[f157,f232]) ).
fof(f240,definition,
( spl17_1
<=> l1_group_1(sK1) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f241,plain,
( l1_group_1(sK1)
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( ~ l1_group_1(sK1)
| spl17_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f244,definition,
( spl17_2
<=> v3_struct_0(sK1) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f245,plain,
( ~ v3_struct_0(sK1)
| spl17_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f246,plain,
( v3_struct_0(sK1)
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl17_3
<=> m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f250,plain,
( m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ spl17_1
| spl17_2
| spl17_3 ),
inference(avatar_split_clause,[],[f238,f248,f244,f240]) ).
fof(f253,plain,
( ! [X0] :
( ~ m1_group_2(sK1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) )
| spl17_1 ),
inference(resolution,[],[f242,f159]) ).
fof(f273,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| spl17_1 ),
inference(resolution,[],[f253,f134]) ).
fof(f274,plain,
( ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f273,f133]) ).
fof(f275,plain,
( ~ l1_group_1(sK0)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f274,f132]) ).
fof(f276,plain,
( $false
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f275,f130]) ).
fof(f277,plain,
spl17_1,
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f278,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,[],[f206,f156]) ).
fof(f279,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,[],[f278,f155]) ).
fof(f280,plain,
! [X3,X0] :
( ~ v4_group_1(X0)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f279,f154]) ).
fof(f281,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f280,f131]) ).
fof(f282,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| ~ v3_group_1(sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f281,f133]) ).
fof(f283,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f282,f132]) ).
fof(f284,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| ~ v1_group_1(X0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0) ),
inference(forward_subsumption_resolution,[],[f283,f130]) ).
fof(f285,plain,
( r2_hidden(k2_group_1(sK0),u1_struct_0(sK1))
| v1_xboole_0(u1_struct_0(sK1))
| ~ spl17_3 ),
inference(resolution,[],[f250,f198]) ).
fof(f287,definition,
( spl17_7
<=> v1_xboole_0(u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f289,plain,
( v1_xboole_0(u1_struct_0(sK1))
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f291,definition,
( spl17_8
<=> r2_hidden(k2_group_1(sK0),u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f294,plain,
( spl17_7
| spl17_8
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f285,f248,f291,f287]) ).
fof(f295,plain,
( ~ v1_group_1(sK1)
| k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1) ),
inference(resolution,[],[f284,f134]) ).
fof(f298,plain,
k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1),
inference(forward_subsumption_resolution,[],[f295,f135]) ).
fof(f310,plain,
( ! [X0] :
( ~ m1_group_2(sK1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) )
| ~ spl17_2 ),
inference(resolution,[],[f246,f161]) ).
fof(f319,plain,
~ r2_hidden(k2_group_1(sK0),u1_struct_0(sK1)),
inference(superposition,[],[f136,f298]) ).
fof(f326,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl17_2 ),
inference(resolution,[],[f310,f134]) ).
fof(f327,plain,
( ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f326,f133]) ).
fof(f328,plain,
( ~ l1_group_1(sK0)
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f327,f132]) ).
fof(f329,plain,
( $false
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f328,f130]) ).
fof(f330,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f331,plain,
( v3_struct_0(sK1)
| ~ l1_struct_0(sK1)
| ~ spl17_7 ),
inference(resolution,[],[f289,f173]) ).
fof(f334,plain,
( ~ l1_struct_0(sK1)
| spl17_2
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f331,f245]) ).
fof(f335,plain,
( ~ l1_group_1(sK1)
| spl17_2
| ~ spl17_7 ),
inference(resolution,[],[f334,f158]) ).
fof(f336,plain,
( $false
| ~ spl17_1
| spl17_2
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f335,f241]) ).
fof(f337,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_7 ),
inference(avatar_contradiction_clause,[],[f336]) ).
fof(f338,plain,
~ spl17_8,
inference(avatar_split_clause,[],[f319,f291]) ).
cnf(s1,plain,
( ~ spl17_1
| spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
spl17_1,
inference(sat_conversion,[],[f277]) ).
cnf(s4,plain,
( ~ spl17_3
| spl17_7
| spl17_8 ),
inference(sat_conversion,[],[f294]) ).
cnf(s7,plain,
~ spl17_2,
inference(sat_conversion,[],[f330]) ).
cnf(s8,plain,
( ~ spl17_1
| spl17_2
| ~ spl17_7 ),
inference(sat_conversion,[],[f337]) ).
cnf(s9,plain,
~ spl17_8,
inference(sat_conversion,[],[f338]) ).
cnf(s10,plain,
( ~ spl17_3
| spl17_7 ),
inference(rat,[],[s4,s9]) ).
cnf(s11,plain,
~ spl17_7,
inference(rat,[],[s8,s7,s3]) ).
cnf(s12,plain,
~ spl17_3,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s7,s3]) ).
fof(f339,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:22:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.53/1.26 % (3300179)Detected formulas, will run a generic FOF schedule.
% 2.53/1.26 % (3300186)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=2194917561:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/1.26 % (3300187)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1971825768:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/1.26 % (3300185)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=1373949668:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/1.26 % (3300184)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=248318885:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/1.26 % (3300189)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2767696023:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/1.26 % (3300188)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3911905720:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/1.26 % (3300190)dis-21_1_sil=8000:lcm=predicate:random_seed=2189566836: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)
% 2.53/1.26 % (3300189)First to succeed.
% 2.53/1.26 % (3300189)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3300179"
% 2.53/1.26 % (3300187)Instruction limit reached!
% 2.53/1.26 % (3300187)------------------------------
% 2.53/1.26 % (3300187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (3300187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (3300187)CaDiCaL version: 2.1.3
% 2.53/1.26 % (3300187)Termination reason: Instruction limit
% 2.53/1.26 % (3300187)Termination phase: Saturation
% 2.53/1.26 % (3300187)Time elapsed: 0.050 s
% 2.53/1.26 % (3300187)Peak memory usage: 88 MB
% 2.53/1.26 % (3300187)Instructions burned: 111 (million)
% 2.53/1.26 % (3300188)Instruction limit reached!
% 2.53/1.26 % (3300188)------------------------------
% 2.53/1.26 % (3300188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (3300188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (3300188)CaDiCaL version: 2.1.3
% 2.53/1.26 % (3300188)Termination reason: Instruction limit
% 2.53/1.26 % (3300188)Termination phase: Saturation
% 2.53/1.26 % (3300188)Time elapsed: 0.056 s
% 2.53/1.26 % (3300188)Peak memory usage: 88 MB
% 2.53/1.26 % (3300188)Instructions burned: 120 (million)
% 2.53/1.26 % (3300190)Instruction limit reached!
% 2.53/1.26 % (3300190)------------------------------
% 2.53/1.26 % (3300190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (3300190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (3300190)CaDiCaL version: 2.1.3
% 2.53/1.26 % (3300190)Termination reason: Instruction limit
% 2.53/1.26 % (3300190)Termination phase: Saturation
% 2.53/1.26 % (3300190)Time elapsed: 0.070 s
% 2.53/1.26 % (3300190)Peak memory usage: 91 MB
% 2.53/1.26 % (3300190)Instructions burned: 129 (million)
% 2.53/1.26 % (3300198)lrs+10_1_sil=8000:sp=occurrence:random_seed=2794523610:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.53/1.26 % (3300198)Also succeeded, but the first one will report.
% 2.53/1.26 % (3300199)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2015102355:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.53/1.26 % (3300200)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4138338898:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.53/1.26 % (3300200)Also succeeded, but the first one will report.
% 2.53/1.26 % (3300189)Refutation found. Thanks to Tanya!
% 2.53/1.26 % SZS status Theorem for theBenchmark
% 2.53/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.35 % (3300189)------------------------------
% 3.45/1.35 % (3300189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (3300189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (3300189)CaDiCaL version: 2.1.3
% 3.45/1.35 % (3300189)Termination reason: Refutation
% 3.45/1.35 % (3300189)Time elapsed: 0.009 s
% 3.45/1.35 % (3300189)Peak memory usage: 90 MB
% 3.45/1.35 % (3300189)Instructions burned: 12 (million)
% 3.45/1.35 % (3300189)------------------------------
% 3.45/1.35 % (3300189)------------------------------
% 3.45/1.35 % (3300179)Success in time 0.421 s
% 3.45/1.35 % Vampire exiting
%------------------------------------------------------------------------------