%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP640+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 : n003.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 2.11s 1.13s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 367 ( 29 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 522 ( 205 ~; 205 |; 87 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 90 ( 78 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_group_2(X3,X0)
=> ! [X4] :
( ( v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
=> k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) = k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_group_2(X3,X0)
=> ! [X4] :
( ( v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
=> k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) = k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5))) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f51,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& v1_group_1(X1)
& m1_group_2(X1,X0)
& v1_group_1(X2)
& m1_group_2(X2,X0) )
=> ( r1_group_2(X0,X1,X2)
<=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
fof(f55,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( v1_group_1(k5_group_4(X0,X1))
& m1_group_2(k5_group_4(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_4) ).
fof(f56,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(k8_group_4(X0,X1,X2))
& m1_group_2(k8_group_4(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_4) ).
fof(f64,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> ( X3 = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
=> r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_latsubgr) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) != k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5)))
& X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
& m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1)) )
& m1_group_2(X3,X0) )
& m1_group_2(X2,X0) )
& ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k8_group_4(X0,X2,X3))) != k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X4,u1_struct_0(k5_group_4(X0,X5)))
& X5 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
& m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_funct_1(X4)
& v1_funct_2(X4,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X4,u1_struct_0(X0),u1_struct_0(X1)) )
& m1_group_2(X3,X0) )
& m1_group_2(X2,X0) )
& ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f66]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ m1_group_2(X2,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,[],[f64]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ m1_group_2(X2,X0) )
| ~ 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,X2] :
( ( v1_group_1(k8_group_4(X0,X1,X2))
& m1_group_2(k8_group_4(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,[],[f56]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( v1_group_1(k8_group_4(X0,X1,X2))
& m1_group_2(k8_group_4(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,[],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( ( v1_group_1(k5_group_4(X0,X1))
& m1_group_2(k5_group_4(X0,X1),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f55]) ).
fof(f83,plain,
! [X0,X1] :
( ( v1_group_1(k5_group_4(X0,X1))
& m1_group_2(k5_group_4(X0,X1),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f82]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( r1_group_2(X0,X1,X2)
<=> X1 = X2 )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( r1_group_2(X0,X1,X2)
<=> X1 = X2 )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(flattening,[],[f85]) ).
fof(f93,plain,
( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k8_group_4(sK0,sK2,sK3))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5)))
& sK5 = k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3))
& m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0)))
& v1_funct_1(sK4)
& v1_funct_2(sK4,u1_struct_0(sK0),u1_struct_0(sK1))
& m2_relset_1(sK4,u1_struct_0(sK0),u1_struct_0(sK1))
& m1_group_2(sK3,sK0)
& m1_group_2(sK2,sK0)
& ~ v3_struct_0(sK1)
& v3_group_1(sK1)
& v4_group_1(sK1)
& l1_group_1(sK1)
& ~ 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,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f67]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( ( r1_group_2(X0,X1,X2)
| X1 != X2 )
& ( X1 = X2
| ~ r1_group_2(X0,X1,X2) ) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f105,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f106,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f107,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f108,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f113,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f114,plain,
m1_group_2(sK3,sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f118,plain,
m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f93]) ).
fof(f119,plain,
sK5 = k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3)),
inference(cnf_transformation,[],[f93]) ).
fof(f120,plain,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k8_group_4(sK0,sK2,sK3))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5))),
inference(cnf_transformation,[],[f93]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) != X3
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(X2,X0)
| ~ 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(f136,plain,
! [X2,X0,X1] :
( m1_group_2(k8_group_4(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,[],[f79]) ).
fof(f137,plain,
! [X2,X0,X1] :
( v1_group_1(k8_group_4(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,[],[f79]) ).
fof(f140,plain,
! [X0,X1] :
( m1_group_2(k5_group_4(X0,X1),X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v1_group_1(k5_group_4(X0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ r1_group_2(X0,X1,X2)
| X1 = X2
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f155,plain,
! [X2,X0,X1] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))))
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f231,plain,
! [X0] :
( r1_group_2(X0,k8_group_4(X0,sK2,sK3),k5_group_4(X0,sK5))
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(superposition,[],[f155,f119]) ).
fof(f241,plain,
! [X0] :
( ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(k8_group_4(X0,sK2,sK3))
| ~ m1_group_2(k8_group_4(X0,sK2,sK3),X0)
| ~ v1_group_1(k5_group_4(X0,sK5))
| ~ m1_group_2(k5_group_4(X0,sK5),X0) ),
inference(resolution,[],[f231,f149]) ).
fof(f242,plain,
! [X0] :
( ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| ~ v1_group_1(k8_group_4(X0,sK2,sK3))
| ~ m1_group_2(k8_group_4(X0,sK2,sK3),X0)
| ~ v1_group_1(k5_group_4(X0,sK5))
| ~ m1_group_2(k5_group_4(X0,sK5),X0) ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f243,plain,
! [X0] :
( ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| ~ v1_group_1(k8_group_4(X0,sK2,sK3))
| ~ m1_group_2(k8_group_4(X0,sK2,sK3),X0)
| ~ m1_group_2(k5_group_4(X0,sK5),X0) ),
inference(forward_subsumption_resolution,[],[f242,f141]) ).
fof(f244,plain,
! [X0] :
( ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| ~ v1_group_1(k8_group_4(X0,sK2,sK3))
| ~ m1_group_2(k8_group_4(X0,sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f243,f140]) ).
fof(f245,plain,
! [X0] :
( ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| ~ m1_group_2(k8_group_4(X0,sK2,sK3),X0) ),
inference(forward_subsumption_resolution,[],[f244,f137]) ).
fof(f246,plain,
! [X0] :
( k8_group_4(X0,sK2,sK3) = k5_group_4(X0,sK5)
| ~ m1_group_2(sK3,X0)
| ~ m1_group_2(sK2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(forward_subsumption_resolution,[],[f245,f136]) ).
fof(f247,plain,
( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5))) != k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK4,u1_struct_0(k5_group_4(sK0,sK5)))
| ~ m1_group_2(sK3,sK0)
| ~ m1_group_2(sK2,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(superposition,[],[f120,f246]) ).
fof(f256,plain,
( ~ m1_group_2(sK3,sK0)
| ~ m1_group_2(sK2,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(trivial_inequality_removal,[],[f247]) ).
fof(f258,plain,
( ~ m1_group_2(sK2,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f256,f114]) ).
fof(f261,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f258,f113]) ).
fof(f262,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f261,f108]) ).
fof(f263,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f262,f107]) ).
fof(f264,plain,
( ~ l1_group_1(sK0)
| ~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f263,f106]) ).
fof(f265,plain,
~ m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))),
inference(forward_subsumption_resolution,[],[f264,f105]) ).
fof(f266,plain,
$false,
inference(forward_subsumption_resolution,[],[f265,f118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:23:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.11/1.13 % (309093)Detected formulas, will run a generic FOF schedule.
% 2.11/1.13 % (309102)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3346389528:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.11/1.13 % (309102)First to succeed.
% 2.11/1.13 % (309102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-309093"
% 2.11/1.13 % (309100)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=1338793866:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.11/1.13 % (309099)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=4253013315:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.11/1.13 % (309098)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=3339007426:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.11/1.13 % (309103)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1348567478:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.11/1.13 % (309101)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1691725508:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.11/1.13 % (309101)Refutation not found, incomplete strategy
% 2.11/1.13 % (309101)------------------------------
% 2.11/1.13 % (309101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.13 % (309101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.13 % (309101)CaDiCaL version: 2.1.3
% 2.11/1.13 % (309101)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.13 % (309101)Time elapsed: 0.004 s
% 2.11/1.13 % (309101)Peak memory usage: 88 MB
% 2.11/1.13 % (309101)Instructions burned: 4 (million)
% 2.11/1.13 % (309104)dis-21_1_sil=8000:lcm=predicate:random_seed=3987803160: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)
% 2.11/1.13 % (309103)Also succeeded, but the first one will report.
% 2.11/1.13 % (309104)Instruction limit reached!
% 2.11/1.13 % (309104)------------------------------
% 2.11/1.13 % (309104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.13 % (309104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.13 % (309104)CaDiCaL version: 2.1.3
% 2.11/1.13 % (309104)Termination reason: Instruction limit
% 2.11/1.13 % (309104)Termination phase: Saturation
% 2.11/1.13 % (309104)Time elapsed: 0.073 s
% 2.11/1.13 % (309104)Peak memory usage: 92 MB
% 2.11/1.13 % (309104)Instructions burned: 130 (million)
% 2.11/1.13 % (309102)Refutation found. Thanks to Tanya!
% 2.11/1.13 % SZS status Theorem for theBenchmark
% 2.11/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/1.22 % (309102)------------------------------
% 2.44/1.22 % (309102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/1.22 % (309102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/1.22 % (309102)CaDiCaL version: 2.1.3
% 2.44/1.22 % (309102)Termination reason: Refutation
% 2.44/1.22 % (309102)Time elapsed: 0.004 s
% 2.44/1.22 % (309102)Peak memory usage: 88 MB
% 2.44/1.22 % (309102)Instructions burned: 10 (million)
% 2.44/1.22 % (309102)------------------------------
% 2.44/1.22 % (309102)------------------------------
% 2.44/1.22 % (309093)Success in time 0.272 s
% 2.44/1.22 % Vampire exiting
%------------------------------------------------------------------------------