%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 10:18:21 AM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 360 ( 36 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 502 ( 192 ~; 198 |; 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(f71,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(f72,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,[],[f71]) ).
fof(f113,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(f114,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,[],[f113]) ).
fof(f117,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(f118,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,[],[f117]) ).
fof(f119,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(f120,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,[],[f119]) ).
fof(f126,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(f127,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,[],[f126]) ).
fof(f128,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)],[f72]) ).
fof(f144,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,[],[f114]) ).
fof(f145,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f148,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f153,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f154,plain,
m1_group_2(sK3,sK0),
inference(cnf_transformation,[],[f128]) ).
fof(f158,plain,
m1_subset_1(sK5,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f128]) ).
fof(f159,plain,
sK5 = k2_xboole_0(u1_struct_0(sK2),u1_struct_0(sK3)),
inference(cnf_transformation,[],[f128]) ).
fof(f160,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,[],[f128]) ).
fof(f221,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,[],[f144]) ).
fof(f224,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)
| m1_group_2(k5_group_4(X0,X1),X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f225,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,[],[f118]) ).
fof(f226,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,[],[f120]) ).
fof(f227,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,[],[f120]) ).
fof(f235,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,[],[f127]) ).
fof(f237,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,[],[f235]) ).
fof(f550,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,[],[f237,f159]) ).
fof(f578,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,[],[f550,f221]) ).
fof(f579,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,[],[f578]) ).
fof(f581,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,[],[f579,f225]) ).
fof(f583,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,[],[f581,f224]) ).
fof(f585,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,[],[f583,f227]) ).
fof(f587,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) ),
inference(forward_subsumption_resolution,[],[f585,f226]) ).
fof(f653,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)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(resolution,[],[f587,f158]) ).
fof(f655,plain,
( ~ m1_group_2(sK2,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(forward_subsumption_resolution,[],[f653,f154]) ).
fof(f656,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(forward_subsumption_resolution,[],[f655,f153]) ).
fof(f657,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(forward_subsumption_resolution,[],[f656,f148]) ).
fof(f658,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(forward_subsumption_resolution,[],[f657,f147]) ).
fof(f659,plain,
( ~ l1_group_1(sK0)
| k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5) ),
inference(forward_subsumption_resolution,[],[f658,f146]) ).
fof(f660,plain,
k8_group_4(sK0,sK2,sK3) = k5_group_4(sK0,sK5),
inference(forward_subsumption_resolution,[],[f659,f145]) ).
fof(f663,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))),
inference(superposition,[],[f160,f660]) ).
fof(f668,plain,
$false,
inference(trivial_inequality_removal,[],[f663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:24:45 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50 % (1451034)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (1451043)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2580156894:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % (1451040)% WARNING: option uhcvi not known.
% 0.18/0.50 % (1451039)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2647289050_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % (1451040)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4194243586:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (1451041)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=105802662:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (1451042)dis+10_1_sil=32000:sp=arity:random_seed=3979676593:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (1451044)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1035816861:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (1451045)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2961123515:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % TRYING [1]
% 0.18/0.50 % TRYING [2]
% 0.18/0.50 % TRYING [3]
% 0.18/0.50 % (1451042) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1451034-1451042"...
% 0.18/0.50 % TRYING [4]
% 0.18/0.50 % (1451042)...printing done.
% 0.18/0.50 % (1451042)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (1451042)------------------------------
% 0.18/0.50 % (1451042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (1451042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (1451042)CaDiCaL version: 2.1.3
% 0.18/0.50 % (1451042)Termination reason: Refutation
% 0.18/0.50 % (1451042)Time elapsed: 0.015 s
% 0.18/0.50 % (1451042)Peak memory usage: 12 MB
% 0.18/0.50 % (1451042)Instructions burned: 21 (million)
% 0.18/0.50 % (1451034)Success in time 0.064 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------