%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP639+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 : n006.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 10:15:12 AM UTC 2026
% Result : Theorem 2.67s 1.29s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 82 ( 18 unt; 3 def)
% Number of atoms : 375 ( 19 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 475 ( 182 ~; 177 |; 90 &)
% ( 7 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 128 ( 0 sgn 117 !; 11 ?)
% 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] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_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] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
=> r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3)))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f9,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> ( X2 = k5_group_4(X0,X1)
<=> ( r1_tarski(X1,u1_struct_0(X2))
& ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X0) )
=> ( r1_tarski(X1,u1_struct_0(X3))
=> m1_group_2(X2,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_4) ).
fof(f15,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(f22,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m1_relset_1(X2,X0,X1) )
=> k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f45,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f47,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X0,X1)
=> r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
fof(f57,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
& ~ 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(f58,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,X3),k2_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(k5_group_4(X0,X3))))
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_funct_1(X2)
& v1_funct_2(X2,u1_struct_0(X0),u1_struct_0(X1))
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
& ~ 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,[],[f57]) ).
fof(f64,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k5_group_4(X0,X1)
<=> ( r1_tarski(X1,u1_struct_0(X2))
& ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) ) ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k5_group_4(X0,X1)
<=> ( r1_tarski(X1,u1_struct_0(X2))
& ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) ) ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(flattening,[],[f69]) ).
fof(f75,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,[],[f15]) ).
fof(f76,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,[],[f75]) ).
fof(f80,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f96,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f95]) ).
fof(f106,plain,
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3))))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& v1_funct_1(sK2)
& v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
& ~ 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]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f58]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_group_4(X0,X1)
| ~ r1_tarski(X1,u1_struct_0(X2))
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& v1_group_1(X3)
& m1_group_2(X3,X0) ) )
& ( ( r1_tarski(X1,u1_struct_0(X2))
& ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) ) )
| k5_group_4(X0,X1) != X2 ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(nnf_transformation,[],[f70]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_group_4(X0,X1)
| ~ r1_tarski(X1,u1_struct_0(X2))
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& v1_group_1(X3)
& m1_group_2(X3,X0) ) )
& ( ( r1_tarski(X1,u1_struct_0(X2))
& ! [X3] :
( m1_group_2(X2,X3)
| ~ r1_tarski(X1,u1_struct_0(X3))
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) ) )
| k5_group_4(X0,X1) != X2 ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_group_4(X0,X1)
| ~ r1_tarski(X1,u1_struct_0(X2))
| ? [X3] :
( ~ m1_group_2(X2,X3)
& r1_tarski(X1,u1_struct_0(X3))
& v1_group_1(X3)
& m1_group_2(X3,X0) ) )
& ( ( r1_tarski(X1,u1_struct_0(X2))
& ! [X4] :
( m1_group_2(X2,X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| ~ v1_group_1(X4)
| ~ m1_group_2(X4,X0) ) )
| k5_group_4(X0,X1) != X2 ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = k5_group_4(X0,X1)
| ~ r1_tarski(X1,u1_struct_0(X2))
| ( ~ m1_group_2(X2,sK4(X0,X1,X2))
& r1_tarski(X1,u1_struct_0(sK4(X0,X1,X2)))
& v1_group_1(sK4(X0,X1,X2))
& m1_group_2(sK4(X0,X1,X2),X0) ) )
& ( ( r1_tarski(X1,u1_struct_0(X2))
& ! [X4] :
( m1_group_2(X2,X4)
| ~ r1_tarski(X1,u1_struct_0(X4))
| ~ v1_group_1(X4)
| ~ m1_group_2(X4,X0) ) )
| k5_group_4(X0,X1) != X2 ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ 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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f109]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f127,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f128,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f129,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f130,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f135,plain,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f106]) ).
fof(f136,plain,
v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f106]) ).
fof(f137,plain,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f106]) ).
fof(f138,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f106]) ).
fof(f139,plain,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(cnf_transformation,[],[f106]) ).
fof(f144,plain,
! [X2,X0,X1] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f153,plain,
! [X2,X0,X1] :
( r1_tarski(X1,u1_struct_0(X2))
| k5_group_4(X0,X1) != X2
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0)
| ~ 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) ),
inference(cnf_transformation,[],[f110]) ).
fof(f161,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,[],[f76]) ).
fof(f162,plain,
! [X0,X1] :
( v1_group_1(k5_group_4(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))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f167,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( ~ v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f201,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f204,plain,
! [X2,X0,X1] :
( r1_tarski(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f214,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ v1_group_1(k5_group_4(X0,X1))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ 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) ),
inference(equality_resolution,[],[f153]) ).
fof(f295,definition,
( spl19_5
<=> m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f296,plain,
( m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| spl19_5 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f303,plain,
( ~ m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| spl19_5 ),
inference(resolution,[],[f297,f201]) ).
fof(f304,plain,
( $false
| spl19_5 ),
inference(forward_subsumption_resolution,[],[f303,f135]) ).
fof(f305,plain,
spl19_5,
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f324,plain,
! [X0] :
( ~ v1_funct_1(sK2)
| k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0)
| ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)) ),
inference(resolution,[],[f200,f136]) ).
fof(f329,plain,
! [X0] :
( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0)
| ~ m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f324,f137]) ).
fof(f331,plain,
( ! [X0] : k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0)
| ~ spl19_5 ),
inference(forward_subsumption_resolution,[],[f329,f296]) ).
fof(f335,plain,
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,sK3),k9_relat_1(sK2,u1_struct_0(k5_group_4(sK0,sK3))))
| ~ spl19_5 ),
inference(superposition,[],[f139,f331]) ).
fof(f338,plain,
( ~ r1_tarski(k9_relat_1(sK2,sK3),k9_relat_1(sK2,u1_struct_0(k5_group_4(sK0,sK3))))
| ~ spl19_5 ),
inference(forward_demodulation,[],[f335,f331]) ).
fof(f346,plain,
( ~ r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| ~ v1_relat_1(sK2)
| ~ spl19_5 ),
inference(resolution,[],[f338,f204]) ).
fof(f349,definition,
( spl19_9
<=> v1_relat_1(sK2) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
fof(f351,plain,
( ~ v1_relat_1(sK2)
| spl19_9 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f353,definition,
( spl19_10
<=> r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3))) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f355,plain,
( ~ r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| spl19_10 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,plain,
( ~ spl19_9
| ~ spl19_10
| ~ spl19_5 ),
inference(avatar_split_clause,[],[f346,f295,f353,f349]) ).
fof(f357,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ 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) ),
inference(forward_subsumption_resolution,[],[f214,f162]) ).
fof(f358,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(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) ),
inference(forward_subsumption_resolution,[],[f357,f161]) ).
fof(f359,plain,
( ! [X0,X1] : ~ m1_subset_1(sK2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| spl19_9 ),
inference(resolution,[],[f351,f144]) ).
fof(f361,plain,
( ! [X0,X1] : ~ m2_relset_1(sK2,X0,X1)
| spl19_9 ),
inference(resolution,[],[f359,f167]) ).
fof(f364,plain,
( $false
| spl19_9 ),
inference(resolution,[],[f361,f135]) ).
fof(f366,plain,
spl19_9,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f367,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_10 ),
inference(resolution,[],[f355,f358]) ).
fof(f369,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f367,f138]) ).
fof(f370,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f369,f130]) ).
fof(f371,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f370,f129]) ).
fof(f372,plain,
( ~ l1_group_1(sK0)
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f371,f128]) ).
fof(f373,plain,
( $false
| spl19_10 ),
inference(forward_subsumption_resolution,[],[f372,f127]) ).
fof(f374,plain,
spl19_10,
inference(avatar_contradiction_clause,[],[f373]) ).
cnf(s3,plain,
spl19_5,
inference(sat_conversion,[],[f305]) ).
cnf(s5,plain,
( ~ spl19_5
| ~ spl19_9
| ~ spl19_10 ),
inference(sat_conversion,[],[f356]) ).
cnf(s6,plain,
spl19_9,
inference(sat_conversion,[],[f366]) ).
cnf(s7,plain,
spl19_10,
inference(sat_conversion,[],[f374]) ).
cnf(s8,plain,
~ spl19_5,
inference(rat,[],[s5,s7,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8]) ).
fof(f375,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP639+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 : n006.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 10:20:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 2.67/1.29 % (2771468)Detected formulas, will run a generic FOF schedule.
% 2.67/1.29 % (2771477)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2418061227:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.29 % (2771477)Refutation not found, incomplete strategy
% 2.67/1.29 % (2771477)------------------------------
% 2.67/1.29 % (2771477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2771477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2771477)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2771477)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.29 % (2771477)Time elapsed: 0.004 s
% 2.67/1.29 % (2771477)Peak memory usage: 88 MB
% 2.67/1.29 % (2771477)Instructions burned: 11 (million)
% 2.67/1.29 % (2771473)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=4069961514:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.29 % (2771474)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=3365763827:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.29 % (2771476)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4043875623:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.29 % (2771475)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=1892531740:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.29 % (2771476)Refutation not found, incomplete strategy
% 2.67/1.29 % (2771476)------------------------------
% 2.67/1.29 % (2771476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2771476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2771476)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2771476)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.29 % (2771476)Time elapsed: 0.004 s
% 2.67/1.29 % (2771476)Peak memory usage: 88 MB
% 2.67/1.29 % (2771476)Instructions burned: 4 (million)
% 2.67/1.29 % (2771479)dis-21_1_sil=8000:lcm=predicate:random_seed=1989652439: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)
% 2.67/1.29 % (2771478)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2750347723:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.29 % (2771478)First to succeed.
% 2.67/1.29 % (2771478)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2771468"
% 2.67/1.29 % (2771479)Instruction limit reached!
% 2.67/1.29 % (2771479)------------------------------
% 2.67/1.29 % (2771479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2771479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2771479)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2771479)Termination reason: Instruction limit
% 2.67/1.29 % (2771479)Termination phase: Saturation
% 2.67/1.29 % (2771479)Time elapsed: 0.073 s
% 2.67/1.29 % (2771479)Peak memory usage: 92 MB
% 2.67/1.29 % (2771479)Instructions burned: 130 (million)
% 2.67/1.29 % (2771477)------------------------------
% 2.67/1.29 % (2771477)------------------------------
% 2.67/1.29 % (2771488)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1903154033:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.67/1.29 % (2771487)lrs+10_1_sil=8000:sp=occurrence:random_seed=1178851762:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.67/1.29 % (2771487)Also succeeded, but the first one will report.
% 2.67/1.29 % (2771488)Instruction limit reached!
% 2.67/1.29 % (2771488)------------------------------
% 2.67/1.29 % (2771488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2771488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2771488)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2771488)Termination reason: Instruction limit
% 2.67/1.29 % (2771488)Termination phase: Saturation
% 2.67/1.29 % (2771488)Time elapsed: 0.048 s
% 2.67/1.29 % (2771488)Peak memory usage: 89 MB
% 2.67/1.29 % (2771488)Instructions burned: 158 (million)
% 2.67/1.29 % (2771476)------------------------------
% 2.67/1.29 % (2771476)------------------------------
% 2.67/1.29 % (2771478)Refutation found. Thanks to Tanya!
% 2.67/1.29 % SZS status Theorem for theBenchmark
% 2.67/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.38 % (2771478)------------------------------
% 3.54/1.38 % (2771478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.38 % (2771478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.38 % (2771478)CaDiCaL version: 2.1.3
% 3.54/1.38 % (2771478)Termination reason: Refutation
% 3.54/1.38 % (2771478)Time elapsed: 0.012 s
% 3.54/1.38 % (2771478)Peak memory usage: 90 MB
% 3.54/1.38 % (2771478)Instructions burned: 14 (million)
% 3.54/1.38 % (2771478)------------------------------
% 3.54/1.38 % (2771478)------------------------------
% 3.54/1.38 % (2771468)Success in time 0.434 s
% 3.54/1.38 % Vampire exiting
%------------------------------------------------------------------------------