%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 20 unt; 2 def)
% Number of atoms : 352 ( 19 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 449 ( 170 ~; 164 |; 90 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 127 ( 0 sgn 116 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
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_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,[],[f76]) ).
fof(f162,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,[],[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] :
( ~ m1_relset_1(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| k2_funct_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_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(f243,plain,
m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(resolution,[],[f201,f135]) ).
fof(f287,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f167,f144]) ).
fof(f453,plain,
! [X0] :
( ~ v1_funct_1(sK2)
| ~ v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0) ),
inference(resolution,[],[f200,f243]) ).
fof(f454,plain,
! [X0] :
( ~ v1_funct_2(sK2,u1_struct_0(sK0),u1_struct_0(sK1))
| k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f453,f137]) ).
fof(f457,plain,
! [X0] : k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k9_relat_1(sK2,X0),
inference(forward_subsumption_resolution,[],[f454,f136]) ).
fof(f462,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(f463,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,[],[f462,f161]) ).
fof(f465,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)))),
inference(superposition,[],[f139,f457]) ).
fof(f468,plain,
~ r1_tarski(k9_relat_1(sK2,sK3),k9_relat_1(sK2,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(forward_demodulation,[],[f465,f457]) ).
fof(f574,plain,
( ~ r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| ~ v1_relat_1(sK2) ),
inference(resolution,[],[f468,f204]) ).
fof(f576,definition,
( spl19_10
<=> v1_relat_1(sK2) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f580,definition,
( spl19_11
<=> r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3))) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f582,plain,
( ~ r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| spl19_11 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,plain,
( ~ spl19_10
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f574,f580,f576]) ).
fof(f585,plain,
v1_relat_1(sK2),
inference(resolution,[],[f287,f135]) ).
fof(f590,plain,
spl19_10,
inference(avatar_split_clause,[],[f585,f576]) ).
fof(f595,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_11 ),
inference(resolution,[],[f582,f463]) ).
fof(f596,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f595,f138]) ).
fof(f597,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f596,f130]) ).
fof(f598,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f597,f129]) ).
fof(f599,plain,
( ~ l1_group_1(sK0)
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f598,f128]) ).
fof(f600,plain,
( $false
| spl19_11 ),
inference(forward_subsumption_resolution,[],[f599,f127]) ).
fof(f601,plain,
spl19_11,
inference(avatar_contradiction_clause,[],[f600]) ).
cnf(s13,plain,
( ~ spl19_10
| ~ spl19_11 ),
inference(sat_conversion,[],[f583]) ).
cnf(s14,plain,
spl19_10,
inference(sat_conversion,[],[f590]) ).
cnf(s15,plain,
spl19_11,
inference(sat_conversion,[],[f601]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s13,s15,s14]) ).
fof(f602,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.35 % Computer : n001.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 10:27:00 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.44 % (3351708)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (3351713)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1600262776_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.44 % TRYING [1]
% 0.13/0.44 % TRYING [2]
% 0.13/0.44 % (3351714)% WARNING: option uhcvi not known.
% 0.13/0.44 % TRYING [3]
% 0.13/0.44 % (3351714)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1047541340:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.44 % (3351715)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4163851863:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.44 % (3351716)dis+10_1_sil=32000:sp=arity:random_seed=2540146765:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.44 % (3351719)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=917372897:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.44 % (3351717)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2930990685:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.44 % (3351718)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1317480871:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.44 % TRYING [4]
% 0.13/0.44 % TRYING [5]
% 0.13/0.44 % (3351716) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3351708-3351716"...
% 0.13/0.44 % (3351716)...printing done.
% 0.13/0.44 % (3351716)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (3351716)------------------------------
% 0.13/0.44 % (3351716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (3351716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (3351716)CaDiCaL version: 2.1.3
% 0.13/0.44 % (3351716)Termination reason: Refutation
% 0.13/0.44 % (3351716)Time elapsed: 0.013 s
% 0.13/0.44 % (3351716)Peak memory usage: 12 MB
% 0.13/0.44 % (3351716)Instructions burned: 18 (million)
% 0.13/0.44 % (3351708)Success in time 0.05 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------