%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP638+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 : n008.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 10:18:20 AM UTC 2026
% Result : Theorem 0.22s 0.59s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 143 ( 37 unt; 4 def)
% Number of atoms : 554 ( 23 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 647 ( 236 ~; 271 |; 91 &)
% ( 11 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 5 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 191 ( 0 sgn 177 !; 14 ?)
% 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))
& v1_group_6(X2,X0,X1)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X3] :
( m1_group_2(X3,X1)
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X0)
=> ! [X6] :
( m1_group_2(X6,X0)
=> ( ( u1_struct_0(X5) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X3))
& u1_struct_0(X6) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X4))
& m1_group_6(X3,X1,X4) )
=> m1_group_6(X5,X0,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_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))
& v1_group_6(X2,X0,X1)
& m2_relset_1(X2,u1_struct_0(X0),u1_struct_0(X1)) )
=> ! [X3] :
( m1_group_2(X3,X1)
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X0)
=> ! [X6] :
( m1_group_2(X6,X0)
=> ( ( u1_struct_0(X5) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X3))
& u1_struct_0(X6) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X4))
& m1_group_6(X3,X1,X4) )
=> m1_group_6(X5,X0,X6) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,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(f8,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ( m1_group_2(X1,X0)
<=> ( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
& u1_group_1(X1) = k1_realset1(u1_group_1(X0),u1_struct_0(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_group_2) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(f21,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(f43,axiom,
! [X0,X1,X2,X3] :
( ( v1_funct_1(X2)
& m1_relset_1(X2,X0,X1) )
=> k3_funct_2(X0,X1,X2,X3) = k10_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
fof(f44,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0) )
=> ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
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(k10_relat_1(X2,X0),k10_relat_1(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f53,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)
=> ( r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
=> m1_group_2(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_group_2) ).
fof(f58,plain,
~ ! [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_group_2(X3,X1)
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X0)
=> ! [X6] :
( m1_group_2(X6,X0)
=> ( ( u1_struct_0(X5) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X3))
& u1_struct_0(X6) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X4))
& m1_group_6(X3,X1,X4) )
=> m1_group_6(X5,X0,X6) ) ) ) ) ) ) ) ),
inference(pure_predicate_removal,[],[f2]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ~ m1_group_6(X5,X0,X6)
& u1_struct_0(X5) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X3))
& u1_struct_0(X6) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X4))
& m1_group_6(X3,X1,X4)
& m1_group_2(X6,X0) )
& m1_group_2(X5,X0) )
& m1_group_2(X4,X1) )
& m1_group_2(X3,X1) )
& 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,[],[f58]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ~ m1_group_6(X5,X0,X6)
& u1_struct_0(X5) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X3))
& u1_struct_0(X6) = k3_funct_2(u1_struct_0(X0),u1_struct_0(X1),X2,u1_struct_0(X4))
& m1_group_6(X3,X1,X4)
& m1_group_2(X6,X0) )
& m1_group_2(X5,X0) )
& m1_group_2(X4,X1) )
& m1_group_2(X3,X1) )
& 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,[],[f59]) ).
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,[],[f5]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( m1_group_2(X1,X0)
<=> ( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
& u1_group_1(X1) = k1_realset1(u1_group_1(X0),u1_struct_0(X1)) ) )
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( m1_group_2(X1,X0)
<=> ( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
& u1_group_1(X1) = k1_realset1(u1_group_1(X0),u1_struct_0(X1)) ) )
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f69]) ).
fof(f74,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,[],[f17]) ).
fof(f75,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,[],[f74]) ).
fof(f78,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,[],[f21]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( k3_funct_2(X0,X1,X2,X3) = k10_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( k3_funct_2(X0,X1,X2,X3) = k10_relat_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( r1_tarski(k10_relat_1(X2,X0),k10_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f96,plain,
! [X0,X1,X2] :
( r1_tarski(k10_relat_1(X2,X0),k10_relat_1(X2,X1))
| ~ r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f95]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_group_2(X1,X2)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ 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,[],[f53]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_group_2(X1,X2)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ 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,[],[f103]) ).
fof(f108,plain,
m1_group_2(sK6,sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f109,plain,
m1_group_6(sK3,sK1,sK4),
inference(cnf_transformation,[],[f60]) ).
fof(f110,plain,
u1_struct_0(sK6) = k3_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK4)),
inference(cnf_transformation,[],[f60]) ).
fof(f111,plain,
u1_struct_0(sK5) = k3_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f60]) ).
fof(f112,plain,
~ m1_group_6(sK5,sK0,sK6),
inference(cnf_transformation,[],[f60]) ).
fof(f113,plain,
m1_group_2(sK5,sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f114,plain,
m1_group_2(sK4,sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f116,plain,
m2_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(cnf_transformation,[],[f60]) ).
fof(f118,plain,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f60]) ).
fof(f119,plain,
l1_group_1(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f120,plain,
v4_group_1(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f121,plain,
v3_group_1(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f122,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f124,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f125,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f126,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f129,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(f134,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f138,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f139,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| v3_group_1(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f140,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ v3_struct_0(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f142,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,[],[f78]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( ~ v1_funct_1(X2)
| ~ m1_relset_1(X2,X0,X1)
| k3_funct_2(X0,X1,X2,X3) = k10_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X2,X1)
| m1_group_6(X2,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_group_2(X2,X1)
| ~ m1_group_6(X2,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(k10_relat_1(X2,X0),k10_relat_1(X2,X1)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| m1_group_2(X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f191,plain,
~ l1_group_1(sK0),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f192,plain,
~ l1_group_1(sK1),
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f199,plain,
! [X0,X1] :
( l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| l1_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0) ),
inference(consistent_polarity_flipping,[],[f134]) ).
fof(f202,plain,
! [X0,X1] :
( ~ v3_struct_0(X1)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X0) ),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f203,plain,
! [X0,X1] :
( ~ v3_group_1(X0)
| l1_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| v3_group_1(X1) ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f204,plain,
! [X0,X1] :
( ~ l1_group_1(X1)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X0) ),
inference(consistent_polarity_flipping,[],[f138]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| m1_group_2(X2,X1)
| ~ m1_group_6(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f176]) ).
fof(f227,plain,
! [X2,X0,X1] :
( m1_group_6(X2,X0,X1)
| l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X1,X0) ),
inference(consistent_polarity_flipping,[],[f175]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ r1_tarski(k10_relat_1(X2,X0),k10_relat_1(X2,X1))
| r1_tarski(X0,X1)
| ~ v1_relat_1(X2) ),
inference(consistent_polarity_flipping,[],[f180]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0)
| r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| m1_group_2(X1,X2) ),
inference(consistent_polarity_flipping,[],[f187]) ).
fof(f261,plain,
m1_relset_1(sK2,u1_struct_0(sK0),u1_struct_0(sK1)),
inference(resolution,[],[f178,f116]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f142,f129]) ).
fof(f270,plain,
! [X0] :
( l1_group_1(sK1)
| v3_struct_0(sK1)
| ~ m1_group_2(X0,sK1)
| v3_group_1(X0) ),
inference(resolution,[],[f203,f121]) ).
fof(f273,plain,
! [X0] :
( v3_struct_0(sK1)
| ~ m1_group_2(X0,sK1)
| v3_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f270,f192]) ).
fof(f275,plain,
! [X0] :
( ~ m1_group_2(X0,sK1)
| v3_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f273,f122]) ).
fof(f323,plain,
v3_group_1(sK4),
inference(resolution,[],[f275,f114]) ).
fof(f341,definition,
( spl22_11
<=> v3_struct_0(sK4) ),
introduced(definition,[new_symbols(definition,[spl22_11])],[avatar_definition]) ).
fof(f342,plain,
( ~ v3_struct_0(sK4)
| spl22_11 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f343,plain,
( v3_struct_0(sK4)
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f345,definition,
( spl22_12
<=> l1_group_1(sK4) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
fof(f346,plain,
( ~ l1_group_1(sK4)
| spl22_12 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f347,plain,
( l1_group_1(sK4)
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ m1_relset_1(sK2,X0,X1)
| k3_funct_2(X0,X1,sK2,X2) = k10_relat_1(sK2,X2) ),
inference(resolution,[],[f174,f118]) ).
fof(f418,plain,
! [X0,X1] :
( l1_group_1(sK1)
| ~ m1_group_2(X0,sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1)
| m1_group_2(X1,X0)
| ~ m1_group_6(X1,sK1,X0) ),
inference(resolution,[],[f226,f120]) ).
fof(f421,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1)
| m1_group_2(X1,X0)
| ~ m1_group_6(X1,sK1,X0) ),
inference(forward_subsumption_resolution,[],[f418,f192]) ).
fof(f423,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK1)
| v3_struct_0(sK1)
| m1_group_2(X1,X0)
| ~ m1_group_6(X1,sK1,X0) ),
inference(forward_subsumption_resolution,[],[f421,f121]) ).
fof(f425,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK1)
| m1_group_2(X1,X0)
| ~ m1_group_6(X1,sK1,X0) ),
inference(forward_subsumption_resolution,[],[f423,f122]) ).
fof(f426,plain,
( l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK0) ),
inference(resolution,[],[f227,f112]) ).
fof(f427,plain,
( ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK0) ),
inference(forward_subsumption_resolution,[],[f426,f191]) ).
fof(f428,plain,
( ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK0) ),
inference(forward_subsumption_resolution,[],[f427,f124]) ).
fof(f429,plain,
( v3_struct_0(sK0)
| ~ m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK0) ),
inference(forward_subsumption_resolution,[],[f428,f125]) ).
fof(f430,plain,
( ~ m1_group_2(sK5,sK6)
| ~ m1_group_2(sK6,sK0) ),
inference(forward_subsumption_resolution,[],[f429,f126]) ).
fof(f431,plain,
~ m1_group_2(sK5,sK6),
inference(forward_subsumption_resolution,[],[f430,f108]) ).
fof(f432,plain,
! [X0,X1] :
( l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f199,f204]) ).
fof(f433,plain,
! [X0,X1] :
( l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| v3_struct_0(X1)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f432,f203]) ).
fof(f434,plain,
! [X0,X1] :
( ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f433,f202]) ).
fof(f444,plain,
! [X0,X1] :
( l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| m1_group_2(X0,X1) ),
inference(resolution,[],[f234,f124]) ).
fof(f445,plain,
! [X0,X1] :
( ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| m1_group_2(X0,X1) ),
inference(forward_subsumption_resolution,[],[f444,f191]) ).
fof(f447,plain,
! [X0,X1] :
( v3_struct_0(sK0)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| m1_group_2(X0,X1) ),
inference(forward_subsumption_resolution,[],[f445,f125]) ).
fof(f449,plain,
! [X0,X1] :
( r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| m1_group_2(X0,X1) ),
inference(forward_subsumption_resolution,[],[f447,f126]) ).
fof(f493,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| l1_group_1(X0) )
| ~ spl22_11 ),
inference(resolution,[],[f343,f202]) ).
fof(f529,plain,
! [X0] :
( ~ m1_group_6(X0,sK1,sK4)
| m1_group_2(X0,sK4) ),
inference(resolution,[],[f425,f114]) ).
fof(f548,plain,
! [X0] : k3_funct_2(u1_struct_0(sK0),u1_struct_0(sK1),sK2,X0) = k10_relat_1(sK2,X0),
inference(resolution,[],[f350,f261]) ).
fof(f586,plain,
v1_relat_1(sK2),
inference(resolution,[],[f268,f116]) ).
fof(f858,plain,
m1_group_2(sK3,sK4),
inference(resolution,[],[f529,f109]) ).
fof(f968,plain,
u1_struct_0(sK6) = k10_relat_1(sK2,u1_struct_0(sK4)),
inference(superposition,[],[f548,f110]) ).
fof(f969,plain,
u1_struct_0(sK5) = k10_relat_1(sK2,u1_struct_0(sK3)),
inference(superposition,[],[f548,f111]) ).
fof(f2141,plain,
( v3_struct_0(sK1)
| ~ v3_group_1(sK1)
| l1_group_1(sK1)
| ~ spl22_11 ),
inference(resolution,[],[f493,f114]) ).
fof(f2143,plain,
( ~ v3_group_1(sK1)
| l1_group_1(sK1)
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f2141,f122]) ).
fof(f2144,plain,
( l1_group_1(sK1)
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f2143,f121]) ).
fof(f2145,plain,
( $false
| ~ spl22_11 ),
inference(forward_subsumption_resolution,[],[f2144,f192]) ).
fof(f2146,plain,
~ spl22_11,
inference(avatar_contradiction_clause,[],[f2145]) ).
fof(f2180,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| l1_group_1(X0) )
| ~ spl22_12 ),
inference(resolution,[],[f347,f204]) ).
fof(f2485,plain,
! [X0] :
( ~ r1_tarski(k10_relat_1(sK2,X0),u1_struct_0(sK6))
| r1_tarski(X0,u1_struct_0(sK4))
| ~ v1_relat_1(sK2) ),
inference(superposition,[],[f229,f968]) ).
fof(f2488,plain,
! [X0] :
( ~ r1_tarski(k10_relat_1(sK2,X0),u1_struct_0(sK6))
| r1_tarski(X0,u1_struct_0(sK4)) ),
inference(forward_subsumption_resolution,[],[f2485,f586]) ).
fof(f2566,plain,
( v3_struct_0(sK1)
| ~ v3_group_1(sK1)
| l1_group_1(sK1)
| ~ spl22_12 ),
inference(resolution,[],[f2180,f114]) ).
fof(f2568,plain,
( ~ v3_group_1(sK1)
| l1_group_1(sK1)
| ~ spl22_12 ),
inference(forward_subsumption_resolution,[],[f2566,f122]) ).
fof(f2569,plain,
( l1_group_1(sK1)
| ~ spl22_12 ),
inference(forward_subsumption_resolution,[],[f2568,f121]) ).
fof(f2570,plain,
( $false
| ~ spl22_12 ),
inference(forward_subsumption_resolution,[],[f2569,f192]) ).
fof(f2571,plain,
~ spl22_12,
inference(avatar_contradiction_clause,[],[f2570]) ).
fof(f2728,definition,
( spl22_211
<=> r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4)) ),
introduced(definition,[new_symbols(definition,[spl22_211])],[avatar_definition]) ).
fof(f2730,plain,
( r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4))
| ~ spl22_211 ),
inference(avatar_component_clause,[],[f2728]) ).
fof(f2732,definition,
( spl22_212
<=> r1_tarski(u1_struct_0(sK5),u1_struct_0(sK6)) ),
introduced(definition,[new_symbols(definition,[spl22_212])],[avatar_definition]) ).
fof(f2734,plain,
( ~ r1_tarski(u1_struct_0(sK5),u1_struct_0(sK6))
| spl22_212 ),
inference(avatar_component_clause,[],[f2732]) ).
fof(f2922,plain,
( ~ r1_tarski(u1_struct_0(sK5),u1_struct_0(sK6))
| r1_tarski(u1_struct_0(sK3),u1_struct_0(sK4)) ),
inference(superposition,[],[f2488,f969]) ).
fof(f2924,plain,
( spl22_211
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2922,f2732,f2728]) ).
fof(f3187,plain,
( ~ m1_group_2(sK6,sK0)
| ~ m1_group_2(sK5,sK0)
| m1_group_2(sK5,sK6)
| spl22_212 ),
inference(resolution,[],[f2734,f449]) ).
fof(f3190,plain,
( ~ m1_group_2(sK5,sK0)
| m1_group_2(sK5,sK6)
| spl22_212 ),
inference(forward_subsumption_resolution,[],[f3187,f108]) ).
fof(f3192,plain,
( m1_group_2(sK5,sK6)
| spl22_212 ),
inference(forward_subsumption_resolution,[],[f3190,f113]) ).
fof(f3195,plain,
( $false
| spl22_212 ),
inference(forward_subsumption_resolution,[],[f3192,f431]) ).
fof(f3196,plain,
spl22_212,
inference(avatar_contradiction_clause,[],[f3195]) ).
fof(f3201,plain,
( ~ v3_group_1(sK4)
| v3_struct_0(sK4)
| l1_group_1(sK4)
| ~ m1_group_2(sK3,sK4)
| ~ spl22_211 ),
inference(resolution,[],[f2730,f434]) ).
fof(f3203,plain,
( v3_struct_0(sK4)
| l1_group_1(sK4)
| ~ m1_group_2(sK3,sK4)
| ~ spl22_211 ),
inference(forward_subsumption_resolution,[],[f3201,f323]) ).
fof(f3204,plain,
( l1_group_1(sK4)
| ~ m1_group_2(sK3,sK4)
| spl22_11
| ~ spl22_211 ),
inference(forward_subsumption_resolution,[],[f3203,f342]) ).
fof(f3205,plain,
( ~ m1_group_2(sK3,sK4)
| spl22_11
| spl22_12
| ~ spl22_211 ),
inference(forward_subsumption_resolution,[],[f3204,f346]) ).
fof(f3206,plain,
( $false
| spl22_11
| spl22_12
| ~ spl22_211 ),
inference(forward_subsumption_resolution,[],[f3205,f858]) ).
fof(f3207,plain,
( spl22_11
| spl22_12
| ~ spl22_211 ),
inference(avatar_contradiction_clause,[],[f3206]) ).
cnf(s119,plain,
~ spl22_11,
inference(sat_conversion,[],[f2146]) ).
cnf(s174,plain,
~ spl22_12,
inference(sat_conversion,[],[f2571]) ).
cnf(s206,plain,
( spl22_211
| ~ spl22_212 ),
inference(sat_conversion,[],[f2924]) ).
cnf(s224,plain,
spl22_212,
inference(sat_conversion,[],[f3196]) ).
cnf(s225,plain,
( spl22_11
| spl22_12
| ~ spl22_211 ),
inference(sat_conversion,[],[f3207]) ).
cnf(s227,plain,
spl22_211,
inference(rat,[],[s206,s224]) ).
cnf(s229,plain,
spl22_11,
inference(rat,[],[s225,s227,s174]) ).
cnf(s235,plain,
$false,
inference(rat,[],[s119,s229]) ).
fof(f3208,plain,
$false,
inference(avatar_sat_refutation,[],[s235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP638+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n008.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 10:21:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45 Running first-order model finding
% 0.14/0.45 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
% 0.22/0.59 % (1011084)Will run a generic schedule for satisfiability detection.
% 0.22/0.59 % (1011093)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2929977030:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.59 % (1011090)% WARNING: option uhcvi not known.
% 0.22/0.59 % (1011089)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2207154261_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.59 % (1011090)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2319720512:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.59 % (1011095)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=913264139:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.59 % (1011092)dis+10_1_sil=32000:sp=arity:random_seed=2363870638:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.59 % (1011091)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1964981071:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.59 % (1011094)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3152670307:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.59 % TRYING [1]
% 0.22/0.59 % TRYING [2]
% 0.22/0.59 % TRYING [3]
% 0.22/0.59 % TRYING [4]
% 0.22/0.59 % (1011093)Instruction limit reached!
% 0.22/0.59 % (1011093)------------------------------
% 0.22/0.59 % (1011093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.59 % (1011093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.59 % (1011093)CaDiCaL version: 2.1.3
% 0.22/0.59 % (1011093)Termination reason: Instruction limit
% 0.22/0.59 % (1011093)Termination phase: Saturation
% 0.22/0.59 % (1011093)Time elapsed: 0.060 s
% 0.22/0.59 % (1011093)Peak memory usage: 12 MB
% 0.22/0.59 % (1011093)Instructions burned: 118 (million)
% 0.22/0.59 % TRYING [5]
% 0.22/0.59 % (1011090) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1011084-1011090"...
% 0.22/0.59 % (1011090)...printing done.
% 0.22/0.59 % (1011103)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=689511393:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.59 % (1011090)Refutation found. Thanks to Tanya!
% 0.22/0.59 % SZS status Theorem for theBenchmark
% 0.22/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.59 % (1011090)------------------------------
% 0.22/0.59 % (1011090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.59 % (1011090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.59 % (1011090)CaDiCaL version: 2.1.3
% 0.22/0.59 % (1011090)Termination reason: Refutation
% 0.22/0.59 % (1011090)Time elapsed: 0.081 s
% 0.22/0.59 % (1011090)Peak memory usage: 14 MB
% 0.22/0.59 % (1011090)Instructions burned: 99 (million)
% 0.22/0.59 % (1011084)Success in time 0.122 s
% 0.22/0.59 % Vampire exiting
%------------------------------------------------------------------------------