%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP628+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 : n002.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 10:18:17 AM UTC 2026
% Result : Theorem 0.42s 0.49s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 93 ( 20 unt; 2 def)
% Number of atoms : 471 ( 52 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 641 ( 263 ~; 277 |; 74 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k5_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k5_autgroup(X0),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f22,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& l1_group_1(k3_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_autgroup) ).
fof(f25,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_group_1(k5_autgroup(X0))
& v1_group_3(k5_autgroup(X0),k3_autgroup(X0))
& m1_group_2(k5_autgroup(X0),k3_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_autgroup) ).
fof(f67,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
=> ( X1 = X2
=> k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_autgroup) ).
fof(f68,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f73,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> m1_subset_1(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_group_2) ).
fof(f74,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ( X3 = X1
=> k3_group_1(X2,X3) = k3_group_1(X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_group_2) ).
fof(f82,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_group_1(k5_autgroup(X0))
& m1_group_2(k5_autgroup(X0),k3_autgroup(X0)) ) ),
inference(pure_predicate_removal,[],[f25]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2)
& X1 = X2
& m1_subset_1(X2,u1_struct_0(k5_autgroup(X0))) )
& m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f91,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k2_funct_1(X1) != k3_group_1(k5_autgroup(X0),X2)
& X1 = X2
& m1_subset_1(X2,u1_struct_0(k5_autgroup(X0))) )
& m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f90]) ).
fof(f120,plain,
! [X0] :
( ( ~ v3_struct_0(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& l1_group_1(k3_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f121,plain,
! [X0] :
( ( ~ v3_struct_0(k3_autgroup(X0))
& v1_group_1(k3_autgroup(X0))
& v3_group_1(k3_autgroup(X0))
& v4_group_1(k3_autgroup(X0))
& l1_group_1(k3_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f120]) ).
fof(f126,plain,
! [X0] :
( ( v1_group_1(k5_autgroup(X0))
& m1_group_2(k5_autgroup(X0),k3_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f127,plain,
! [X0] :
( ( v1_group_1(k5_autgroup(X0))
& m1_group_2(k5_autgroup(X0),k3_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f126]) ).
fof(f154,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
| X1 != X2
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0))) )
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f155,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
| X1 != X2
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0))) )
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f154]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f156]) ).
fof(f164,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X1)) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f165,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X1)) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f164]) ).
fof(f166,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k3_group_1(X2,X3) = k3_group_1(X0,X1)
| X1 != X3
| ~ m1_subset_1(X3,u1_struct_0(X2)) )
| ~ m1_group_2(X2,X0) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f167,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k3_group_1(X2,X3) = k3_group_1(X0,X1)
| X1 != X3
| ~ m1_subset_1(X3,u1_struct_0(X2)) )
| ~ m1_group_2(X2,X0) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f166]) ).
fof(f172,plain,
( k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2)
& sK1 = sK2
& m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0)))
& m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& ~ v3_struct_0(sK0)
& v1_group_1(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f91]) ).
fof(f199,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f200,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f201,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f202,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f203,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f204,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f172]) ).
fof(f205,plain,
m1_subset_1(sK2,u1_struct_0(k5_autgroup(sK0))),
inference(cnf_transformation,[],[f172]) ).
fof(f206,plain,
sK1 = sK2,
inference(cnf_transformation,[],[f172]) ).
fof(f207,plain,
k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK2),
inference(cnf_transformation,[],[f172]) ).
fof(f236,plain,
! [X0] :
( l1_group_1(k3_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f237,plain,
! [X0] :
( v4_group_1(k3_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f238,plain,
! [X0] :
( v3_group_1(k3_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f240,plain,
! [X0] :
( ~ v3_struct_0(k3_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f243,plain,
! [X0] :
( m1_group_2(k5_autgroup(X0),k3_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f322,plain,
! [X2,X0,X1] :
( k2_funct_1(X1) = k3_group_1(k3_autgroup(X0),X2)
| X1 != X2
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f323,plain,
! [X0,X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f328,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f329,plain,
! [X2,X3,X0,X1] :
( k3_group_1(X0,X1) = k3_group_1(X2,X3)
| X1 != X3
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f334,plain,
k3_group_1(k5_autgroup(sK0),sK2) != k2_funct_1(sK2),
inference(definition_unfolding,[],[f207,f206]) ).
fof(f335,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(definition_unfolding,[],[f204,f206]) ).
fof(f336,plain,
! [X2,X0] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| k3_group_1(k3_autgroup(X0),X2) = k2_funct_1(X2)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f322]) ).
fof(f337,plain,
! [X2,X3,X0] :
( k3_group_1(X2,X3) = k3_group_1(X0,X3)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f329]) ).
fof(f669,plain,
! [X0] :
( ~ m1_group_2(k5_autgroup(sK0),X0)
| m1_subset_1(sK2,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(resolution,[],[f328,f205]) ).
fof(f904,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f323,f335]) ).
fof(f911,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f904,f203]) ).
fof(f913,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f911,f202]) ).
fof(f915,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f913,f201]) ).
fof(f917,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f915,f200]) ).
fof(f919,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(forward_subsumption_resolution,[],[f917,f199]) ).
fof(f921,plain,
! [X2,X3,X0] :
( ~ m1_subset_1(X3,u1_struct_0(X2))
| k3_group_1(X2,X3) = k3_group_1(X0,X3)
| ~ m1_group_2(X2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f337,f328]) ).
fof(f923,plain,
! [X0] :
( ~ m1_group_2(k5_autgroup(sK0),X0)
| k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(X0,sK2)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(resolution,[],[f921,f205]) ).
fof(f996,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f919,f336]) ).
fof(f1002,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f996,f203]) ).
fof(f1012,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1002,f202]) ).
fof(f1013,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1012,f201]) ).
fof(f1014,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1013,f200]) ).
fof(f1015,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2) ),
inference(forward_subsumption_resolution,[],[f1014,f199]) ).
fof(f1017,definition,
( spl27_60
<=> k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2) ),
introduced(definition,[new_symbols(definition,[spl27_60])],[avatar_definition]) ).
fof(f1019,plain,
( k2_funct_1(sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ spl27_60 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1021,definition,
( spl27_61
<=> m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0))) ),
introduced(definition,[new_symbols(definition,[spl27_61])],[avatar_definition]) ).
fof(f1024,plain,
( spl27_60
| ~ spl27_61 ),
inference(avatar_split_clause,[],[f1015,f1021,f1017]) ).
fof(f1025,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| v3_struct_0(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f669,f243]) ).
fof(f1026,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1025,f240]) ).
fof(f1027,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1026,f238]) ).
fof(f1028,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1027,f236]) ).
fof(f1029,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1028,f203]) ).
fof(f1030,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1029,f202]) ).
fof(f1031,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1030,f201]) ).
fof(f1032,plain,
( m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0)))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1031,f200]) ).
fof(f1033,plain,
m1_subset_1(sK2,u1_struct_0(k3_autgroup(sK0))),
inference(forward_subsumption_resolution,[],[f1032,f199]) ).
fof(f1034,plain,
spl27_61,
inference(avatar_split_clause,[],[f1033,f1021]) ).
fof(f1049,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| v3_struct_0(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f923,f243]) ).
fof(f1050,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v3_group_1(k3_autgroup(sK0))
| ~ v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1049,f240]) ).
fof(f1051,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v4_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1050,f238]) ).
fof(f1052,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ l1_group_1(k3_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1051,f237]) ).
fof(f1053,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1052,f236]) ).
fof(f1054,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1053,f203]) ).
fof(f1055,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1054,f202]) ).
fof(f1056,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1055,f201]) ).
fof(f1057,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f1056,f200]) ).
fof(f1058,plain,
k3_group_1(k5_autgroup(sK0),sK2) = k3_group_1(k3_autgroup(sK0),sK2),
inference(forward_subsumption_resolution,[],[f1057,f199]) ).
fof(f1638,plain,
( k3_group_1(k5_autgroup(sK0),sK2) = k2_funct_1(sK2)
| ~ spl27_60 ),
inference(forward_demodulation,[],[f1058,f1019]) ).
fof(f1639,plain,
( $false
| ~ spl27_60 ),
inference(forward_subsumption_resolution,[],[f1638,f334]) ).
fof(f1640,plain,
~ spl27_60,
inference(avatar_contradiction_clause,[],[f1639]) ).
cnf(s40,plain,
( spl27_60
| ~ spl27_61 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s41,plain,
spl27_61,
inference(sat_conversion,[],[f1034]) ).
cnf(s79,plain,
~ spl27_60,
inference(sat_conversion,[],[f1640]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s40,s41,s79]) ).
fof(f1641,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP628+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:13:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.42/0.49 % (3323057)Will run a generic schedule for satisfiability detection.
% 0.42/0.49 % (3323062)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1974206858_2999 on theBenchmark for (2999ds/0Mi)
% 0.42/0.49 % TRYING [1]
% 0.42/0.49 % TRYING [2]
% 0.42/0.49 % TRYING [3]
% 0.42/0.49 % (3323066)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1994531361:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.42/0.49 % (3323068)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2307105737:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.42/0.49 % (3323064)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3672832848:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.42/0.49 % (3323065)dis+10_1_sil=32000:sp=arity:random_seed=1685618384:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.42/0.49 % (3323067)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1495761055:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.49 % (3323063)% WARNING: option uhcvi not known.
% 0.42/0.49 % TRYING [4]
% 0.42/0.49 % (3323063)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4038814210:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.42/0.49 % (3323065) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3323057-3323065"...
% 0.42/0.49 % (3323065)...printing done.
% 0.42/0.49 % (3323065)Refutation found. Thanks to Tanya!
% 0.42/0.49 % SZS status Theorem for theBenchmark
% 0.42/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.42/0.49 % (3323065)------------------------------
% 0.42/0.49 % (3323065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.49 % (3323065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.49 % (3323065)CaDiCaL version: 2.1.3
% 0.42/0.49 % (3323065)Termination reason: Refutation
% 0.42/0.49 % (3323065)Time elapsed: 0.035 s
% 0.42/0.49 % (3323065)Peak memory usage: 13 MB
% 0.42/0.49 % (3323065)Instructions burned: 47 (million)
% 0.42/0.49 % (3323057)Success in time 0.076 s
% 0.42/0.49 % Vampire exiting
%------------------------------------------------------------------------------