%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n014.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 10:15:05 AM UTC 2026
% Result : Theorem 2.63s 1.29s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 25 unt; 6 def)
% Number of atoms : 578 ( 45 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 803 ( 353 ~; 345 |; 74 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 87 !; 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),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(cnf_transformation,[],[f157]) ).
fof(f328,plain,
! [X2,X0,X1] :
( 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(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,
! [X2,X0] :
( k3_group_1(k3_autgroup(X0),X2) = k2_funct_1(X2)
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X0)))
| ~ m2_fraenkel(X2,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(equality_resolution,[],[f322]) ).
fof(f335,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(f336,plain,
m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0))),
inference(forward_demodulation,[],[f205,f206]) ).
fof(f337,plain,
k2_funct_1(sK1) != k3_group_1(k5_autgroup(sK0),sK1),
inference(forward_demodulation,[],[f207,f206]) ).
fof(f484,plain,
! [X2,X3,X0] :
( ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| k3_group_1(X2,X3) = k3_group_1(X0,X3)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f335,f328]) ).
fof(f501,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(k5_autgroup(X1)))
| k3_group_1(k5_autgroup(X1),X0) = k3_group_1(k3_autgroup(X1),X0)
| v3_struct_0(k3_autgroup(X1))
| ~ v3_group_1(k3_autgroup(X1))
| ~ v4_group_1(k3_autgroup(X1))
| ~ l1_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(resolution,[],[f484,f243]) ).
fof(f505,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(k5_autgroup(X1)))
| k3_group_1(k5_autgroup(X1),X0) = k3_group_1(k3_autgroup(X1),X0)
| ~ v3_group_1(k3_autgroup(X1))
| ~ v4_group_1(k3_autgroup(X1))
| ~ l1_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f501,f240]) ).
fof(f506,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(k5_autgroup(X1)))
| k3_group_1(k5_autgroup(X1),X0) = k3_group_1(k3_autgroup(X1),X0)
| ~ v4_group_1(k3_autgroup(X1))
| ~ l1_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f505,f238]) ).
fof(f507,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(k5_autgroup(X1)))
| k3_group_1(k5_autgroup(X1),X0) = k3_group_1(k3_autgroup(X1),X0)
| ~ l1_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f506,f237]) ).
fof(f508,plain,
! [X0,X1] :
( k3_group_1(k5_autgroup(X1),X0) = k3_group_1(k3_autgroup(X1),X0)
| ~ m1_subset_1(X0,u1_struct_0(k5_autgroup(X1)))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f507,f236]) ).
fof(f578,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| ~ m1_subset_1(sK1,u1_struct_0(k5_autgroup(sK0)))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f337,f508]) ).
fof(f581,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f578,f336]) ).
fof(f582,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f581,f203]) ).
fof(f583,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f582,f202]) ).
fof(f584,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f583,f201]) ).
fof(f585,plain,
( k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f584,f200]) ).
fof(f586,plain,
k2_funct_1(sK1) != k3_group_1(k3_autgroup(sK0),sK1),
inference(forward_subsumption_resolution,[],[f585,f199]) ).
fof(f599,plain,
( k2_funct_1(sK1) != k2_funct_1(sK1)
| ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,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(superposition,[],[f586,f334]) ).
fof(f600,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,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(trivial_inequality_removal,[],[f599]) ).
fof(f601,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,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,[],[f600,f203]) ).
fof(f602,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,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,[],[f601,f202]) ).
fof(f603,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f602,f201]) ).
fof(f604,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f603,f200]) ).
fof(f605,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| ~ m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f604,f199]) ).
fof(f607,definition,
( spl27_12
<=> m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_12])],[avatar_definition]) ).
fof(f609,plain,
( ~ m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| spl27_12 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f611,definition,
( spl27_13
<=> m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0))) ),
introduced(definition,[new_symbols(definition,[spl27_13])],[avatar_definition]) ).
fof(f613,plain,
( ~ m1_subset_1(sK1,u1_struct_0(k3_autgroup(sK0)))
| spl27_13 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f614,plain,
( ~ spl27_12
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f605,f611,f607]) ).
fof(f616,plain,
( ~ 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)
| spl27_12 ),
inference(resolution,[],[f609,f323]) ).
fof(f631,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f616,f204]) ).
fof(f632,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f631,f203]) ).
fof(f633,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f632,f202]) ).
fof(f634,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f633,f201]) ).
fof(f635,plain,
( ~ l1_group_1(sK0)
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f634,f200]) ).
fof(f636,plain,
( $false
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f635,f199]) ).
fof(f637,plain,
spl27_12,
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f639,plain,
( ! [X0] :
( ~ m1_subset_1(sK1,u1_struct_0(X0))
| ~ m1_group_2(X0,k3_autgroup(sK0))
| v3_struct_0(k3_autgroup(sK0))
| ~ v3_group_1(k3_autgroup(sK0))
| ~ l1_group_1(k3_autgroup(sK0)) )
| spl27_13 ),
inference(resolution,[],[f613,f328]) ).
fof(f643,definition,
( spl27_17
<=> l1_group_1(k3_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_17])],[avatar_definition]) ).
fof(f645,plain,
( ~ l1_group_1(k3_autgroup(sK0))
| spl27_17 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f647,definition,
( spl27_18
<=> v3_group_1(k3_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_18])],[avatar_definition]) ).
fof(f649,plain,
( ~ v3_group_1(k3_autgroup(sK0))
| spl27_18 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f651,definition,
( spl27_19
<=> v3_struct_0(k3_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_19])],[avatar_definition]) ).
fof(f653,plain,
( v3_struct_0(k3_autgroup(sK0))
| ~ spl27_19 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f655,definition,
( spl27_20
<=> ! [X0] :
( ~ m1_subset_1(sK1,u1_struct_0(X0))
| ~ m1_group_2(X0,k3_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl27_20])],[avatar_definition]) ).
fof(f656,plain,
( ! [X0] :
( ~ m1_subset_1(sK1,u1_struct_0(X0))
| ~ m1_group_2(X0,k3_autgroup(sK0)) )
| ~ spl27_20 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f657,plain,
( ~ spl27_17
| ~ spl27_18
| spl27_19
| spl27_20
| spl27_13 ),
inference(avatar_split_clause,[],[f639,f611,f655,f651,f647,f643]) ).
fof(f659,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_17 ),
inference(resolution,[],[f645,f236]) ).
fof(f661,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f659,f203]) ).
fof(f662,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f661,f202]) ).
fof(f663,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f662,f201]) ).
fof(f664,plain,
( ~ l1_group_1(sK0)
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f663,f200]) ).
fof(f665,plain,
( $false
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f664,f199]) ).
fof(f666,plain,
spl27_17,
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f671,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_18 ),
inference(resolution,[],[f649,f238]) ).
fof(f673,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_18 ),
inference(forward_subsumption_resolution,[],[f671,f203]) ).
fof(f674,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_18 ),
inference(forward_subsumption_resolution,[],[f673,f202]) ).
fof(f675,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl27_18 ),
inference(forward_subsumption_resolution,[],[f674,f201]) ).
fof(f676,plain,
( ~ l1_group_1(sK0)
| spl27_18 ),
inference(forward_subsumption_resolution,[],[f675,f200]) ).
fof(f677,plain,
( $false
| spl27_18 ),
inference(forward_subsumption_resolution,[],[f676,f199]) ).
fof(f678,plain,
spl27_18,
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f680,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_19 ),
inference(resolution,[],[f653,f240]) ).
fof(f684,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f680,f203]) ).
fof(f698,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f684,f202]) ).
fof(f699,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f698,f201]) ).
fof(f700,plain,
( ~ l1_group_1(sK0)
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f699,f200]) ).
fof(f701,plain,
( $false
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f700,f199]) ).
fof(f702,plain,
~ spl27_19,
inference(avatar_contradiction_clause,[],[f701]) ).
fof(f799,plain,
( ~ m1_group_2(k5_autgroup(sK0),k3_autgroup(sK0))
| ~ spl27_20 ),
inference(resolution,[],[f656,f336]) ).
fof(f809,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_20 ),
inference(resolution,[],[f799,f243]) ).
fof(f810,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_20 ),
inference(forward_subsumption_resolution,[],[f809,f203]) ).
fof(f811,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_20 ),
inference(forward_subsumption_resolution,[],[f810,f202]) ).
fof(f812,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_20 ),
inference(forward_subsumption_resolution,[],[f811,f201]) ).
fof(f813,plain,
( ~ l1_group_1(sK0)
| ~ spl27_20 ),
inference(forward_subsumption_resolution,[],[f812,f200]) ).
fof(f814,plain,
( $false
| ~ spl27_20 ),
inference(forward_subsumption_resolution,[],[f813,f199]) ).
fof(f815,plain,
~ spl27_20,
inference(avatar_contradiction_clause,[],[f814]) ).
cnf(s6,plain,
( ~ spl27_12
| ~ spl27_13 ),
inference(sat_conversion,[],[f614]) ).
cnf(s8,plain,
spl27_12,
inference(sat_conversion,[],[f637]) ).
cnf(s9,plain,
( spl27_13
| ~ spl27_17
| ~ spl27_18
| spl27_19
| spl27_20 ),
inference(sat_conversion,[],[f657]) ).
cnf(s10,plain,
spl27_17,
inference(sat_conversion,[],[f666]) ).
cnf(s11,plain,
spl27_18,
inference(sat_conversion,[],[f678]) ).
cnf(s13,plain,
~ spl27_19,
inference(sat_conversion,[],[f702]) ).
cnf(s21,plain,
~ spl27_20,
inference(sat_conversion,[],[f815]) ).
cnf(s22,plain,
spl27_13,
inference(rat,[],[s9,s21,s13,s11,s10]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s6,s22,s8]) ).
fof(f816,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:11:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/1.29 % (582498)Detected formulas, will run a generic FOF schedule.
% 2.63/1.29 % (582507)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2458021187:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.29 % (582507)Instruction limit reached!
% 2.63/1.29 % (582507)------------------------------
% 2.63/1.29 % (582507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.29 % (582507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.29 % (582507)CaDiCaL version: 2.1.3
% 2.63/1.29 % (582507)Termination reason: Instruction limit
% 2.63/1.29 % (582507)Termination phase: Saturation
% 2.63/1.29 % (582507)Time elapsed: 0.030 s
% 2.63/1.29 % (582507)Peak memory usage: 88 MB
% 2.63/1.29 % (582507)Instructions burned: 120 (million)
% 2.63/1.29 % (582509)dis-21_1_sil=8000:lcm=predicate:random_seed=908544799: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)
% 2.63/1.29 % (582505)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=2755980950:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.29 % (582506)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=437887096:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.29 % (582503)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=2038932095:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.29 % (582504)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=4257029738:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.29 % (582508)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2141014626:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.29 % (582508)First to succeed.
% 2.63/1.29 % (582508)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-582498"
% 2.63/1.29 % (582506)Instruction limit reached!
% 2.63/1.29 % (582506)------------------------------
% 2.63/1.29 % (582506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.29 % (582506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.29 % (582506)CaDiCaL version: 2.1.3
% 2.63/1.29 % (582506)Termination reason: Instruction limit
% 2.63/1.29 % (582506)Termination phase: Saturation
% 2.63/1.29 % (582506)Time elapsed: 0.048 s
% 2.63/1.29 % (582506)Peak memory usage: 89 MB
% 2.63/1.29 % (582506)Instructions burned: 110 (million)
% 2.63/1.29 % (582509)Instruction limit reached!
% 2.63/1.29 % (582509)------------------------------
% 2.63/1.29 % (582509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.29 % (582509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.29 % (582509)CaDiCaL version: 2.1.3
% 2.63/1.29 % (582509)Termination reason: Instruction limit
% 2.63/1.29 % (582509)Termination phase: Saturation
% 2.63/1.29 % (582509)Time elapsed: 0.072 s
% 2.63/1.29 % (582509)Peak memory usage: 91 MB
% 2.63/1.29 % (582509)Instructions burned: 130 (million)
% 2.63/1.29 % (582511)lrs+10_1_sil=8000:sp=occurrence:random_seed=2329215266:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.63/1.29 % (582511)Also succeeded, but the first one will report.
% 2.63/1.29 % (582518)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1078704255:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.63/1.29 % (582519)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3985759835:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.63/1.29 % (582519)Also succeeded, but the first one will report.
% 2.63/1.29 % (582518)Instruction limit reached!
% 2.63/1.29 % (582518)------------------------------
% 2.63/1.29 % (582518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.29 % (582518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.29 % (582518)CaDiCaL version: 2.1.3
% 2.63/1.29 % (582518)Termination reason: Instruction limit
% 2.63/1.29 % (582518)Termination phase: Saturation
% 2.63/1.29 % (582518)Time elapsed: 0.073 s
% 2.63/1.29 % (582518)Peak memory usage: 88 MB
% 2.63/1.29 % (582518)Instructions burned: 159 (million)
% 2.63/1.29 % (582508)Refutation found. Thanks to Tanya!
% 2.63/1.29 % SZS status Theorem for theBenchmark
% 2.63/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.38 % (582508)------------------------------
% 3.59/1.38 % (582508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.38 % (582508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.38 % (582508)CaDiCaL version: 2.1.3
% 3.59/1.38 % (582508)Termination reason: Refutation
% 3.59/1.38 % (582508)Time elapsed: 0.026 s
% 3.59/1.38 % (582508)Peak memory usage: 90 MB
% 3.59/1.38 % (582508)Instructions burned: 33 (million)
% 3.59/1.38 % (582508)------------------------------
% 3.59/1.38 % (582508)------------------------------
% 3.59/1.38 % (582498)Success in time 0.44 s
% 3.59/1.38 % Vampire exiting
%------------------------------------------------------------------------------