%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP645+2 : 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 : 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 10:15:16 AM UTC 2026
% Result : Theorem 2.53s 1.85s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 89 ( 18 unt; 3 def)
% Number of atoms : 428 ( 52 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 581 ( 242 ~; 250 |; 69 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4553,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0)
& m1_group_2(X2,X0) )
=> ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).
fof(f5636,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f5639,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)
=> u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsubgr) ).
fof(f5653,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) )
=> ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(X1,X2) = u1_struct_0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f5663,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(f5664,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_group_1(X1)
& m1_group_2(X1,X0) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f5663]) ).
fof(f5667,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) != k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2))
& v1_group_1(X2)
& m1_group_2(X2,X0) )
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f5664]) ).
fof(f5668,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) != k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2))
& v1_group_1(X2)
& m1_group_2(X2,X0) )
& v1_group_1(X1)
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f5667]) ).
fof(f5730,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(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,[],[f5639]) ).
fof(f5731,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(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,[],[f5730]) ).
fof(f5756,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(ennf_transformation,[],[f4553]) ).
fof(f5757,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(flattening,[],[f5756]) ).
fof(f5792,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[],[f5653]) ).
fof(f5793,plain,
! [X0] :
( ! [X1] :
( ( X1 = k1_latsubgr(X0)
<=> ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[],[f5792]) ).
fof(f5794,plain,
! [X0] :
( ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5636]) ).
fof(f5795,plain,
! [X0] :
( ( v1_funct_1(k1_latsubgr(X0))
& v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
& m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5794]) ).
fof(f5796,plain,
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),sK2)) != k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2))
& v1_group_1(sK2)
& m1_group_2(sK2,sK0)
& v1_group_1(sK1)
& m1_group_2(sK1,sK0)
& ~ 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]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5668]) ).
fof(f5819,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ? [X2] :
( k1_funct_1(X1,X2) != u1_struct_0(X2)
& v1_group_1(X2)
& m1_group_2(X2,X0) ) )
& ( ! [X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[],[f5793]) ).
fof(f5820,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ? [X2] :
( k1_funct_1(X1,X2) != u1_struct_0(X2)
& v1_group_1(X2)
& m1_group_2(X2,X0) ) )
& ( ! [X3] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[],[f5819]) ).
fof(f5821,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ( k1_funct_1(X1,sK21(X0,X1)) != u1_struct_0(sK21(X0,X1))
& v1_group_1(sK21(X0,X1))
& m1_group_2(sK21(X0,X1),X0) ) )
& ( ! [X3] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0) )
| k1_latsubgr(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[sK21]),skolemize(X2,sK21(X0,X1))],[f5820]) ).
fof(f5822,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5823,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5824,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5825,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5826,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5827,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f5796]) ).
fof(f5828,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f5796]) ).
fof(f5829,plain,
v1_group_1(sK2),
inference(cnf_transformation,[],[f5796]) ).
fof(f5830,plain,
k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),sK2)) != k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f5796]) ).
fof(f5917,plain,
! [X2,X0,X1] :
( ~ v4_group_1(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) = u1_struct_0(k9_group_2(X0,X1,X2))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f5731]) ).
fof(f5941,plain,
! [X2,X0,X1] :
( m1_group_2(k9_group_2(X0,X1,X2),X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f5757]) ).
fof(f5942,plain,
! [X2,X0,X1] :
( v1_group_1(k9_group_2(X0,X1,X2))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f5757]) ).
fof(f5966,plain,
! [X3,X0,X1] :
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| k1_latsubgr(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),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,[],[f5821]) ).
fof(f5970,plain,
! [X0] :
( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5795]) ).
fof(f5971,plain,
! [X0] :
( v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5795]) ).
fof(f5972,plain,
! [X0] :
( v1_funct_1(k1_latsubgr(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f5795]) ).
fof(f5986,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5966]) ).
fof(f5987,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5986,f5972]) ).
fof(f5992,plain,
! [X3,X0] :
( u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),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,[],[f5987,f5971]) ).
fof(f5994,plain,
! [X3,X0] :
( ~ v4_group_1(X0)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f5992,f5970]) ).
fof(f8231,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f5994,f5823]) ).
fof(f8234,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| ~ v3_group_1(sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f8231,f5825]) ).
fof(f8236,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f8234,f5824]) ).
fof(f8238,plain,
! [X0] :
( u1_struct_0(X0) = k1_funct_1(k1_latsubgr(sK0),X0)
| ~ m1_group_2(X0,sK0)
| ~ v1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f8236,f5822]) ).
fof(f8239,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2))
| ~ m1_group_2(sK1,sK0)
| ~ v1_group_1(sK1) ),
inference(superposition,[],[f5830,f8238]) ).
fof(f8248,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2))
| ~ v1_group_1(sK1) ),
inference(forward_subsumption_resolution,[],[f8239,f5826]) ).
fof(f8252,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2)),
inference(forward_subsumption_resolution,[],[f8248,f5827]) ).
fof(f8266,plain,
( k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| ~ v1_group_1(k9_group_2(sK0,sK1,sK2)) ),
inference(superposition,[],[f8252,f8238]) ).
fof(f8268,definition,
( spl22_1
<=> v1_group_1(k9_group_2(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f8270,plain,
( ~ v1_group_1(k9_group_2(sK0,sK1,sK2))
| spl22_1 ),
inference(avatar_component_clause,[],[f8268]) ).
fof(f8272,definition,
( spl22_2
<=> m1_group_2(k9_group_2(sK0,sK1,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f8274,plain,
( ~ m1_group_2(k9_group_2(sK0,sK1,sK2),sK0)
| spl22_2 ),
inference(avatar_component_clause,[],[f8272]) ).
fof(f8276,definition,
( spl22_3
<=> k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f8278,plain,
( k3_xboole_0(u1_struct_0(sK1),k1_funct_1(k1_latsubgr(sK0),sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2))
| spl22_3 ),
inference(avatar_component_clause,[],[f8276]) ).
fof(f8279,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f8266,f8276,f8272,f8268]) ).
fof(f8280,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(resolution,[],[f8270,f5942]) ).
fof(f8281,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8280,f5825]) ).
fof(f8282,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8281,f5824]) ).
fof(f8283,plain,
( ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8282,f5823]) ).
fof(f8284,plain,
( ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8283,f5822]) ).
fof(f8285,plain,
( ~ m1_group_2(sK2,sK0)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8284,f5826]) ).
fof(f8286,plain,
( $false
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f8285,f5828]) ).
fof(f8287,plain,
spl22_1,
inference(avatar_contradiction_clause,[],[f8286]) ).
fof(f8288,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(resolution,[],[f8274,f5941]) ).
fof(f8291,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8288,f5825]) ).
fof(f8293,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8291,f5824]) ).
fof(f8295,plain,
( ~ l1_group_1(sK0)
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8293,f5823]) ).
fof(f8297,plain,
( ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8295,f5822]) ).
fof(f8310,plain,
( ~ m1_group_2(sK2,sK0)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8297,f5826]) ).
fof(f8311,plain,
( $false
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f8310,f5828]) ).
fof(f8312,plain,
spl22_2,
inference(avatar_contradiction_clause,[],[f8311]) ).
fof(f8313,plain,
( u1_struct_0(k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2))
| ~ m1_group_2(sK2,sK0)
| ~ v1_group_1(sK2)
| spl22_3 ),
inference(superposition,[],[f8278,f8238]) ).
fof(f8314,plain,
( u1_struct_0(k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2))
| ~ v1_group_1(sK2)
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f8313,f5828]) ).
fof(f8315,plain,
( u1_struct_0(k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2))
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f8314,f5829]) ).
fof(f8839,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)) = u1_struct_0(k9_group_2(sK0,X1,X0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f5917,f5823]) ).
fof(f8842,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| ~ v3_group_1(sK0)
| k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)) = u1_struct_0(k9_group_2(sK0,X1,X0))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f8839,f5825]) ).
fof(f8844,plain,
! [X0,X1] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)) = u1_struct_0(k9_group_2(sK0,X1,X0))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f8842,f5824]) ).
fof(f8846,plain,
! [X0,X1] :
( k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)) = u1_struct_0(k9_group_2(sK0,X1,X0))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f8844,f5822]) ).
fof(f9783,plain,
( k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)) != k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2))
| ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_3 ),
inference(superposition,[],[f8315,f8846]) ).
fof(f9795,plain,
( ~ m1_group_2(sK1,sK0)
| ~ m1_group_2(sK2,sK0)
| spl22_3 ),
inference(trivial_inequality_removal,[],[f9783]) ).
fof(f9797,plain,
( ~ m1_group_2(sK2,sK0)
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f9795,f5826]) ).
fof(f9799,plain,
( $false
| spl22_3 ),
inference(forward_subsumption_resolution,[],[f9797,f5828]) ).
fof(f9800,plain,
spl22_3,
inference(avatar_contradiction_clause,[],[f9799]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2
| ~ spl22_3 ),
inference(sat_conversion,[],[f8279]) ).
cnf(s2,plain,
spl22_1,
inference(sat_conversion,[],[f8287]) ).
cnf(s4,plain,
spl22_2,
inference(sat_conversion,[],[f8312]) ).
cnf(s13,plain,
spl22_3,
inference(sat_conversion,[],[f9800]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s13,s4,s2]) ).
fof(f9818,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP645+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % 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 10:26:20 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.53/1.85 % (3339430)Detected formulas, will run a generic FOF schedule.
% 2.53/1.85 % (3339435)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=1335943271:i=141193_2997 on theBenchmark for (2997ds/141193Mi)
% 2.53/1.85 % (3339440)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=317558782:s2a=on:i=139:gtg=position_2997 on theBenchmark for (2997ds/139Mi)
% 2.53/1.85 % (3339436)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=3622590801:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2997 on theBenchmark for (2997ds/134677Mi)
% 2.53/1.85 % (3339439)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4113094794:i=119:av=off:ss=axioms_2997 on theBenchmark for (2997ds/119Mi)
% 2.53/1.85 % (3339437)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=1320132634:i=141695:sd=1:nm=32:gsp=on:ss=included_2997 on theBenchmark for (2997ds/141695Mi)
% 2.53/1.85 % (3339438)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3011276670:i=109:sd=1:ins=1:gsp=on:ss=axioms_2997 on theBenchmark for (2997ds/109Mi)
% 2.53/1.85 % (3339441)dis-21_1_sil=8000:lcm=predicate:random_seed=965608822:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2997 on theBenchmark for (2997ds/129Mi)
% 2.53/1.85 % (3339438)Instruction limit reached!
% 2.53/1.85 % (3339438)------------------------------
% 2.53/1.85 % (3339438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339438)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339438)Termination reason: Instruction limit
% 2.53/1.85 % (3339438)Termination phase: Saturation
% 2.53/1.85 % (3339438)Time elapsed: 0.069 s
% 2.53/1.85 % (3339438)Peak memory usage: 95 MB
% 2.53/1.85 % (3339438)Instructions burned: 111 (million)
% 2.53/1.85 % (3339440)Instruction limit reached!
% 2.53/1.85 % (3339440)------------------------------
% 2.53/1.85 % (3339440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339440)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339440)Termination reason: Instruction limit
% 2.53/1.85 % (3339440)Termination phase: Unused predicate definition removal
% 2.53/1.85 % (3339440)Time elapsed: 0.083 s
% 2.53/1.85 % (3339440)Peak memory usage: 93 MB
% 2.53/1.85 % (3339440)Instructions burned: 139 (million)
% 2.53/1.85 % (3339439)Instruction limit reached!
% 2.53/1.85 % (3339439)------------------------------
% 2.53/1.85 % (3339439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339439)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339439)Termination reason: Instruction limit
% 2.53/1.85 % (3339439)Termination phase: Saturation
% 2.53/1.85 % (3339439)Time elapsed: 0.081 s
% 2.53/1.85 % (3339439)Peak memory usage: 96 MB
% 2.53/1.85 % (3339439)Instructions burned: 119 (million)
% 2.53/1.85 % (3339441)Instruction limit reached!
% 2.53/1.85 % (3339441)------------------------------
% 2.53/1.85 % (3339441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339441)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339441)Termination reason: Instruction limit
% 2.53/1.85 % (3339441)Termination phase: Preprocessing 3
% 2.53/1.85 % (3339441)Time elapsed: 0.094 s
% 2.53/1.85 % (3339441)Peak memory usage: 97 MB
% 2.53/1.85 % (3339441)Instructions burned: 130 (million)
% 2.53/1.85 % (3339449)lrs+10_1_sil=8000:sp=occurrence:random_seed=3915425907:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 2.53/1.85 % (3339450)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1538127267:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 2.53/1.85 % (3339451)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1959201287:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 2.53/1.85 % (3339452)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2752859150:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 2.53/1.85 % (3339450)Instruction limit reached!
% 2.53/1.85 % (3339450)------------------------------
% 2.53/1.85 % (3339450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339450)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339450)Termination reason: Instruction limit
% 2.53/1.85 % (3339450)Termination phase: Saturation
% 2.53/1.85 % (3339450)Time elapsed: 0.089 s
% 2.53/1.85 % (3339450)Peak memory usage: 96 MB
% 2.53/1.85 % (3339450)Instructions burned: 158 (million)
% 2.53/1.85 % (3339451)First to succeed.
% 2.53/1.85 % (3339451)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3339430"
% 2.53/1.85 % (3339452)Instruction limit reached!
% 2.53/1.85 % (3339452)------------------------------
% 2.53/1.85 % (3339452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339452)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339452)Termination reason: Instruction limit
% 2.53/1.85 % (3339452)Termination phase: Preprocessing 3
% 2.53/1.85 % (3339452)Time elapsed: 0.151 s
% 2.53/1.85 % (3339452)Peak memory usage: 100 MB
% 2.53/1.85 % (3339452)Instructions burned: 250 (million)
% 2.53/1.85 % (3339449)Instruction limit reached!
% 2.53/1.85 % (3339449)------------------------------
% 2.53/1.85 % (3339449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.85 % (3339449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.85 % (3339449)CaDiCaL version: 2.1.3
% 2.53/1.85 % (3339449)Termination reason: Instruction limit
% 2.53/1.85 % (3339449)Termination phase: Saturation
% 2.53/1.85 % (3339449)Time elapsed: 0.195 s
% 2.53/1.85 % (3339449)Peak memory usage: 99 MB
% 2.53/1.85 % (3339449)Instructions burned: 285 (million)
% 2.53/1.85 % (3339457)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=21778062:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 2.53/1.85 % (3339459)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3474529979:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 2.53/1.85 % (3339458)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1674860215:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 2.53/1.85 % (3339451)Refutation found. Thanks to Tanya!
% 2.53/1.85 % SZS status Theorem for theBenchmark
% 2.53/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 6.14/2.04 % (3339451)------------------------------
% 6.14/2.04 % (3339451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/2.04 % (3339451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/2.04 % (3339451)CaDiCaL version: 2.1.3
% 6.14/2.04 % (3339451)Termination reason: Refutation
% 6.14/2.04 % (3339451)Time elapsed: 0.122 s
% 6.14/2.04 % (3339451)Peak memory usage: 99 MB
% 6.14/2.04 % (3339451)Instructions burned: 174 (million)
% 6.14/2.04 % (3339451)------------------------------
% 6.14/2.04 % (3339451)------------------------------
% 6.14/2.04 % (3339430)Success in time 0.988 s
% 6.14/2.04 % Vampire exiting
%------------------------------------------------------------------------------