%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP645+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 10:18:23 AM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 21 unt; 0 def)
% Number of atoms : 427 ( 72 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 593 ( 245 ~; 260 |; 71 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 102 ( 94 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(f2,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)],[f1]) ).
fof(f9,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(f15,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/sandbox2/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p',dt_k9_group_2) ).
fof(f55,axiom,
! [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) )
=> u1_struct_0(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/sandbox2/benchmark/theBenchmark.p',t23_latsubgr) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( 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))
& 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,[],[f2]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( 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))
& 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,[],[f70]) ).
fof(f83,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,[],[f11]) ).
fof(f84,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,[],[f83]) ).
fof(f87,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,[],[f15]) ).
fof(f88,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,[],[f87]) ).
fof(f91,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,[],[f21]) ).
fof(f92,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,[],[f91]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),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,[],[f55]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( u1_struct_0(k9_group_2(X0,X1,X2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),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,[],[f114]) ).
fof(f125,plain,
( k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),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)],[f71]) ).
fof(f126,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,[],[f84]) ).
fof(f127,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,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k1_latsubgr(X0)
| ( k1_funct_1(X1,sK3(X0,X1)) != u1_struct_0(sK3(X0,X1))
& v1_group_1(sK3(X0,X1))
& m1_group_2(sK3(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,[sK3]),skolemize(X2,sK3(X0,X1))],[f127]) ).
fof(f144,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f147,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f148,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f149,plain,
v1_group_1(sK1),
inference(cnf_transformation,[],[f125]) ).
fof(f150,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f125]) ).
fof(f151,plain,
v1_group_1(sK2),
inference(cnf_transformation,[],[f125]) ).
fof(f152,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),sK1),k1_funct_1(k1_latsubgr(sK0),sK2)),
inference(cnf_transformation,[],[f125]) ).
fof(f164,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f166,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,[],[f128]) ).
fof(f172,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,[],[f88]) ).
fof(f173,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,[],[f88]) ).
fof(f174,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,[],[f88]) ).
fof(f177,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,[],[f92]) ).
fof(f178,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,[],[f92]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| k3_xboole_0(k1_funct_1(k1_latsubgr(X0),X1),k1_funct_1(k1_latsubgr(X0),X2)) = u1_struct_0(k9_group_2(X0,X1,X2))
| ~ 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(cnf_transformation,[],[f115]) ).
fof(f230,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,[],[f166]) ).
fof(f544,plain,
! [X0] :
( ~ v1_group_1(sK2)
| k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f221,f150]) ).
fof(f553,plain,
! [X0] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f544,f151]) ).
fof(f555,plain,
! [X0] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f553,f147]) ).
fof(f557,plain,
! [X0] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f555,f146]) ).
fof(f559,plain,
! [X0] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f557,f145]) ).
fof(f561,plain,
! [X0] :
( k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),k1_funct_1(k1_latsubgr(sK0),sK2)) = u1_struct_0(k9_group_2(sK0,X0,sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f559,f144]) ).
fof(f581,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,[],[f230,f174]) ).
fof(f582,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,[],[f581,f173]) ).
fof(f583,plain,
! [X3,X0] :
( ~ m1_group_2(X3,X0)
| ~ v1_group_1(X3)
| u1_struct_0(X3) = k1_funct_1(k1_latsubgr(X0),X3)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f582,f172]) ).
fof(f586,plain,
( ~ v1_group_1(sK1)
| k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f583,f148]) ).
fof(f587,plain,
( ~ v1_group_1(sK2)
| k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f583,f150]) ).
fof(f590,plain,
! [X2,X0,X1] :
( ~ v1_group_1(k9_group_2(X0,X1,X2))
| k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = u1_struct_0(k9_group_2(X0,X1,X2))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(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(resolution,[],[f583,f177]) ).
fof(f591,plain,
! [X2,X0,X1] :
( ~ v1_group_1(k9_group_2(X0,X1,X2))
| k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = u1_struct_0(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(duplicate_literal_removal,[],[f590]) ).
fof(f594,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| k1_funct_1(k1_latsubgr(X0),k9_group_2(X0,X1,X2)) = u1_struct_0(k9_group_2(X0,X1,X2)) ),
inference(forward_subsumption_resolution,[],[f591,f178]) ).
fof(f596,plain,
( k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f587,f151]) ).
fof(f597,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f586,f149]) ).
fof(f598,plain,
( k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f596,f147]) ).
fof(f599,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f597,f147]) ).
fof(f600,plain,
( k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f598,f146]) ).
fof(f601,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f599,f146]) ).
fof(f602,plain,
( k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f600,f145]) ).
fof(f603,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f601,f145]) ).
fof(f604,plain,
k1_funct_1(k1_latsubgr(sK0),sK2) = u1_struct_0(sK2),
inference(forward_subsumption_resolution,[],[f602,f144]) ).
fof(f605,plain,
k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1),
inference(forward_subsumption_resolution,[],[f603,f144]) ).
fof(f608,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(superposition,[],[f152,f605]) ).
fof(f609,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),
inference(forward_demodulation,[],[f608,f604]) ).
fof(f647,plain,
! [X0] :
( u1_struct_0(k9_group_2(sK0,X0,sK2)) = k3_xboole_0(k1_funct_1(k1_latsubgr(sK0),X0),u1_struct_0(sK2))
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_demodulation,[],[f561,f604]) ).
fof(f648,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| ~ v1_group_1(X0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k3_xboole_0(u1_struct_0(sK2),k1_funct_1(k1_latsubgr(sK0),X0)) ),
inference(forward_demodulation,[],[f647,f164]) ).
fof(f663,plain,
( ~ v1_group_1(sK1)
| k3_xboole_0(u1_struct_0(sK2),k1_funct_1(k1_latsubgr(sK0),sK1)) = u1_struct_0(k9_group_2(sK0,sK1,sK2)) ),
inference(resolution,[],[f648,f148]) ).
fof(f672,plain,
k3_xboole_0(u1_struct_0(sK2),k1_funct_1(k1_latsubgr(sK0),sK1)) = u1_struct_0(k9_group_2(sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[],[f663,f149]) ).
fof(f677,plain,
u1_struct_0(k9_group_2(sK0,sK1,sK2)) = k3_xboole_0(u1_struct_0(sK2),u1_struct_0(sK1)),
inference(forward_demodulation,[],[f672,f605]) ).
fof(f682,plain,
k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)) = u1_struct_0(k9_group_2(sK0,sK1,sK2)),
inference(forward_demodulation,[],[f677,f164]) ).
fof(f1220,plain,
! [X0] :
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,X0,sK2)) ),
inference(resolution,[],[f594,f150]) ).
fof(f1231,plain,
! [X0] :
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,X0,sK2)) ),
inference(forward_subsumption_resolution,[],[f1220,f147]) ).
fof(f1235,plain,
! [X0] :
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,X0,sK2)) ),
inference(forward_subsumption_resolution,[],[f1231,f146]) ).
fof(f1239,plain,
! [X0] :
( ~ l1_group_1(sK0)
| ~ m1_group_2(X0,sK0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,X0,sK2)) ),
inference(forward_subsumption_resolution,[],[f1235,f145]) ).
fof(f1243,plain,
! [X0] :
( ~ m1_group_2(X0,sK0)
| u1_struct_0(k9_group_2(sK0,X0,sK2)) = k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,X0,sK2)) ),
inference(forward_subsumption_resolution,[],[f1239,f144]) ).
fof(f1626,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) != u1_struct_0(k9_group_2(sK0,sK1,sK2)),
inference(forward_demodulation,[],[f609,f682]) ).
fof(f1646,plain,
k1_funct_1(k1_latsubgr(sK0),k9_group_2(sK0,sK1,sK2)) = u1_struct_0(k9_group_2(sK0,sK1,sK2)),
inference(resolution,[],[f1243,f148]) ).
fof(f1657,plain,
$false,
inference(forward_subsumption_resolution,[],[f1646,f1626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP645+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 10:23:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 % (2168260)Will run a generic schedule for satisfiability detection.
% 0.07/0.38 % (2168266)% WARNING: option uhcvi not known.
% 0.07/0.38 % (2168265)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2387607375_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.38 % (2168268)dis+10_1_sil=32000:sp=arity:random_seed=3705114681:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.38 % (2168269)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3403690259:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.38 % (2168266)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3143332820:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.38 % (2168267)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2230961513:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.38 % (2168270)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=767343477:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.38 % (2168271)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1165342198:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.38 % TRYING [1]
% 0.07/0.38 % TRYING [2]
% 0.07/0.38 % TRYING [3]
% 0.07/0.38 % TRYING [4]
% 0.07/0.38 % (2168268) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2168260-2168268"...
% 0.07/0.38 % (2168268)...printing done.
% 0.07/0.38 % (2168268)Refutation found. Thanks to Tanya!
% 0.07/0.38 % SZS status Theorem for theBenchmark
% 0.07/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.38 % (2168268)------------------------------
% 0.07/0.38 % (2168268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.38 % (2168268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.38 % (2168268)CaDiCaL version: 2.1.3
% 0.07/0.38 % (2168268)Termination reason: Refutation
% 0.07/0.38 % (2168268)Time elapsed: 0.019 s
% 0.07/0.38 % (2168268)Peak memory usage: 12 MB
% 0.07/0.38 % (2168268)Instructions burned: 53 (million)
% 0.07/0.38 % (2168260)Success in time 0.045 s
% 0.07/0.38 % Vampire exiting
%------------------------------------------------------------------------------