%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:19:23 AM UTC 2026
% Result : Theorem 3.12s 1.21s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 10
% Syntax : Number of formulae : 140 ( 34 unt; 2 def)
% Number of atoms : 1171 ( 93 equ)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 1814 ( 783 ~; 840 |; 168 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 105 ( 0 sgn 99 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v7_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& ~ v10_vectsp_1(X0)
& v2_vectsp_2(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v3_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( X2 = u1_struct_0(X1)
=> ( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_rmod_5) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v7_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& ~ v10_vectsp_1(X0)
& v2_vectsp_2(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v3_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( X2 = u1_struct_0(X1)
=> ( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( ( l1_struct_0(X0)
& l1_vectsp_2(X1,X0) )
=> ( v3_vectsp_2(X1,X0)
=> X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
fof(f8,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_rmod_2) ).
fof(f15,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0)
& ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ( v3_vectsp_2(k2_rmod_2(X0,X1),X0)
& m1_rmod_2(k2_rmod_2(X0,X1),X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
fof(f22,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f23,axiom,
! [X0] :
( l2_vectsp_1(X0)
=> ( l1_vectsp_1(X0)
& l2_struct_0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(f24,axiom,
! [X0] :
( l3_vectsp_1(X0)
=> ( l1_rlvect_1(X0)
& l2_vectsp_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(f65,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v7_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& ~ v10_vectsp_1(X0)
& v2_vectsp_2(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( ( v3_vectsp_2(X3,X0)
& m1_rmod_2(X3,X0,X1) )
=> ( X2 = u1_struct_0(X3)
=> ( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_rmod_5) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rlvect_1(X0) != k2_group_1(X0)
& k1_rmod_5(X0,X1,X2) != X1
& X2 = u1_struct_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
& ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v3_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v7_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& ~ v10_vectsp_1(X0)
& v2_vectsp_2(X0)
& l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rlvect_1(X0) != k2_group_1(X0)
& k1_rmod_5(X0,X1,X2) != X1
& X2 = u1_struct_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
& ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v3_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v7_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& ~ v10_vectsp_1(X0)
& v2_vectsp_2(X0)
& l3_vectsp_1(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1))
| ~ v3_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0,X1] :
( X1 = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1))
| ~ v3_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(flattening,[],[f81]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( k2_rmod_2(X0,X1) = g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(flattening,[],[f88]) ).
fof(f97,plain,
! [X0,X1] :
( ( v3_vectsp_2(k2_rmod_2(X0,X1),X0)
& m1_rmod_2(k2_rmod_2(X0,X1),X0,X1) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f98,plain,
! [X0,X1] :
( ( v3_vectsp_2(k2_rmod_2(X0,X1),X0)
& m1_rmod_2(k2_rmod_2(X0,X1),X0,X1) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(flattening,[],[f97]) ).
fof(f103,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f104,plain,
! [X0] :
( ( l1_vectsp_1(X0)
& l2_struct_0(X0) )
| ~ l2_vectsp_1(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f105,plain,
! [X0] :
( ( l1_rlvect_1(X0)
& l2_vectsp_1(X0) )
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X3
| u1_struct_0(X3) != X2
| ~ v3_vectsp_2(X3,X0)
| ~ m1_rmod_2(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v7_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| v10_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X3
| u1_struct_0(X3) != X2
| ~ v3_vectsp_2(X3,X0)
| ~ m1_rmod_2(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v7_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| v10_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ l3_vectsp_1(X0) ),
inference(flattening,[],[f135]) ).
fof(f147,plain,
( k1_rlvect_1(sK0) != k2_group_1(sK0)
& sK1 != k1_rmod_5(sK0,sK1,sK2)
& sK2 = u1_struct_0(sK1)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v3_struct_0(sK1)
& v3_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v6_rlvect_1(sK1)
& v3_vectsp_2(sK1,sK0)
& v5_vectsp_2(sK1,sK0)
& l1_vectsp_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v6_rlvect_1(sK0)
& v4_group_1(sK0)
& v7_group_1(sK0)
& v6_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& ~ v10_vectsp_1(sK0)
& v2_vectsp_2(sK0)
& l3_vectsp_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f80]) ).
fof(f173,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f174,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f175,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f176,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f178,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f179,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f180,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f181,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f182,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f183,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f184,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f185,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f186,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f187,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f188,plain,
v3_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f189,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f190,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f191,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f192,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f193,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f194,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f147]) ).
fof(f195,plain,
sK2 = u1_struct_0(sK1),
inference(cnf_transformation,[],[f147]) ).
fof(f196,plain,
sK1 != k1_rmod_5(sK0,sK1,sK2),
inference(cnf_transformation,[],[f147]) ).
fof(f197,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f198,plain,
! [X0,X1] :
( g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = X1
| ~ v3_vectsp_2(X1,X0)
| ~ l1_struct_0(X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f206,plain,
! [X0,X1] :
( ~ v7_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| g1_vectsp_2(X0,u1_struct_0(X1),u1_rlvect_1(X1),u2_struct_0(X1),u1_vectsp_2(X0,X1)) = k2_rmod_2(X0,X1)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f213,plain,
! [X0,X1] :
( m1_rmod_2(k2_rmod_2(X0,X1),X0,X1)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f219,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f220,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f222,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rmod_5(X0,X1,X2) = X3
| u1_struct_0(X3) != X2
| ~ v3_vectsp_2(X3,X0)
| ~ m1_rmod_2(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v7_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| v10_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f313,plain,
! [X3,X0,X1] :
( ~ v2_vectsp_2(X0)
| k1_rmod_5(X0,X1,u1_struct_0(X3)) = X3
| ~ v3_vectsp_2(X3,X0)
| ~ m1_rmod_2(X3,X0,X1)
| ~ m1_subset_1(u1_struct_0(X3),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v7_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| v10_vectsp_1(X0)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(equality_resolution,[],[f304]) ).
fof(f314,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK2)),
inference(forward_demodulation,[],[f194,f195]) ).
fof(f403,plain,
! [X0] :
( sK1 = g1_vectsp_2(X0,sK2,u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(X0,sK1))
| ~ v3_vectsp_2(sK1,X0)
| ~ l1_struct_0(X0)
| ~ l1_vectsp_2(sK1,X0) ),
inference(superposition,[],[f198,f195]) ).
fof(f485,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f206,f177]) ).
fof(f486,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f485,f185]) ).
fof(f487,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f486,f184]) ).
fof(f488,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f487,f183]) ).
fof(f489,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f488,f182]) ).
fof(f490,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f489,f181]) ).
fof(f491,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v6_vectsp_1(sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f490,f180]) ).
fof(f492,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f491,f178]) ).
fof(f493,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f492,f176]) ).
fof(f494,plain,
! [X0] :
( ~ v5_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X0,sK0)
| g1_vectsp_2(sK0,u1_struct_0(X0),u1_rlvect_1(X0),u2_struct_0(X0),u1_vectsp_2(sK0,X0)) = k2_rmod_2(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f493,f173]) ).
fof(f527,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f313,f174]) ).
fof(f528,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f527,f185]) ).
fof(f529,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f528,f184]) ).
fof(f530,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f529,f183]) ).
fof(f531,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f530,f182]) ).
fof(f532,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f531,f181]) ).
fof(f533,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f532,f180]) ).
fof(f534,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f533,f179]) ).
fof(f535,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f534,f178]) ).
fof(f536,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f535,f177]) ).
fof(f537,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| v10_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f536,f176]) ).
fof(f538,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f537,f175]) ).
fof(f539,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f538,f197]) ).
fof(f540,plain,
! [X0,X1] :
( k1_rmod_5(sK0,X0,u1_struct_0(X1)) = X1
| ~ v3_vectsp_2(X1,sK0)
| ~ m1_rmod_2(X1,sK0,X0)
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f539,f173]) ).
fof(f543,plain,
( ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(resolution,[],[f494,f187]) ).
fof(f548,plain,
( ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f543,f192]) ).
fof(f552,plain,
( ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f548,f191]) ).
fof(f556,plain,
( ~ v6_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f552,f190]) ).
fof(f560,plain,
( v3_struct_0(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f556,f189]) ).
fof(f564,plain,
( ~ l1_vectsp_2(sK1,sK0)
| g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f560,f193]) ).
fof(f568,plain,
g1_vectsp_2(sK0,u1_struct_0(sK1),u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)) = k2_rmod_2(sK0,sK1),
inference(forward_subsumption_resolution,[],[f564,f186]) ).
fof(f572,plain,
k2_rmod_2(sK0,sK1) = g1_vectsp_2(sK0,sK2,u1_rlvect_1(sK1),u2_struct_0(sK1),u1_vectsp_2(sK0,sK1)),
inference(forward_demodulation,[],[f568,f195]) ).
fof(f596,plain,
! [X0] :
( sK1 = k1_rmod_5(sK0,X0,sK2)
| ~ v3_vectsp_2(sK1,sK0)
| ~ m1_rmod_2(sK1,sK0,X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(superposition,[],[f540,f195]) ).
fof(f601,plain,
! [X0] :
( ~ m1_rmod_2(sK1,sK0,X0)
| sK1 = k1_rmod_5(sK0,X0,sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,sK0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f596,f188]) ).
fof(f602,plain,
( sK1 = k2_rmod_2(sK0,sK1)
| ~ v3_vectsp_2(sK1,sK0)
| ~ l1_struct_0(sK0)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(superposition,[],[f572,f403]) ).
fof(f607,plain,
( sK1 = k2_rmod_2(sK0,sK1)
| ~ l1_struct_0(sK0)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f602,f188]) ).
fof(f610,plain,
( sK1 = k2_rmod_2(sK0,sK1)
| ~ l1_struct_0(sK0) ),
inference(forward_subsumption_resolution,[],[f607,f186]) ).
fof(f613,definition,
( spl27_13
<=> l1_struct_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_13])],[avatar_definition]) ).
fof(f615,plain,
( ~ l1_struct_0(sK0)
| spl27_13 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f617,definition,
( spl27_14
<=> sK1 = k2_rmod_2(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl27_14])],[avatar_definition]) ).
fof(f619,plain,
( sK1 = k2_rmod_2(sK0,sK1)
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f621,plain,
( ~ spl27_13
| spl27_14 ),
inference(avatar_split_clause,[],[f610,f617,f613]) ).
fof(f653,plain,
( ~ l2_struct_0(sK0)
| spl27_13 ),
inference(resolution,[],[f615,f219]) ).
fof(f655,plain,
( ~ l2_vectsp_1(sK0)
| spl27_13 ),
inference(resolution,[],[f653,f220]) ).
fof(f662,plain,
( ~ l3_vectsp_1(sK0)
| spl27_13 ),
inference(resolution,[],[f655,f222]) ).
fof(f663,plain,
( $false
| spl27_13 ),
inference(forward_subsumption_resolution,[],[f662,f173]) ).
fof(f664,plain,
spl27_13,
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f671,plain,
( m1_rmod_2(sK1,sK0,sK1)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(superposition,[],[f213,f619]) ).
fof(f673,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f671,f185]) ).
fof(f674,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f673,f184]) ).
fof(f675,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f674,f183]) ).
fof(f676,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f675,f182]) ).
fof(f677,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f676,f181]) ).
fof(f678,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f677,f180]) ).
fof(f679,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f678,f178]) ).
fof(f680,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f679,f177]) ).
fof(f681,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f680,f176]) ).
fof(f682,plain,
( m1_rmod_2(sK1,sK0,sK1)
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f681,f173]) ).
fof(f683,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f682,f193]) ).
fof(f684,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f683,f192]) ).
fof(f685,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f684,f191]) ).
fof(f686,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f685,f190]) ).
fof(f687,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f686,f189]) ).
fof(f688,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f687,f187]) ).
fof(f689,plain,
( m1_rmod_2(sK1,sK0,sK1)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f688,f186]) ).
fof(f879,plain,
( sK1 = k1_rmod_5(sK0,sK1,sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(resolution,[],[f601,f689]) ).
fof(f880,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f879,f196]) ).
fof(f881,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f880,f193]) ).
fof(f882,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f881,f192]) ).
fof(f883,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f882,f191]) ).
fof(f884,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f883,f190]) ).
fof(f885,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f884,f189]) ).
fof(f886,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l1_vectsp_2(sK1,sK0)
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f885,f187]) ).
fof(f887,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f886,f186]) ).
fof(f888,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(sK2))
| ~ spl27_14 ),
inference(forward_demodulation,[],[f887,f195]) ).
fof(f889,plain,
( $false
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f888,f314]) ).
fof(f890,plain,
~ spl27_14,
inference(avatar_contradiction_clause,[],[f889]) ).
cnf(s12,plain,
( ~ spl27_13
| spl27_14 ),
inference(sat_conversion,[],[f621]) ).
cnf(s14,plain,
spl27_13,
inference(sat_conversion,[],[f664]) ).
cnf(s24,plain,
~ spl27_14,
inference(sat_conversion,[],[f890]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s12,s24,s14]) ).
fof(f891,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG219+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.28 % Computer : n015.cluster.edu
% 0.15/0.28 % Model : x86_64 x86_64
% 0.15/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.28 % Memory : 8046.5625MB
% 0.15/0.28 % OS : Linux 6.8.0-71-generic
% 0.15/0.28 % CPULimit : 300
% 0.15/0.28 % WCLimit : 300
% 0.15/0.28 % DateTime : Mon Sep 28 19:50:02 UTC 2026
% 0.15/0.28 % CPUTime :
% 0.15/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.32 Running first-order theorem proving
% 0.15/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.12/1.21 % (2941308)Detected formulas, will run a generic FOF schedule.
% 3.12/1.21 % (2941317)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1541326525:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.21 % (2941317)Refutation not found, incomplete strategy
% 3.12/1.21 % (2941317)------------------------------
% 3.12/1.21 % (2941317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.21 % (2941317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.21 % (2941317)CaDiCaL version: 2.1.3
% 3.12/1.21 % (2941317)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.21 % (2941317)Time elapsed: 0.006 s
% 3.12/1.21 % (2941317)Peak memory usage: 88 MB
% 3.12/1.21 % (2941317)Instructions burned: 19 (million)
% 3.12/1.21 % (2941313)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=1200309539:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.21 % (2941316)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3508683005:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.21 % (2941314)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=2679187093:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.21 % (2941315)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=733652609:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.21 % (2941316)Refutation not found, incomplete strategy
% 3.12/1.21 % (2941316)------------------------------
% 3.12/1.21 % (2941316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.21 % (2941316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.21 % (2941316)CaDiCaL version: 2.1.3
% 3.12/1.21 % (2941316)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.21 % (2941316)Time elapsed: 0.005 s
% 3.12/1.21 % (2941316)Peak memory usage: 88 MB
% 3.12/1.21 % (2941316)Instructions burned: 7 (million)
% 3.12/1.21 % (2941319)dis-21_1_sil=8000:lcm=predicate:random_seed=19710942: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)
% 3.12/1.21 % (2941318)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=418082553:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.21 % (2941318)First to succeed.
% 3.12/1.21 % (2941318)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2941308"
% 3.12/1.21 % (2941319)Instruction limit reached!
% 3.12/1.21 % (2941319)------------------------------
% 3.12/1.21 % (2941319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.21 % (2941319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.21 % (2941319)CaDiCaL version: 2.1.3
% 3.12/1.21 % (2941319)Termination reason: Instruction limit
% 3.12/1.21 % (2941319)Termination phase: Saturation
% 3.12/1.21 % (2941319)Time elapsed: 0.073 s
% 3.12/1.21 % (2941319)Peak memory usage: 90 MB
% 3.12/1.21 % (2941319)Instructions burned: 129 (million)
% 3.12/1.21 % (2941317)------------------------------
% 3.12/1.21 % (2941317)------------------------------
% 3.12/1.21 % (2941328)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2852756119:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.12/1.21 % (2941327)lrs+10_1_sil=8000:sp=occurrence:random_seed=3425884996:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.21 % (2941328)Instruction limit reached!
% 3.12/1.21 % (2941328)------------------------------
% 3.12/1.21 % (2941328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.21 % (2941328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.21 % (2941328)CaDiCaL version: 2.1.3
% 3.12/1.21 % (2941328)Termination reason: Instruction limit
% 3.12/1.21 % (2941328)Termination phase: Saturation
% 3.12/1.21 % (2941328)Time elapsed: 0.034 s
% 3.12/1.21 % (2941328)Peak memory usage: 89 MB
% 3.12/1.21 % (2941328)Instructions burned: 159 (million)
% 3.12/1.21 % (2941316)------------------------------
% 3.12/1.21 % (2941316)------------------------------
% 3.12/1.21 % (2941327)Also succeeded, but the first one will report.
% 3.12/1.21 % (2941318)Refutation found. Thanks to Tanya!
% 3.12/1.21 % SZS status Theorem for theBenchmark
% 3.12/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.41 % (2941318)------------------------------
% 0.21/1.41 % (2941318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.41 % (2941318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.41 % (2941318)CaDiCaL version: 2.1.3
% 0.21/1.41 % (2941318)Termination reason: Refutation
% 0.21/1.41 % (2941318)Time elapsed: 0.039 s
% 0.21/1.41 % (2941318)Peak memory usage: 90 MB
% 0.21/1.41 % (2941318)Instructions burned: 58 (million)
% 0.21/1.41 % (2941318)------------------------------
% 0.21/1.41 % (2941318)------------------------------
% 0.21/1.41 % (2941308)Success in time 0.462 s
% 0.21/1.41 % Vampire exiting
%------------------------------------------------------------------------------