%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG216+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 : n009.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 09:19:21 AM UTC 2026
% Result : Theorem 2.82s 1.06s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 126 ( 27 unt; 5 def)
% Number of atoms : 819 ( 39 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 1263 ( 570 ~; 557 |; 111 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 122 ( 0 sgn 116 !; 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)
& 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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_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)
& 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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f31,axiom,
! [X0] :
( l1_rlvect_1(X0)
=> l2_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(f33,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f34,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(f47,axiom,
! [X0] :
( l2_struct_0(X0)
=> m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
fof(f50,axiom,
! [X0] :
( l1_struct_0(X0)
=> ! [X1] :
( l1_vectsp_2(X1,X0)
=> l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
fof(f51,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(f54,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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
=> ( k1_rlvect_1(X0) = k2_group_1(X0)
| ( X2 != k1_rlvect_1(X1)
& X3 != k1_rlvect_1(X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1) )
& k1_rlvect_1(X0) != k2_group_1(X0)
& m1_subset_1(X2,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)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1) )
& k1_rlvect_1(X0) != k2_group_1(X0)
& m1_subset_1(X2,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)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) ),
inference(flattening,[],[f59]) ).
fof(f78,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f79,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f80,plain,
! [X0] :
( ( l1_vectsp_1(X0)
& l2_struct_0(X0) )
| ~ l2_vectsp_1(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f90,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0) )
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f96,plain,
! [X0] :
( ( l1_rlvect_1(X0)
& l2_vectsp_1(X0) )
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ( X2 != k1_rlvect_1(X1)
& X3 != k1_rlvect_1(X1) )
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| ~ m1_subset_1(X2,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ( X2 != k1_rlvect_1(X1)
& X3 != k1_rlvect_1(X1) )
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| ~ m1_subset_1(X2,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
( ( v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(sK2,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)
& ~ 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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f60]) ).
fof(f118,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f119,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f120,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f121,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f122,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f123,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f124,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f125,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f126,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f127,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f128,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f129,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f130,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f131,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f132,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f133,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f134,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f135,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f99]) ).
fof(f136,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f137,plain,
( v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f167,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f168,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f169,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f186,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f189,plain,
! [X0,X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f190,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rlvect_1(X1) != X3
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| k1_rlvect_1(X1) != X2
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f194,plain,
! [X3,X0,X1] :
( ~ v8_vectsp_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ v8_vectsp_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(equality_resolution,[],[f192]) ).
fof(f197,definition,
( spl21_1
<=> v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f199,plain,
( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl21_2
<=> v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f203,plain,
( v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f137,f201,f197]) ).
fof(f232,definition,
( spl21_3
<=> m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f234,plain,
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| spl21_3 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f244,plain,
( ~ l2_struct_0(sK1)
| spl21_3 ),
inference(resolution,[],[f234,f186]) ).
fof(f249,plain,
( ~ l1_rlvect_1(sK1)
| spl21_3 ),
inference(resolution,[],[f244,f167]) ).
fof(f264,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f194,f119]) ).
fof(f265,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f264,f127]) ).
fof(f266,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f265,f126]) ).
fof(f267,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f266,f125]) ).
fof(f268,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f267,f124]) ).
fof(f269,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f268,f123]) ).
fof(f270,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f269,f122]) ).
fof(f271,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f270,f121]) ).
fof(f272,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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,[],[f271,f120]) ).
fof(f273,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),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,[],[f272,f136]) ).
fof(f274,plain,
! [X0,X1] :
( ~ v5_vectsp_2(X0,sK0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),sK0,X0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f273,f118]) ).
fof(f275,plain,
( ! [X0] :
( ~ l1_vectsp_2(sK1,X0)
| ~ l1_struct_0(X0) )
| spl21_3 ),
inference(resolution,[],[f249,f189]) ).
fof(f277,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f195,f119]) ).
fof(f278,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f277,f127]) ).
fof(f279,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f278,f126]) ).
fof(f280,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f279,f125]) ).
fof(f281,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f280,f124]) ).
fof(f282,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f281,f123]) ).
fof(f283,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f282,f122]) ).
fof(f284,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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)
| k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f283,f121]) ).
fof(f285,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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,[],[f284,f120]) ).
fof(f286,plain,
! [X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,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,[],[f285,f136]) ).
fof(f287,plain,
! [X0,X1] :
( ~ v5_vectsp_2(X0,sK0)
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),sK0,X0)
| ~ l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f286,f118]) ).
fof(f288,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(resolution,[],[f274,f129]) ).
fof(f289,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(resolution,[],[f287,f129]) ).
fof(f290,plain,
( ~ l1_struct_0(sK0)
| spl21_3 ),
inference(resolution,[],[f275,f128]) ).
fof(f292,plain,
( ~ l2_struct_0(sK0)
| spl21_3 ),
inference(resolution,[],[f290,f168]) ).
fof(f299,plain,
( ~ l2_vectsp_1(sK0)
| spl21_3 ),
inference(resolution,[],[f292,f169]) ).
fof(f326,plain,
( ~ l3_vectsp_1(sK0)
| spl21_3 ),
inference(resolution,[],[f299,f190]) ).
fof(f327,plain,
( $false
| spl21_3 ),
inference(forward_subsumption_resolution,[],[f326,f118]) ).
fof(f328,plain,
spl21_3,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f329,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f288,f134]) ).
fof(f330,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f289,f134]) ).
fof(f331,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f329,f133]) ).
fof(f332,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f330,f133]) ).
fof(f333,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f331,f132]) ).
fof(f334,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f332,f132]) ).
fof(f335,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f333,f131]) ).
fof(f336,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v6_rlvect_1(sK1)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f334,f131]) ).
fof(f337,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f335,f130]) ).
fof(f338,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ l1_vectsp_2(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f336,f130]) ).
fof(f339,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f337,f128]) ).
fof(f340,plain,
! [X0] :
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f338,f128]) ).
fof(f342,definition,
( spl21_12
<=> ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
fof(f343,plain,
( ! [X0] :
( ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f344,plain,
( ~ spl21_3
| spl21_12 ),
inference(avatar_split_clause,[],[f339,f342,f232]) ).
fof(f346,definition,
( spl21_13
<=> ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
fof(f347,plain,
( ! [X0] :
( ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) )
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f348,plain,
( spl21_13
| ~ spl21_3 ),
inference(avatar_split_clause,[],[f340,f232,f346]) ).
fof(f357,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ spl21_2
| ~ spl21_13 ),
inference(resolution,[],[f347,f203]) ).
fof(f360,plain,
( $false
| ~ spl21_2
| ~ spl21_13 ),
inference(forward_subsumption_resolution,[],[f357,f135]) ).
fof(f361,plain,
( ~ spl21_2
| ~ spl21_13 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f364,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ spl21_1
| ~ spl21_12 ),
inference(resolution,[],[f199,f343]) ).
fof(f366,plain,
( $false
| ~ spl21_1
| ~ spl21_12 ),
inference(forward_subsumption_resolution,[],[f364,f135]) ).
fof(f367,plain,
( ~ spl21_1
| ~ spl21_12 ),
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f204]) ).
cnf(s6,plain,
spl21_3,
inference(sat_conversion,[],[f328]) ).
cnf(s7,plain,
( ~ spl21_3
| spl21_12 ),
inference(sat_conversion,[],[f344]) ).
cnf(s8,plain,
( ~ spl21_3
| spl21_13 ),
inference(sat_conversion,[],[f348]) ).
cnf(s9,plain,
( ~ spl21_2
| ~ spl21_13 ),
inference(sat_conversion,[],[f361]) ).
cnf(s10,plain,
( ~ spl21_1
| ~ spl21_12 ),
inference(sat_conversion,[],[f367]) ).
cnf(s11,plain,
spl21_13,
inference(rat,[],[s8,s6]) ).
cnf(s12,plain,
spl21_12,
inference(rat,[],[s7,s6]) ).
cnf(s13,plain,
~ spl21_2,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
~ spl21_1,
inference(rat,[],[s10,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s14]) ).
fof(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 19:45:01 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 2.82/1.06 % (3379708)Detected formulas, will run a generic FOF schedule.
% 2.82/1.06 % (3379717)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2304064270:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.06 % (3379717)Refutation not found, incomplete strategy
% 2.82/1.06 % (3379717)------------------------------
% 2.82/1.06 % (3379717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.06 % (3379717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.06 % (3379717)CaDiCaL version: 2.1.3
% 2.82/1.06 % (3379717)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.06 % (3379717)Time elapsed: 0.002 s
% 2.82/1.06 % (3379717)Peak memory usage: 88 MB
% 2.82/1.06 % (3379717)Instructions burned: 4 (million)
% 2.82/1.06 % (3379718)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1430419545:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.06 % (3379713)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=385678296:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.06 % (3379716)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3988626636:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.06 % (3379714)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=3754069637:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.06 % (3379715)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=852845768:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.06 % (3379716)Refutation not found, incomplete strategy
% 2.82/1.06 % (3379716)------------------------------
% 2.82/1.06 % (3379716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.06 % (3379716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.06 % (3379716)CaDiCaL version: 2.1.3
% 2.82/1.06 % (3379716)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.06 % (3379716)Time elapsed: 0.003 s
% 2.82/1.06 % (3379716)Peak memory usage: 88 MB
% 2.82/1.06 % (3379716)Instructions burned: 3 (million)
% 2.82/1.06 % (3379718)First to succeed.
% 2.82/1.06 % (3379719)dis-21_1_sil=8000:lcm=predicate:random_seed=1226068842:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.82/1.06 % (3379718)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3379708"
% 2.82/1.06 % (3379719)Also succeeded, but the first one will report.
% 2.82/1.06 % (3379717)------------------------------
% 2.82/1.06 % (3379717)------------------------------
% 2.82/1.06 % (3379727)lrs+10_1_sil=8000:sp=occurrence:random_seed=3918823044:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.82/1.06 % (3379727)Also succeeded, but the first one will report.
% 2.82/1.06 % (3379716)------------------------------
% 2.82/1.06 % (3379716)------------------------------
% 2.82/1.06 % (3379718)Refutation found. Thanks to Tanya!
% 2.82/1.06 % SZS status Theorem for theBenchmark
% 2.82/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.24 % (3379718)------------------------------
% 3.55/1.24 % (3379718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.24 % (3379718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.24 % (3379718)CaDiCaL version: 2.1.3
% 3.55/1.24 % (3379718)Termination reason: Refutation
% 3.55/1.24 % (3379718)Time elapsed: 0.012 s
% 3.55/1.24 % (3379718)Peak memory usage: 90 MB
% 3.55/1.24 % (3379718)Instructions burned: 15 (million)
% 3.55/1.24 % (3379718)------------------------------
% 3.55/1.24 % (3379718)------------------------------
% 3.55/1.24 % (3379708)Success in time 0.416 s
% 3.55/1.24 % Vampire exiting
%------------------------------------------------------------------------------