%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG222+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 : n026.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 09:29:50 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 205 ( 59 unt; 7 def)
% Number of atoms : 1515 ( 11 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1960 ( 650 ~;1142 |; 139 &)
% ( 7 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 0 sgn 169 !; 8 ?)
% 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)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_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)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,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,X1,X2] :
( ( ~ 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)
& ~ 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)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0)
& m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rmod_5) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
fof(f66,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f69,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] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
=> ( r1_tarski(X2,X3)
=> m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_rmod_5) ).
fof(f70,axiom,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f72,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_rmod_2(X2,X0,X1)
=> ! [X3] :
( m1_rmod_2(X3,X0,X1)
=> ! [X4] :
( m1_rmod_2(X4,X0,X1)
=> ( ( m1_rmod_2(X2,X0,X3)
& m1_rmod_2(X2,X0,X4) )
=> m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_rmod_3) ).
fof(f86,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3)))
& m1_subset_1(X3,k1_zfmisc_1(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)
& 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(f87,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ m1_rmod_2(k1_rmod_5(X0,X1,k5_subset_1(u1_struct_0(X1),X2,X3)),X0,k2_rmod_3(X0,X1,k1_rmod_5(X0,X1,X2),k1_rmod_5(X0,X1,X3)))
& m1_subset_1(X3,k1_zfmisc_1(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)
& 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,[],[f86]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0)
& m1_rmod_2(k1_rmod_5(X0,X1,X2),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)
| ~ 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)
| 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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(ennf_transformation,[],[f11]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( v3_vectsp_2(k1_rmod_5(X0,X1,X2),X0)
& m1_rmod_2(k1_rmod_5(X0,X1,X2),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)
| ~ 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)
| 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)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(flattening,[],[f99]) ).
fof(f103,plain,
! [X0,X1,X2] :
( m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f104,plain,
! [X0,X1,X2] :
( m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f103]) ).
fof(f143,plain,
! [X0,X1,X2] :
( k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f66]) ).
fof(f144,plain,
! [X0,X1,X2] :
( k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(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)
| ~ 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,[],[f69]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3))
| ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(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)
| ~ 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,[],[f145]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4))
| ~ m1_rmod_2(X2,X0,X3)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X4,X0,X1) )
| ~ m1_rmod_2(X3,X0,X1) )
| ~ m1_rmod_2(X2,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,[],[f72]) ).
fof(f149,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4))
| ~ m1_rmod_2(X2,X0,X3)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X4,X0,X1) )
| ~ m1_rmod_2(X3,X0,X1) )
| ~ m1_rmod_2(X2,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,[],[f148]) ).
fof(f158,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f87]) ).
fof(f159,plain,
~ m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k2_rmod_3(sK0,sK1,k1_rmod_5(sK0,sK1,sK2),k1_rmod_5(sK0,sK1,sK3))),
inference(cnf_transformation,[],[f87]) ).
fof(f160,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f87]) ).
fof(f161,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f163,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f164,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f165,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f166,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f167,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f168,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f169,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f170,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f171,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f172,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f173,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f174,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f175,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f176,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f177,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f178,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f179,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f180,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f185,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f193,plain,
! [X2,X0,X1] :
( m1_subset_1(k5_subset_1(X0,X1,X2),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| k5_subset_1(X0,X1,X2) = k3_xboole_0(X1,X2) ),
inference(cnf_transformation,[],[f144]) ).
fof(f286,plain,
! [X2,X3,X0,X1] :
( ~ l3_vectsp_1(X0)
| ~ v2_vectsp_2(X0)
| v10_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X2,X3)
| m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f287,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[],[f70]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X4] :
( ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ m1_rmod_2(X2,X0,X1)
| ~ m1_rmod_2(X3,X0,X1)
| ~ m1_rmod_2(X4,X0,X1)
| ~ m1_rmod_2(X2,X0,X4)
| ~ m1_rmod_2(X2,X0,X3)
| m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4)) ),
inference(cnf_transformation,[],[f149]) ).
fof(f299,plain,
~ v4_rlvect_1(sK0),
inference(consistent_polarity_flipping,[],[f178]) ).
fof(f300,plain,
~ v5_rlvect_1(sK0),
inference(consistent_polarity_flipping,[],[f177]) ).
fof(f301,plain,
~ v4_group_1(sK0),
inference(consistent_polarity_flipping,[],[f175]) ).
fof(f302,plain,
~ v6_vectsp_1(sK0),
inference(consistent_polarity_flipping,[],[f173]) ).
fof(f303,plain,
~ v7_vectsp_1(sK0),
inference(consistent_polarity_flipping,[],[f172]) ).
fof(f304,plain,
~ v8_vectsp_1(sK0),
inference(consistent_polarity_flipping,[],[f171]) ).
fof(f305,plain,
~ l3_vectsp_1(sK0),
inference(consistent_polarity_flipping,[],[f168]) ).
fof(f306,plain,
~ v4_rlvect_1(sK1),
inference(consistent_polarity_flipping,[],[f165]) ).
fof(f307,plain,
~ v5_rlvect_1(sK1),
inference(consistent_polarity_flipping,[],[f164]) ).
fof(f308,plain,
~ v5_vectsp_2(sK1,sK0),
inference(consistent_polarity_flipping,[],[f162]) ).
fof(f309,plain,
~ l1_vectsp_2(sK1,sK0),
inference(consistent_polarity_flipping,[],[f161]) ).
fof(f310,plain,
m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k2_rmod_3(sK0,sK1,k1_rmod_5(sK0,sK1,sK2),k1_rmod_5(sK0,sK1,sK3))),
inference(consistent_polarity_flipping,[],[f159]) ).
fof(f317,plain,
! [X2,X0,X1] :
( ~ v2_vectsp_2(X0)
| l1_vectsp_2(X1,X0)
| v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| v5_rlvect_1(X1)
| v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| l3_vectsp_1(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v10_vectsp_1(X0)
| v8_vectsp_1(X0)
| v7_vectsp_1(X0)
| v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,X1) ),
inference(consistent_polarity_flipping,[],[f189]) ).
fof(f379,plain,
! [X2,X3,X0,X1] :
( ~ v2_vectsp_2(X0)
| l3_vectsp_1(X0)
| v10_vectsp_1(X0)
| v8_vectsp_1(X0)
| v7_vectsp_1(X0)
| v6_vectsp_1(X0)
| ~ v7_group_1(X0)
| v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| l1_vectsp_2(X1,X0)
| v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| v5_rlvect_1(X1)
| v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_tarski(X2,X3)
| ~ m1_rmod_2(k1_rmod_5(X0,X1,X2),X0,k1_rmod_5(X0,X1,X3)) ),
inference(consistent_polarity_flipping,[],[f286]) ).
fof(f380,plain,
! [X2,X3,X0,X1,X4] :
( ~ m1_rmod_2(X2,X0,k2_rmod_3(X0,X1,X3,X4))
| v8_vectsp_1(X0)
| v7_vectsp_1(X0)
| v6_vectsp_1(X0)
| v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| l1_vectsp_2(X1,X0)
| v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| v5_rlvect_1(X1)
| v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| m1_rmod_2(X2,X0,X1)
| m1_rmod_2(X3,X0,X1)
| m1_rmod_2(X4,X0,X1)
| m1_rmod_2(X2,X0,X4)
| m1_rmod_2(X2,X0,X3)
| l3_vectsp_1(X0) ),
inference(consistent_polarity_flipping,[],[f289]) ).
fof(f406,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(superposition,[],[f287,f185]) ).
fof(f486,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| k5_subset_1(u1_struct_0(sK1),sK3,X0) = k3_xboole_0(sK3,X0) ),
inference(resolution,[],[f282,f158]) ).
fof(f487,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| k5_subset_1(u1_struct_0(sK1),sK2,X0) = k3_xboole_0(sK2,X0) ),
inference(resolution,[],[f282,f160]) ).
fof(f541,plain,
k5_subset_1(u1_struct_0(sK1),sK3,sK2) = k3_xboole_0(sK3,sK2),
inference(resolution,[],[f486,f160]) ).
fof(f559,plain,
k5_subset_1(u1_struct_0(sK1),sK3,sK2) = k3_xboole_0(sK2,sK3),
inference(forward_demodulation,[],[f541,f185]) ).
fof(f575,plain,
( m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(superposition,[],[f193,f559]) ).
fof(f576,plain,
( m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f575,f158]) ).
fof(f577,plain,
m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1))),
inference(forward_subsumption_resolution,[],[f576,f160]) ).
fof(f701,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| l3_vectsp_1(sK0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v10_vectsp_1(sK0)
| v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(resolution,[],[f317,f169]) ).
fof(f702,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v10_vectsp_1(sK0)
| v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f701,f305]) ).
fof(f703,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f702,f170]) ).
fof(f704,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f703,f304]) ).
fof(f705,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f704,f303]) ).
fof(f706,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f705,f302]) ).
fof(f707,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f706,f174]) ).
fof(f708,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f707,f301]) ).
fof(f709,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f708,f176]) ).
fof(f710,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f709,f300]) ).
fof(f711,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f710,f299]) ).
fof(f712,plain,
! [X0,X1] :
( l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(sK0)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0) ),
inference(forward_subsumption_resolution,[],[f711,f179]) ).
fof(f713,plain,
! [X0,X1] :
( ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,X0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f712,f180]) ).
fof(f714,plain,
( v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(resolution,[],[f380,f310]) ).
fof(f719,plain,
( v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f714,f304]) ).
fof(f720,plain,
( v6_vectsp_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f719,f303]) ).
fof(f721,plain,
( v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f720,f302]) ).
fof(f722,plain,
( ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f721,f301]) ).
fof(f723,plain,
( v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f722,f176]) ).
fof(f724,plain,
( v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f723,f300]) ).
fof(f725,plain,
( ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f724,f299]) ).
fof(f726,plain,
( v3_struct_0(sK0)
| l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f725,f179]) ).
fof(f727,plain,
( l1_vectsp_2(sK1,sK0)
| v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f726,f180]) ).
fof(f728,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f727,f309]) ).
fof(f729,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f728,f308]) ).
fof(f730,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f729,f163]) ).
fof(f731,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f730,f307]) ).
fof(f732,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f731,f306]) ).
fof(f733,plain,
( v3_struct_0(sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f732,f166]) ).
fof(f734,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f733,f167]) ).
fof(f735,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[],[f734,f305]) ).
fof(f737,definition,
( spl28_16
<=> m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl28_16])],[avatar_definition]) ).
fof(f739,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK2))
| ~ spl28_16 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f741,definition,
( spl28_17
<=> m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3)) ),
introduced(definition,[new_symbols(definition,[spl28_17])],[avatar_definition]) ).
fof(f743,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| ~ spl28_17 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f745,definition,
( spl28_18
<=> m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl28_18])],[avatar_definition]) ).
fof(f747,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,sK3),sK0,sK1)
| ~ spl28_18 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f749,definition,
( spl28_19
<=> m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl28_19])],[avatar_definition]) ).
fof(f751,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,sK2),sK0,sK1)
| ~ spl28_19 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f753,definition,
( spl28_20
<=> m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl28_20])],[avatar_definition]) ).
fof(f755,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k5_subset_1(u1_struct_0(sK1),sK2,sK3)),sK0,sK1)
| ~ spl28_20 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f756,plain,
( spl28_16
| spl28_17
| spl28_18
| spl28_19
| spl28_20 ),
inference(avatar_split_clause,[],[f735,f753,f749,f745,f741,f737]) ).
fof(f767,plain,
! [X2,X0,X1] :
( l3_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(resolution,[],[f379,f169]) ).
fof(f768,plain,
! [X2,X0,X1] :
( v10_vectsp_1(sK0)
| v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f767,f305]) ).
fof(f769,plain,
! [X2,X0,X1] :
( v8_vectsp_1(sK0)
| v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f768,f170]) ).
fof(f770,plain,
! [X2,X0,X1] :
( v7_vectsp_1(sK0)
| v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f769,f304]) ).
fof(f771,plain,
! [X2,X0,X1] :
( v6_vectsp_1(sK0)
| ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f770,f303]) ).
fof(f772,plain,
! [X2,X0,X1] :
( ~ v7_group_1(sK0)
| v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f771,f302]) ).
fof(f773,plain,
! [X2,X0,X1] :
( v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f772,f174]) ).
fof(f774,plain,
! [X2,X0,X1] :
( ~ v6_rlvect_1(sK0)
| v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f773,f301]) ).
fof(f775,plain,
! [X2,X0,X1] :
( v5_rlvect_1(sK0)
| v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f774,f176]) ).
fof(f776,plain,
! [X2,X0,X1] :
( v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f775,f300]) ).
fof(f777,plain,
! [X2,X0,X1] :
( ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f776,f299]) ).
fof(f778,plain,
! [X2,X0,X1] :
( v3_struct_0(sK0)
| l1_vectsp_2(X0,sK0)
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f777,f179]) ).
fof(f779,plain,
! [X2,X0,X1] :
( ~ m1_rmod_2(k1_rmod_5(sK0,X0,X1),sK0,k1_rmod_5(sK0,X0,X2))
| v5_vectsp_2(X0,sK0)
| ~ v6_rlvect_1(X0)
| v5_rlvect_1(X0)
| v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r1_tarski(X1,X2)
| l1_vectsp_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f778,f180]) ).
fof(f785,plain,
k5_subset_1(u1_struct_0(sK1),sK2,sK3) = k3_xboole_0(sK2,sK3),
inference(resolution,[],[f487,f158]) ).
fof(f888,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(resolution,[],[f779,f739]) ).
fof(f893,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f888,f308]) ).
fof(f896,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f893,f163]) ).
fof(f899,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f896,f307]) ).
fof(f902,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f899,f306]) ).
fof(f905,plain,
( v3_struct_0(sK1)
| ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f902,f166]) ).
fof(f908,plain,
( ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f905,f167]) ).
fof(f911,plain,
( ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f908,f160]) ).
fof(f914,plain,
( ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| ~ spl28_16 ),
inference(forward_subsumption_resolution,[],[f911,f309]) ).
fof(f918,definition,
( spl28_25
<=> r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl28_25])],[avatar_definition]) ).
fof(f920,plain,
( ~ r1_tarski(k5_subset_1(u1_struct_0(sK1),sK2,sK3),sK2)
| spl28_25 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f922,definition,
( spl28_26
<=> m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1))) ),
introduced(definition,[new_symbols(definition,[spl28_26])],[avatar_definition]) ).
fof(f924,plain,
( ~ m1_subset_1(k5_subset_1(u1_struct_0(sK1),sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| spl28_26 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f925,plain,
( ~ spl28_25
| ~ spl28_26
| ~ spl28_16 ),
inference(avatar_split_clause,[],[f914,f737,f922,f918]) ).
fof(f938,plain,
( ~ r1_tarski(k3_xboole_0(sK2,sK3),sK2)
| spl28_25 ),
inference(superposition,[],[f920,f785]) ).
fof(f942,plain,
( $false
| spl28_25 ),
inference(forward_subsumption_resolution,[],[f938,f287]) ).
fof(f943,plain,
spl28_25,
inference(avatar_contradiction_clause,[],[f942]) ).
fof(f945,plain,
( ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| spl28_26 ),
inference(forward_demodulation,[],[f924,f785]) ).
fof(f946,plain,
( $false
| spl28_26 ),
inference(forward_subsumption_resolution,[],[f945,f577]) ).
fof(f947,plain,
spl28_26,
inference(avatar_contradiction_clause,[],[f946]) ).
fof(f950,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(resolution,[],[f747,f713]) ).
fof(f951,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f950,f308]) ).
fof(f952,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f951,f163]) ).
fof(f953,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f952,f307]) ).
fof(f954,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f953,f306]) ).
fof(f955,plain,
( v3_struct_0(sK1)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f954,f166]) ).
fof(f956,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f955,f167]) ).
fof(f957,plain,
( l1_vectsp_2(sK1,sK0)
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f956,f158]) ).
fof(f958,plain,
( $false
| ~ spl28_18 ),
inference(forward_subsumption_resolution,[],[f957,f309]) ).
fof(f959,plain,
~ spl28_18,
inference(avatar_contradiction_clause,[],[f958]) ).
fof(f996,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(resolution,[],[f751,f713]) ).
fof(f997,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f996,f308]) ).
fof(f998,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f997,f163]) ).
fof(f999,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f998,f307]) ).
fof(f1000,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f999,f306]) ).
fof(f1001,plain,
( v3_struct_0(sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1000,f166]) ).
fof(f1002,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1001,f167]) ).
fof(f1003,plain,
( l1_vectsp_2(sK1,sK0)
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1002,f160]) ).
fof(f1004,plain,
( $false
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1003,f309]) ).
fof(f1005,plain,
~ spl28_19,
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1006,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k3_xboole_0(sK2,sK3)),sK0,sK1)
| ~ spl28_20 ),
inference(forward_demodulation,[],[f755,f785]) ).
fof(f1043,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(resolution,[],[f1006,f713]) ).
fof(f1044,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1043,f308]) ).
fof(f1045,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1044,f163]) ).
fof(f1046,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1045,f307]) ).
fof(f1047,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1046,f306]) ).
fof(f1048,plain,
( v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1047,f166]) ).
fof(f1049,plain,
( ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1048,f167]) ).
fof(f1050,plain,
( l1_vectsp_2(sK1,sK0)
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1049,f577]) ).
fof(f1051,plain,
( $false
| ~ spl28_20 ),
inference(forward_subsumption_resolution,[],[f1050,f309]) ).
fof(f1052,plain,
~ spl28_20,
inference(avatar_contradiction_clause,[],[f1051]) ).
fof(f1053,plain,
( m1_rmod_2(k1_rmod_5(sK0,sK1,k3_xboole_0(sK2,sK3)),sK0,k1_rmod_5(sK0,sK1,sK3))
| ~ spl28_17 ),
inference(forward_demodulation,[],[f743,f785]) ).
fof(f1151,plain,
( v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(resolution,[],[f1053,f779]) ).
fof(f1152,plain,
( ~ v6_rlvect_1(sK1)
| v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1151,f308]) ).
fof(f1153,plain,
( v5_rlvect_1(sK1)
| v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1152,f163]) ).
fof(f1154,plain,
( v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1153,f307]) ).
fof(f1155,plain,
( ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1154,f306]) ).
fof(f1156,plain,
( v3_struct_0(sK1)
| ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1155,f166]) ).
fof(f1157,plain,
( ~ m1_subset_1(k3_xboole_0(sK2,sK3),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1156,f167]) ).
fof(f1158,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1157,f577]) ).
fof(f1159,plain,
( ~ r1_tarski(k3_xboole_0(sK2,sK3),sK3)
| l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1158,f158]) ).
fof(f1160,plain,
( l1_vectsp_2(sK1,sK0)
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1159,f406]) ).
fof(f1161,plain,
( $false
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1160,f309]) ).
fof(f1162,plain,
~ spl28_17,
inference(avatar_contradiction_clause,[],[f1161]) ).
cnf(s22,plain,
( spl28_16
| spl28_17
| spl28_18
| spl28_19
| spl28_20 ),
inference(sat_conversion,[],[f756]) ).
cnf(s28,plain,
( ~ spl28_16
| ~ spl28_25
| ~ spl28_26 ),
inference(sat_conversion,[],[f925]) ).
cnf(s29,plain,
spl28_25,
inference(sat_conversion,[],[f943]) ).
cnf(s30,plain,
spl28_26,
inference(sat_conversion,[],[f947]) ).
cnf(s31,plain,
~ spl28_18,
inference(sat_conversion,[],[f959]) ).
cnf(s32,plain,
~ spl28_19,
inference(sat_conversion,[],[f1005]) ).
cnf(s33,plain,
~ spl28_20,
inference(sat_conversion,[],[f1052]) ).
cnf(s36,plain,
~ spl28_17,
inference(sat_conversion,[],[f1162]) ).
cnf(s37,plain,
~ spl28_16,
inference(rat,[],[s28,s30,s29]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s22,s33,s32,s31,s36,s37]) ).
fof(f1163,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG222+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 19:50:57 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.30 % (4182364)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (4182374)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=430730766:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (4182370)% WARNING: option uhcvi not known.
% 0.20/0.30 % (4182370)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4282431990:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (4182369)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3751308002_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (4182371)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=606862777:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (4182372)dis+10_1_sil=32000:sp=arity:random_seed=3840993789:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (4182373)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3632168772:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (4182375)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1222688236:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % TRYING [1]
% 0.20/0.30 % TRYING [2]
% 0.20/0.30 % TRYING [3]
% 0.20/0.30 % (4182370) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4182364-4182370"...
% 0.20/0.30 % (4182370)...printing done.
% 0.20/0.30 % (4182370)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (4182370)------------------------------
% 0.20/0.30 % (4182370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (4182370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (4182370)CaDiCaL version: 2.1.3
% 0.20/0.30 % (4182370)Termination reason: Refutation
% 0.20/0.30 % (4182370)Time elapsed: 0.031 s
% 0.20/0.30 % (4182370)Peak memory usage: 13 MB
% 0.20/0.30 % (4182370)Instructions burned: 49 (million)
% 0.20/0.30 % (4182364)Success in time 0.074 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------