%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG218+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:19:23 AM UTC 2026
% Result : Theorem 3.68s 1.18s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 24
% Syntax : Number of formulae : 210 ( 45 unt; 6 def)
% Number of atoms : 1138 ( 118 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1584 ( 656 ~; 718 |; 172 &)
% ( 15 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 241 ( 0 sgn 229 !; 12 ?)
% 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)))
=> ~ ( k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1)
& X2 != k1_xboole_0
& X2 != k7_rlvect_2(X1,k1_rlvect_1(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_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)))
=> ~ ( k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1)
& X2 != k1_xboole_0
& X2 != k7_rlvect_2(X1,k1_rlvect_1(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = k1_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f10,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f12,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(f21,axiom,
! [X0] :
( l1_rlvect_1(X0)
=> l2_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(f24,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(f25,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f26,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(f27,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(f46,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f61,axiom,
! [X0] :
? [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f68,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0)
& m1_subset_1(X1,u1_struct_0(X0)) )
=> k7_rlvect_2(X0,X1) = k1_tarski(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_rlvect_2) ).
fof(f71,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( r2_hidden(X0,X3)
=> r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_rmod_5) ).
fof(f73,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f74,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f75,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_rmod_2) ).
fof(f78,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f87,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1)
& X2 != k1_xboole_0
& X2 != k7_rlvect_2(X1,k1_rlvect_1(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(f88,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_rmod_5(X0,X1,X2) = k1_rmod_2(X0,X1)
& X2 != k1_xboole_0
& X2 != k7_rlvect_2(X1,k1_rlvect_1(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,[],[f87]) ).
fof(f96,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f99,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f107,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0) )
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f110,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f111,plain,
! [X0] :
( ( l1_vectsp_1(X0)
& l2_struct_0(X0) )
| ~ l2_vectsp_1(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f112,plain,
! [X0] :
( ( l1_rlvect_1(X0)
& l2_vectsp_1(X0) )
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f144,plain,
! [X0,X1] :
( k7_rlvect_2(X0,X1) = k1_tarski(X1)
| v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f68]) ).
fof(f145,plain,
! [X0,X1] :
( k7_rlvect_2(X0,X1) = k1_tarski(X1)
| v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0)
| ~ r2_hidden(X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| v10_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l3_vectsp_1(X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f147,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0)
| ~ r2_hidden(X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| v10_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l3_vectsp_1(X1) ),
inference(flattening,[],[f146]) ).
fof(f149,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f150,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( ! [X2] :
( ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) )
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f152,plain,
! [X0,X1] :
( ! [X2] :
( ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
<=> X0 = k1_rlvect_1(X2) )
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(flattening,[],[f151]) ).
fof(f156,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f159,plain,
( k1_rmod_5(sK0,sK1,sK2) = k1_rmod_2(sK0,sK1)
& k1_xboole_0 != sK2
& sK2 != k7_rlvect_2(sK1,k1_rlvect_1(sK1))
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v3_struct_0(sK1)
& v3_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v6_rlvect_1(sK1)
& v5_vectsp_2(sK1,sK0)
& l1_vectsp_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v6_rlvect_1(sK0)
& v4_group_1(sK0)
& v7_group_1(sK0)
& v6_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& ~ v10_vectsp_1(sK0)
& v2_vectsp_2(sK0)
& l3_vectsp_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f88]) ).
fof(f160,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f161,plain,
! [X0,X1] :
( ( X0 = X1
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X0) )
& ( ( r1_tarski(X0,X1)
& r1_tarski(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ( X1 = k1_tarski(X0)
| ? [X2] :
( ( X0 != X2
| ~ r2_hidden(X2,X1) )
& ( X2 = X0
| r2_hidden(X2,X1) ) ) )
& ( ! [X2] :
( ( r2_hidden(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ r2_hidden(X2,X1) ) )
| k1_tarski(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f163,plain,
! [X0,X1] :
( ( X1 = k1_tarski(X0)
| ? [X2] :
( ( X0 != X2
| ~ r2_hidden(X2,X1) )
& ( X2 = X0
| r2_hidden(X2,X1) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ r2_hidden(X3,X1) ) )
| k1_tarski(X0) != X1 ) ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( ( X1 = k1_tarski(X0)
| ( ( sK3(X0,X1) != X0
| ~ r2_hidden(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| r2_hidden(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ r2_hidden(X3,X1) ) )
| k1_tarski(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f163]) ).
fof(f165,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f166,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f165]) ).
fof(f167,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK4(X0,X1),X1)
& r2_hidden(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f166]) ).
fof(f178,plain,
! [X0] : m1_subset_1(sK15(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f46]) ).
fof(f186,plain,
! [X0] :
( m1_subset_1(sK23(X0),k1_zfmisc_1(X0))
& v1_xboole_0(sK23(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f61]) ).
fof(f194,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f195,plain,
! [X0,X1] :
( ! [X2] :
( ( ( r1_rlvect_1(k1_rmod_2(X1,X2),X0)
| k1_rlvect_1(X2) != X0 )
& ( X0 = k1_rlvect_1(X2)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X0) ) )
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(nnf_transformation,[],[f152]) ).
fof(f196,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f197,plain,
v2_vectsp_2(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f198,plain,
~ v10_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f199,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f200,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f201,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f202,plain,
v7_group_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f203,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f204,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f205,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f206,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f207,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f208,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f209,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f210,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f159]) ).
fof(f211,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f212,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f213,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f214,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f215,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f216,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f159]) ).
fof(f217,plain,
sK2 != k7_rlvect_2(sK1,k1_rlvect_1(sK1)),
inference(cnf_transformation,[],[f159]) ).
fof(f218,plain,
k1_xboole_0 != sK2,
inference(cnf_transformation,[],[f159]) ).
fof(f219,plain,
k1_rmod_5(sK0,sK1,sK2) = k1_rmod_2(sK0,sK1),
inference(cnf_transformation,[],[f159]) ).
fof(f230,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| X0 = X1
| ~ r1_tarski(X1,X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f233,plain,
! [X0,X1] :
( sK3(X0,X1) = X0
| k1_tarski(X0) = X1
| r2_hidden(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f164]) ).
fof(f234,plain,
! [X0,X1] :
( sK3(X0,X1) != X0
| k1_tarski(X0) = X1
| ~ r2_hidden(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f164]) ).
fof(f236,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| r2_hidden(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f240,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f247,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f249,plain,
! [X0,X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f250,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f251,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f253,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f280,plain,
! [X0] : m1_subset_1(sK15(X0),X0),
inference(cnf_transformation,[],[f178]) ).
fof(f322,plain,
! [X0] : v1_xboole_0(sK23(X0)),
inference(cnf_transformation,[],[f186]) ).
fof(f323,plain,
! [X0] : m1_subset_1(sK23(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f186]) ).
fof(f335,plain,
! [X0,X1] :
( k7_rlvect_2(X0,X1) = k1_tarski(X1)
| v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f339,plain,
! [X2,X3,X0,X1] :
( ~ v2_vectsp_2(X1)
| ~ r2_hidden(X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| v10_vectsp_1(X1)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X0)
| ~ l3_vectsp_1(X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f341,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f342,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f344,plain,
! [X2,X0,X1] :
( ~ v7_vectsp_1(X1)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X0)
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| k1_rlvect_1(X2) = X0
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(cnf_transformation,[],[f195]) ).
fof(f348,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f358,plain,
! [X0] : k1_xboole_0 = sK23(X0),
inference(resolution,[],[f348,f322]) ).
fof(f361,plain,
! [X0] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X0)),
inference(superposition,[],[f323,f358]) ).
fof(f380,plain,
! [X0,X1] :
( ~ r1_tarski(X1,X0)
| X0 = X1
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(resolution,[],[f230,f342]) ).
fof(f409,plain,
! [X0,X1] :
( X0 != X0
| k1_tarski(X0) = X1
| ~ r2_hidden(X0,X1)
| k1_tarski(X0) = X1
| r2_hidden(sK3(X0,X1),X1) ),
inference(superposition,[],[f234,f233]) ).
fof(f410,plain,
! [X0,X1] :
( X0 != X0
| k1_tarski(X0) = X1
| ~ r2_hidden(X0,X1)
| r2_hidden(sK3(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f411,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| k1_tarski(X0) = X1
| r2_hidden(sK3(X0,X1),X1) ),
inference(trivial_inequality_removal,[],[f410]) ).
fof(f416,plain,
( sK2 != k1_tarski(k1_rlvect_1(sK1))
| v3_struct_0(sK1)
| ~ l1_struct_0(sK1)
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)) ),
inference(superposition,[],[f217,f335]) ).
fof(f417,plain,
( sK2 != k1_tarski(k1_rlvect_1(sK1))
| ~ l1_struct_0(sK1)
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f416,f215]) ).
fof(f419,definition,
( spl30_1
<=> m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f421,plain,
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| spl30_1 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f423,definition,
( spl30_2
<=> l1_struct_0(sK1) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f425,plain,
( ~ l1_struct_0(sK1)
| spl30_2 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f427,definition,
( spl30_3
<=> sK2 = k1_tarski(k1_rlvect_1(sK1)) ),
introduced(definition,[new_symbols(definition,[spl30_3])],[avatar_definition]) ).
fof(f429,plain,
( sK2 != k1_tarski(k1_rlvect_1(sK1))
| spl30_3 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f430,plain,
( ~ spl30_1
| ~ spl30_2
| ~ spl30_3 ),
inference(avatar_split_clause,[],[f417,f427,f423,f419]) ).
fof(f431,plain,
( ~ l2_struct_0(sK1)
| spl30_1 ),
inference(resolution,[],[f421,f240]) ).
fof(f436,plain,
( ~ l1_rlvect_1(sK1)
| spl30_1 ),
inference(resolution,[],[f431,f247]) ).
fof(f439,plain,
( ! [X0] :
( ~ l1_vectsp_2(sK1,X0)
| ~ l1_struct_0(X0) )
| spl30_1 ),
inference(resolution,[],[f436,f249]) ).
fof(f442,plain,
( ~ l1_struct_0(sK0)
| spl30_1 ),
inference(resolution,[],[f439,f209]) ).
fof(f443,plain,
( ~ l2_struct_0(sK0)
| spl30_1 ),
inference(resolution,[],[f442,f250]) ).
fof(f445,plain,
( ~ l2_vectsp_1(sK0)
| spl30_1 ),
inference(resolution,[],[f443,f251]) ).
fof(f448,plain,
( ~ l3_vectsp_1(sK0)
| spl30_1 ),
inference(resolution,[],[f445,f253]) ).
fof(f449,plain,
( $false
| spl30_1 ),
inference(forward_subsumption_resolution,[],[f448,f196]) ).
fof(f450,plain,
spl30_1,
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f451,plain,
( ~ l2_struct_0(sK1)
| spl30_2 ),
inference(resolution,[],[f425,f250]) ).
fof(f454,plain,
( ~ l1_rlvect_1(sK1)
| spl30_2 ),
inference(resolution,[],[f451,f247]) ).
fof(f457,plain,
( ! [X0] :
( ~ l1_vectsp_2(sK1,X0)
| ~ l1_struct_0(X0) )
| spl30_2 ),
inference(resolution,[],[f454,f249]) ).
fof(f460,plain,
( ~ l1_struct_0(sK0)
| spl30_2 ),
inference(resolution,[],[f457,f209]) ).
fof(f461,plain,
( ~ l2_struct_0(sK0)
| spl30_2 ),
inference(resolution,[],[f460,f250]) ).
fof(f463,plain,
( ~ l2_vectsp_1(sK0)
| spl30_2 ),
inference(resolution,[],[f461,f251]) ).
fof(f466,plain,
( ~ l3_vectsp_1(sK0)
| spl30_2 ),
inference(resolution,[],[f463,f253]) ).
fof(f467,plain,
( $false
| spl30_2 ),
inference(forward_subsumption_resolution,[],[f466,f196]) ).
fof(f468,plain,
spl30_2,
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f501,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f344,f200]) ).
fof(f502,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f501,f208]) ).
fof(f503,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f502,f207]) ).
fof(f504,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f503,f206]) ).
fof(f505,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f504,f205]) ).
fof(f506,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f505,f204]) ).
fof(f507,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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)
| k1_rlvect_1(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f506,f203]) ).
fof(f508,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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(X0) = X1
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f507,f201]) ).
fof(f509,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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(X0) = X1
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f508,f199]) ).
fof(f510,plain,
! [X0,X1] :
( ~ r1_rlvect_1(k1_rmod_2(sK0,X0),X1)
| 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(X0) = X1 ),
inference(forward_subsumption_resolution,[],[f509,f196]) ).
fof(f573,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(resolution,[],[f339,f197]) ).
fof(f574,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f573,f208]) ).
fof(f575,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f574,f207]) ).
fof(f576,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f575,f206]) ).
fof(f577,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f576,f205]) ).
fof(f578,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v4_group_1(sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f577,f204]) ).
fof(f579,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v7_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f578,f203]) ).
fof(f580,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f579,f202]) ).
fof(f581,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f580,f201]) ).
fof(f582,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ v8_vectsp_1(sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f581,f200]) ).
fof(f583,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| v10_vectsp_1(sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f582,f199]) ).
fof(f584,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ l3_vectsp_1(sK0) ),
inference(forward_subsumption_resolution,[],[f583,f198]) ).
fof(f585,plain,
! [X2,X0,X1] :
( r1_rlvect_1(k1_rmod_5(sK0,X2,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,sK0)
| ~ l1_vectsp_2(X2,sK0)
| ~ r2_hidden(X0,X1) ),
inference(forward_subsumption_resolution,[],[f584,f196]) ).
fof(f595,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| v3_struct_0(sK1)
| ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(superposition,[],[f585,f219]) ).
fof(f596,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| 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)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f595,f216]) ).
fof(f597,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ 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)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f596,f215]) ).
fof(f598,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f597,f214]) ).
fof(f599,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f598,f213]) ).
fof(f600,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f599,f212]) ).
fof(f601,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f600,f211]) ).
fof(f602,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ l1_vectsp_2(sK1,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f601,f210]) ).
fof(f603,plain,
! [X0] :
( r1_rlvect_1(k1_rmod_2(sK0,sK1),X0)
| ~ r2_hidden(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f602,f209]) ).
fof(f607,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| 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)
| k1_rlvect_1(sK1) = X0 ),
inference(resolution,[],[f603,f510]) ).
fof(f608,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ 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)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f607,f215]) ).
fof(f609,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f608,f214]) ).
fof(f610,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f609,f213]) ).
fof(f611,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f610,f212]) ).
fof(f612,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f611,f211]) ).
fof(f613,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| ~ l1_vectsp_2(sK1,sK0)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f612,f210]) ).
fof(f614,plain,
! [X0] :
( ~ r2_hidden(X0,sK2)
| k1_rlvect_1(sK1) = X0 ),
inference(forward_subsumption_resolution,[],[f613,f209]) ).
fof(f616,plain,
! [X0,X1] :
( r2_hidden(sK4(X1,X0),X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| X0 = X1 ),
inference(resolution,[],[f380,f236]) ).
fof(f618,plain,
! [X0] :
( k1_rlvect_1(sK1) = X0
| v1_xboole_0(sK2)
| ~ m1_subset_1(X0,sK2) ),
inference(resolution,[],[f614,f341]) ).
fof(f620,definition,
( spl30_4
<=> v1_xboole_0(sK2) ),
introduced(definition,[new_symbols(definition,[spl30_4])],[avatar_definition]) ).
fof(f621,plain,
( ~ v1_xboole_0(sK2)
| spl30_4 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f622,plain,
( v1_xboole_0(sK2)
| ~ spl30_4 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f624,definition,
( spl30_5
<=> ! [X0] :
( k1_rlvect_1(sK1) = X0
| ~ m1_subset_1(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl30_5])],[avatar_definition]) ).
fof(f625,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sK2)
| k1_rlvect_1(sK1) = X0 )
| ~ spl30_5 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f626,plain,
( spl30_4
| spl30_5 ),
inference(avatar_split_clause,[],[f618,f624,f620]) ).
fof(f633,plain,
( k1_rlvect_1(sK1) = sK15(sK2)
| ~ spl30_5 ),
inference(resolution,[],[f625,f280]) ).
fof(f648,plain,
! [X0,X1] :
( r2_hidden(sK3(X0,X1),X1)
| k1_tarski(X0) = X1
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(resolution,[],[f411,f341]) ).
fof(f681,plain,
( k1_xboole_0 = sK2
| ~ spl30_4 ),
inference(resolution,[],[f622,f348]) ).
fof(f682,plain,
( $false
| ~ spl30_4 ),
inference(forward_subsumption_resolution,[],[f681,f218]) ).
fof(f683,plain,
~ spl30_4,
inference(avatar_contradiction_clause,[],[f682]) ).
fof(f944,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK2))
| sK2 = X0
| k1_rlvect_1(sK1) = sK4(sK2,X0) ),
inference(resolution,[],[f616,f614]) ).
fof(f1020,plain,
! [X0] :
( k1_tarski(X0) = sK2
| v1_xboole_0(sK2)
| ~ m1_subset_1(X0,sK2)
| k1_rlvect_1(sK1) = sK3(X0,sK2) ),
inference(resolution,[],[f648,f614]) ).
fof(f1034,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sK2)
| k1_tarski(X0) = sK2
| k1_rlvect_1(sK1) = sK3(X0,sK2) )
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f1020,f621]) ).
fof(f2389,plain,
( k1_xboole_0 = sK2
| k1_rlvect_1(sK1) = sK4(sK2,k1_xboole_0) ),
inference(resolution,[],[f944,f361]) ).
fof(f2396,plain,
k1_rlvect_1(sK1) = sK4(sK2,k1_xboole_0),
inference(forward_subsumption_resolution,[],[f2389,f218]) ).
fof(f2412,plain,
( r2_hidden(k1_rlvect_1(sK1),sK2)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(sK2))
| k1_xboole_0 = sK2 ),
inference(superposition,[],[f616,f2396]) ).
fof(f2422,plain,
( r2_hidden(k1_rlvect_1(sK1),sK2)
| k1_xboole_0 = sK2 ),
inference(forward_subsumption_resolution,[],[f2412,f361]) ).
fof(f2436,definition,
( spl30_79
<=> r2_hidden(k1_rlvect_1(sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl30_79])],[avatar_definition]) ).
fof(f2438,plain,
( r2_hidden(k1_rlvect_1(sK1),sK2)
| ~ spl30_79 ),
inference(avatar_component_clause,[],[f2436]) ).
fof(f2449,plain,
r2_hidden(k1_rlvect_1(sK1),sK2),
inference(forward_subsumption_resolution,[],[f2422,f218]) ).
fof(f2450,plain,
spl30_79,
inference(avatar_split_clause,[],[f2449,f2436]) ).
fof(f2454,plain,
( sK2 = k1_tarski(sK15(sK2))
| k1_rlvect_1(sK1) = sK3(sK15(sK2),sK2)
| spl30_4 ),
inference(resolution,[],[f1034,f280]) ).
fof(f2455,plain,
( sK2 = k1_tarski(k1_rlvect_1(sK1))
| k1_rlvect_1(sK1) = sK3(sK15(sK2),sK2)
| spl30_4
| ~ spl30_5 ),
inference(forward_demodulation,[],[f2454,f633]) ).
fof(f2457,plain,
( k1_rlvect_1(sK1) = sK3(sK15(sK2),sK2)
| spl30_3
| spl30_4
| ~ spl30_5 ),
inference(forward_subsumption_resolution,[],[f2455,f429]) ).
fof(f2458,plain,
( k1_rlvect_1(sK1) = sK3(k1_rlvect_1(sK1),sK2)
| spl30_3
| spl30_4
| ~ spl30_5 ),
inference(forward_demodulation,[],[f2457,f633]) ).
fof(f2657,plain,
( k1_rlvect_1(sK1) != k1_rlvect_1(sK1)
| sK2 = k1_tarski(k1_rlvect_1(sK1))
| ~ r2_hidden(k1_rlvect_1(sK1),sK2)
| spl30_3
| spl30_4
| ~ spl30_5 ),
inference(superposition,[],[f234,f2458]) ).
fof(f2658,plain,
( sK2 = k1_tarski(k1_rlvect_1(sK1))
| ~ r2_hidden(k1_rlvect_1(sK1),sK2)
| spl30_3
| spl30_4
| ~ spl30_5 ),
inference(trivial_inequality_removal,[],[f2657]) ).
fof(f2660,plain,
( ~ r2_hidden(k1_rlvect_1(sK1),sK2)
| spl30_3
| spl30_4
| ~ spl30_5 ),
inference(forward_subsumption_resolution,[],[f2658,f429]) ).
fof(f2661,plain,
( $false
| spl30_3
| spl30_4
| ~ spl30_5
| ~ spl30_79 ),
inference(forward_subsumption_resolution,[],[f2660,f2438]) ).
fof(f2662,plain,
( spl30_3
| spl30_4
| ~ spl30_5
| ~ spl30_79 ),
inference(avatar_contradiction_clause,[],[f2661]) ).
cnf(s1,plain,
( ~ spl30_1
| ~ spl30_2
| ~ spl30_3 ),
inference(sat_conversion,[],[f430]) ).
cnf(s2,plain,
spl30_1,
inference(sat_conversion,[],[f450]) ).
cnf(s3,plain,
spl30_2,
inference(sat_conversion,[],[f468]) ).
cnf(s4,plain,
( spl30_4
| spl30_5 ),
inference(sat_conversion,[],[f626]) ).
cnf(s7,plain,
~ spl30_4,
inference(sat_conversion,[],[f683]) ).
cnf(s78,plain,
spl30_79,
inference(sat_conversion,[],[f2450]) ).
cnf(s87,plain,
( spl30_3
| spl30_4
| ~ spl30_5
| ~ spl30_79 ),
inference(sat_conversion,[],[f2662]) ).
cnf(s100,plain,
spl30_5,
inference(rat,[],[s4,s7]) ).
cnf(s102,plain,
spl30_3,
inference(rat,[],[s87,s78,s7,s100]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s1,s102,s3,s2]) ).
fof(f2663,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 19:46:55 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.68/1.18 % (2556359)Detected formulas, will run a generic FOF schedule.
% 3.68/1.18 % (2556367)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2383252507:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.18 % (2556367)Refutation not found, incomplete strategy
% 3.68/1.18 % (2556367)------------------------------
% 3.68/1.18 % (2556367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.18 % (2556367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.18 % (2556367)CaDiCaL version: 2.1.3
% 3.68/1.18 % (2556367)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.18 % (2556367)Time elapsed: 0.001 s
% 3.68/1.18 % (2556367)Peak memory usage: 88 MB
% 3.68/1.18 % (2556367)Instructions burned: 2 (million)
% 3.68/1.18 % (2556369)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=248670326:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.18 % (2556370)dis-21_1_sil=8000:lcm=predicate:random_seed=3149647878:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.68/1.18 % (2556366)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=2477918759:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.18 % (2556364)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=453195903:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.18 % (2556368)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2769373757:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.18 % (2556365)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=3871123818:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.18 % (2556370)Instruction limit reached!
% 3.68/1.18 % (2556370)------------------------------
% 3.68/1.18 % (2556370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.18 % (2556370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.18 % (2556370)CaDiCaL version: 2.1.3
% 3.68/1.18 % (2556370)Termination reason: Instruction limit
% 3.68/1.18 % (2556370)Termination phase: Saturation
% 3.68/1.18 % (2556370)Time elapsed: 0.072 s
% 3.68/1.18 % (2556370)Peak memory usage: 90 MB
% 3.68/1.18 % (2556370)Instructions burned: 130 (million)
% 3.68/1.18 % (2556368)Instruction limit reached!
% 3.68/1.18 % (2556368)------------------------------
% 3.68/1.18 % (2556368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.18 % (2556368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.18 % (2556368)CaDiCaL version: 2.1.3
% 3.68/1.18 % (2556368)Termination reason: Instruction limit
% 3.68/1.18 % (2556368)Termination phase: Saturation
% 3.68/1.18 % (2556368)Time elapsed: 0.072 s
% 3.68/1.18 % (2556368)Peak memory usage: 88 MB
% 3.68/1.18 % (2556368)Instructions burned: 119 (million)
% 3.68/1.18 % (2556369)First to succeed.
% 3.68/1.18 % (2556369)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2556359"
% 3.68/1.18 % (2556367)------------------------------
% 3.68/1.18 % (2556367)------------------------------
% 3.68/1.18 % (2556380)lrs+1011_1_sil=32000:sp=occurrence:random_seed=757471563:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.68/1.18 % (2556379)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1724980603:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.68/1.18 % (2556378)lrs+10_1_sil=8000:sp=occurrence:random_seed=3058014527:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.68/1.18 % (2556379)Refutation not found, incomplete strategy
% 3.68/1.18 % (2556379)------------------------------
% 3.68/1.18 % (2556379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.18 % (2556379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.18 % (2556379)CaDiCaL version: 2.1.3
% 3.68/1.18 % (2556379)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.18 % (2556379)Time elapsed: 0.004 s
% 3.68/1.18 % (2556379)Peak memory usage: 89 MB
% 3.68/1.18 % (2556379)Instructions burned: 5 (million)
% 3.68/1.18 % (2556378)Also succeeded, but the first one will report.
% 3.68/1.18 % (2556380)Instruction limit reached!
% 3.68/1.18 % (2556380)------------------------------
% 3.68/1.18 % (2556380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.18 % (2556380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.18 % (2556380)CaDiCaL version: 2.1.3
% 3.68/1.18 % (2556380)Termination reason: Instruction limit
% 3.68/1.18 % (2556380)Termination phase: Saturation
% 3.68/1.18 % (2556380)Time elapsed: 0.112 s
% 3.68/1.18 % (2556380)Peak memory usage: 91 MB
% 3.68/1.18 % (2556380)Instructions burned: 327 (million)
% 3.68/1.18 % (2556369)Refutation found. Thanks to Tanya!
% 3.68/1.18 % SZS status Theorem for theBenchmark
% 3.68/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.28 % (2556369)------------------------------
% 4.09/1.28 % (2556369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.28 % (2556369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.28 % (2556369)CaDiCaL version: 2.1.3
% 4.09/1.28 % (2556369)Termination reason: Refutation
% 4.09/1.28 % (2556369)Time elapsed: 0.100 s
% 4.09/1.28 % (2556369)Peak memory usage: 91 MB
% 4.09/1.28 % (2556369)Instructions burned: 140 (million)
% 4.09/1.28 % (2556369)------------------------------
% 4.09/1.28 % (2556369)------------------------------
% 4.09/1.28 % (2556359)Success in time 0.508 s
% 4.09/1.28 % Vampire exiting
%------------------------------------------------------------------------------