%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG215+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 : n007.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 09:19:20 AM UTC 2026
% Result : Theorem 3.00s 1.09s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 83 ( 23 unt; 0 def)
% Number of atoms : 916 ( 28 equ)
% Maximal formula atoms : 39 ( 11 avg)
% Number of connectives : 1468 ( 635 ~; 669 |; 140 &)
% ( 7 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 113 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_rmod_5) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X1)),X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( m2_rmod_4(X3,X0,X1,X2)
=> ( k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
=> k2_rmod_4(X0,X1,X3) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(f7,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_rlvect_1(X0)
& v4_rlvect_1(X0)
& v5_rlvect_1(X0)
& v6_rlvect_1(X0)
& v4_group_1(X0)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ! [X3] :
( m1_rmod_4(X3,X0,X1)
=> ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_rmod_4) ).
fof(f12,axiom,
! [X0] :
( v1_xboole_0(k1_subset_1(X0))
& m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
fof(f33,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)
& v6_vectsp_1(X0)
& v7_vectsp_1(X0)
& v8_vectsp_1(X0)
& l3_vectsp_1(X0)
& ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v5_vectsp_2(X1,X0)
& l1_vectsp_2(X1,X0)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ! [X3] :
( m2_rmod_4(X3,X0,X1,X2)
=> m1_rmod_4(X3,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_rmod_4) ).
fof(f72,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(f73,axiom,
! [X0] :
( r1_tarski(X0,k1_xboole_0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f76,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(X1)),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,[],[f2]) ).
fof(f81,plain,
? [X0] :
( ? [X1] :
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(X1)),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,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( k2_rmod_4(X0,X1,X3) = k1_xboole_0
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| ~ m2_rmod_4(X3,X0,X1,X2) ) )
| ~ 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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( v1_rmod_5(X2,X0,X1)
<=> ! [X3] :
( k2_rmod_4(X0,X1,X3) = k1_xboole_0
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| ~ m2_rmod_4(X3,X0,X1,X2) ) )
| ~ 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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(flattening,[],[f82]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) )
| ~ m1_rmod_4(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( m2_rmod_4(X3,X0,X1,X2)
<=> r1_tarski(k2_rmod_4(X0,X1,X3),X2) )
| ~ m1_rmod_4(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f92,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r1_tarski(X0,k1_xboole_0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ! [X3] :
( m1_rmod_4(X3,X0,X1)
| ~ m2_rmod_4(X3,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(ennf_transformation,[],[f33]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ! [X3] :
( m1_rmod_4(X3,X0,X1)
| ~ m2_rmod_4(X3,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(flattening,[],[f95]) ).
fof(f106,plain,
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1)),sK0,sK1)
& ~ v3_struct_0(sK1)
& v3_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v6_rlvect_1(sK1)
& v5_vectsp_2(sK1,sK0)
& l1_vectsp_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v6_rlvect_1(sK0)
& v4_group_1(sK0)
& v6_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& l3_vectsp_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f81]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( v1_rmod_5(X2,X0,X1)
| ? [X3] :
( k2_rmod_4(X0,X1,X3) != k1_xboole_0
& k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
& m2_rmod_4(X3,X0,X1,X2) ) )
& ( ! [X3] :
( k2_rmod_4(X0,X1,X3) = k1_xboole_0
| k5_rmod_4(X0,X1,X3) != k1_rlvect_1(X1)
| ~ m2_rmod_4(X3,X0,X1,X2) )
| ~ v1_rmod_5(X2,X0,X1) ) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( v1_rmod_5(X2,X0,X1)
| ? [X3] :
( k2_rmod_4(X0,X1,X3) != k1_xboole_0
& k5_rmod_4(X0,X1,X3) = k1_rlvect_1(X1)
& m2_rmod_4(X3,X0,X1,X2) ) )
& ( ! [X4] :
( k1_xboole_0 = k2_rmod_4(X0,X1,X4)
| k1_rlvect_1(X1) != k5_rmod_4(X0,X1,X4)
| ~ m2_rmod_4(X4,X0,X1,X2) )
| ~ v1_rmod_5(X2,X0,X1) ) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( v1_rmod_5(X2,X0,X1)
| ( k1_xboole_0 != k2_rmod_4(X0,X1,sK3(X0,X1,X2))
& k1_rlvect_1(X1) = k5_rmod_4(X0,X1,sK3(X0,X1,X2))
& m2_rmod_4(sK3(X0,X1,X2),X0,X1,X2) ) )
& ( ! [X4] :
( k1_xboole_0 = k2_rmod_4(X0,X1,X4)
| k1_rlvect_1(X1) != k5_rmod_4(X0,X1,X4)
| ~ m2_rmod_4(X4,X0,X1,X2) )
| ~ v1_rmod_5(X2,X0,X1) ) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f109]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( m2_rmod_4(X3,X0,X1,X2)
| ~ r1_tarski(k2_rmod_4(X0,X1,X3),X2) )
& ( r1_tarski(k2_rmod_4(X0,X1,X3),X2)
| ~ m2_rmod_4(X3,X0,X1,X2) ) )
| ~ m1_rmod_4(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(nnf_transformation,[],[f90]) ).
fof(f121,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,[],[f72]) ).
fof(f127,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f128,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f129,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f130,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f131,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f132,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f133,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f134,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f135,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f136,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f137,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f138,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f106]) ).
fof(f139,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f140,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f141,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f142,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f143,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f144,plain,
~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1)),sK0,sK1),
inference(cnf_transformation,[],[f106]) ).
fof(f145,plain,
! [X0] : m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f146,plain,
! [X0] : v1_xboole_0(k1_subset_1(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f149,plain,
! [X2,X0,X1] :
( m2_rmod_4(sK3(X0,X1,X2),X0,X1,X2)
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f151,plain,
! [X2,X0,X1] :
( k1_xboole_0 != k2_rmod_4(X0,X1,sK3(X0,X1,X2))
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( r1_tarski(k2_rmod_4(X0,X1,X3),X2)
| ~ m2_rmod_4(X3,X0,X1,X2)
| ~ m1_rmod_4(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f165,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f166,plain,
! [X0] :
( ~ r1_tarski(X0,k1_xboole_0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( ~ m2_rmod_4(X3,X0,X1,X2)
| m1_rmod_4(X3,X0,X1)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f96]) ).
fof(f175,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f176,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f191,plain,
! [X0] : r1_tarski(k1_subset_1(X0),X0),
inference(resolution,[],[f175,f145]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( r1_tarski(k2_rmod_4(X0,X1,X3),X2)
| ~ m2_rmod_4(X3,X0,X1,X2)
| ~ 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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(forward_subsumption_resolution,[],[f163,f169]) ).
fof(f236,plain,
! [X2,X0,X1] :
( k1_xboole_0 = k2_rmod_4(X1,X2,X0)
| ~ m1_subset_1(k1_xboole_0,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)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ m2_rmod_4(X0,X1,X2,k1_xboole_0) ),
inference(resolution,[],[f228,f166]) ).
fof(f246,plain,
! [X2,X0,X1] :
( k1_xboole_0 != k1_xboole_0
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| ~ m1_subset_1(k1_xboole_0,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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| ~ m2_rmod_4(sK3(X0,X1,X2),X0,X1,k1_xboole_0) ),
inference(superposition,[],[f151,f236]) ).
fof(f251,plain,
! [X2,X0,X1] :
( k1_xboole_0 != k1_xboole_0
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_vectsp_2(X1,X0)
| ~ l1_vectsp_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v4_group_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_rmod_4(sK3(X0,X1,X2),X0,X1,k1_xboole_0) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ m2_rmod_4(sK3(X0,X1,X2),X0,X1,k1_xboole_0)
| ~ 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)
| ~ v6_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ l3_vectsp_1(X0)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X1)))
| v1_rmod_5(X2,X0,X1) ),
inference(trivial_inequality_removal,[],[f251]) ).
fof(f275,plain,
! [X0,X1] :
( ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,X1)
| ~ l1_vectsp_2(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)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X0)))
| v1_rmod_5(k1_xboole_0,X1,X0)
| v1_rmod_5(k1_xboole_0,X1,X0)
| ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,X1)
| ~ l1_vectsp_2(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) ),
inference(resolution,[],[f252,f149]) ).
fof(f277,plain,
! [X0,X1] :
( ~ m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,X1)
| ~ l1_vectsp_2(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)
| v1_rmod_5(k1_xboole_0,X1,X0) ),
inference(duplicate_literal_removal,[],[f275]) ).
fof(f283,plain,
! [X0,X1] :
( v1_rmod_5(k1_xboole_0,X1,X0)
| ~ v3_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_vectsp_2(X0,X1)
| ~ l1_vectsp_2(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)
| v3_struct_0(X0)
| ~ r1_tarski(k1_xboole_0,u1_struct_0(X0)) ),
inference(resolution,[],[f277,f176]) ).
fof(f285,plain,
! [X2,X0,X1] :
( v1_rmod_5(X0,X1,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)
| v3_struct_0(X2)
| ~ r1_tarski(X0,u1_struct_0(X2))
| ~ v1_xboole_0(X0) ),
inference(superposition,[],[f283,f165]) ).
fof(f293,plain,
( ~ v3_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(resolution,[],[f285,f144]) ).
fof(f297,plain,
( ~ v4_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f293,f142]) ).
fof(f299,plain,
( ~ v5_rlvect_1(sK1)
| ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f297,f141]) ).
fof(f301,plain,
( ~ v6_rlvect_1(sK1)
| ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f299,f140]) ).
fof(f303,plain,
( ~ v5_vectsp_2(sK1,sK0)
| ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f301,f139]) ).
fof(f305,plain,
( ~ l1_vectsp_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f303,f138]) ).
fof(f307,plain,
( v3_struct_0(sK0)
| ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f305,f137]) ).
fof(f309,plain,
( ~ v3_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f307,f136]) ).
fof(f311,plain,
( ~ v4_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f309,f135]) ).
fof(f313,plain,
( ~ v5_rlvect_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f311,f134]) ).
fof(f315,plain,
( ~ v6_rlvect_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f313,f133]) ).
fof(f317,plain,
( ~ v4_group_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f315,f132]) ).
fof(f319,plain,
( ~ v6_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f317,f131]) ).
fof(f321,plain,
( ~ v7_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f319,f130]) ).
fof(f323,plain,
( ~ v8_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f321,f129]) ).
fof(f325,plain,
( ~ l3_vectsp_1(sK0)
| v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f323,f128]) ).
fof(f327,plain,
( v3_struct_0(sK1)
| ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f325,f127]) ).
fof(f329,plain,
( ~ r1_tarski(k1_subset_1(u1_struct_0(sK1)),u1_struct_0(sK1))
| ~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f327,f143]) ).
fof(f331,plain,
~ v1_xboole_0(k1_subset_1(u1_struct_0(sK1))),
inference(forward_subsumption_resolution,[],[f329,f191]) ).
fof(f332,plain,
$false,
inference(forward_subsumption_resolution,[],[f331,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.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 19:42:26 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.00/1.09 % (2738382)Detected formulas, will run a generic FOF schedule.
% 3.00/1.09 % (2738390)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=647883587:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.09 % (2738390)Refutation not found, incomplete strategy
% 3.00/1.09 % (2738390)------------------------------
% 3.00/1.09 % (2738390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.09 % (2738390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.09 % (2738390)CaDiCaL version: 2.1.3
% 3.00/1.09 % (2738390)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.09 % (2738390)Time elapsed: 0.001 s
% 3.00/1.09 % (2738390)Peak memory usage: 88 MB
% 3.00/1.09 % (2738390)Instructions burned: 2 (million)
% 3.00/1.09 % (2738388)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=757021166:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.09 % (2738393)dis-21_1_sil=8000:lcm=predicate:random_seed=147457804: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)
% 3.00/1.09 % (2738389)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=497746133:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.09 % (2738387)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=1673302192:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.09 % (2738391)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3339067156:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.09 % (2738392)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2972045472:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.09 % (2738391)First to succeed.
% 3.00/1.09 % (2738391)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2738382"
% 3.00/1.09 % (2738392)Also succeeded, but the first one will report.
% 3.00/1.09 % (2738393)Instruction limit reached!
% 3.00/1.09 % (2738393)------------------------------
% 3.00/1.09 % (2738393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.09 % (2738393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.09 % (2738393)CaDiCaL version: 2.1.3
% 3.00/1.09 % (2738393)Termination reason: Instruction limit
% 3.00/1.09 % (2738393)Termination phase: Saturation
% 3.00/1.09 % (2738393)Time elapsed: 0.071 s
% 3.00/1.09 % (2738393)Peak memory usage: 91 MB
% 3.00/1.09 % (2738393)Instructions burned: 129 (million)
% 3.00/1.09 % (2738390)------------------------------
% 3.00/1.09 % (2738390)------------------------------
% 3.00/1.09 % (2738402)lrs+10_1_sil=32000:urr=on:br=off:random_seed=580174017:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.00/1.09 % (2738402)Refutation not found, incomplete strategy
% 3.00/1.09 % (2738402)------------------------------
% 3.00/1.09 % (2738402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.09 % (2738402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.09 % (2738402)CaDiCaL version: 2.1.3
% 3.00/1.09 % (2738402)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.09 % (2738402)Time elapsed: 0.002 s
% 3.00/1.09 % (2738402)Peak memory usage: 88 MB
% 3.00/1.09 % (2738402)Instructions burned: 4 (million)
% 3.00/1.09 % (2738401)lrs+10_1_sil=8000:sp=occurrence:random_seed=4059891708:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.00/1.09 % (2738391)Refutation found. Thanks to Tanya!
% 3.00/1.09 % SZS status Theorem for theBenchmark
% 3.00/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.29 % (2738391)------------------------------
% 3.58/1.29 % (2738391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.29 % (2738391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.29 % (2738391)CaDiCaL version: 2.1.3
% 3.58/1.29 % (2738391)Termination reason: Refutation
% 3.58/1.29 % (2738391)Time elapsed: 0.011 s
% 3.58/1.29 % (2738391)Peak memory usage: 88 MB
% 3.58/1.29 % (2738391)Instructions burned: 17 (million)
% 3.58/1.29 % (2738391)------------------------------
% 3.58/1.29 % (2738391)------------------------------
% 3.58/1.29 % (2738382)Success in time 0.427 s
% 3.58/1.29 % Vampire exiting
%------------------------------------------------------------------------------