%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT313+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 : n012.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 11:46:49 AM UTC 2026
% Result : Theorem 0.59s 0.87s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 132 ( 19 unt; 7 def)
% Number of atoms : 451 ( 37 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 545 ( 226 ~; 239 |; 52 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 8 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 91 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( ( v14_lattices(X0)
& r2_hidden(k6_lattices(X0),X1) )
=> ( r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0))
& X1 = u1_struct_0(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( ( v14_lattices(X0)
& r2_hidden(k6_lattices(X0),X1) )
=> ( r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0))
& X1 = u1_struct_0(X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> k17_filter_2(X0) = u1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).
fof(f8,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> m2_filter_2(k17_filter_2(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).
fof(f18,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(f19,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_lattice4(X1,X0)
=> m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X0)
& m1_subset_1(X1,k1_zfmisc_1(X0))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(f44,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).
fof(f46,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( ( v14_lattices(X0)
& r2_hidden(k6_lattices(X0),X1) )
=> ( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0))
& k19_filter_2(X0,X1) = u1_struct_0(X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( r2_hidden(X0,X1)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f50,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f55,plain,
? [X0] :
( ? [X1] :
( ( ~ r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0))
| u1_struct_0(X0) != X1 )
& v14_lattices(X0)
& r2_hidden(k6_lattices(X0),X1)
& m2_filter_2(X1,X0) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f56,plain,
? [X0] :
( ? [X1] :
( ( ~ r1_filter_2(u1_struct_0(X0),X1,k17_filter_2(X0))
| u1_struct_0(X0) != X1 )
& v14_lattices(X0)
& r2_hidden(k6_lattices(X0),X1)
& m2_filter_2(X1,X0) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(flattening,[],[f55]) ).
fof(f62,plain,
! [X0] :
( k17_filter_2(X0) = u1_struct_0(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0] :
( k17_filter_2(X0) = u1_struct_0(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( m2_filter_2(k17_filter_2(X0),X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( m2_filter_2(k17_filter_2(X0),X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) )
| ~ m2_filter_2(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) )
| ~ m2_filter_2(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_lattice4(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_lattice4(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f75]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 )
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( r1_filter_2(X0,X1,X2)
<=> X1 = X2 )
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f88]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ m2_filter_2(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ m2_filter_2(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f97]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0))
& k19_filter_2(X0,X1) = u1_struct_0(X0) )
| ~ v14_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),k17_filter_2(X0))
& k19_filter_2(X0,X1) = u1_struct_0(X0) )
| ~ v14_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f100]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ v1_xboole_0(X2) ),
inference(ennf_transformation,[],[f48]) ).
fof(f106,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f108,plain,
( ( ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0))
| sK1 != u1_struct_0(sK0) )
& v14_lattices(sK0)
& r2_hidden(k6_lattices(sK0),sK1)
& m2_filter_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v10_lattices(sK0)
& l3_lattices(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f56]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( ( r1_filter_2(X0,X1,X2)
| X1 != X2 )
& ( X1 = X2
| ~ r1_filter_2(X0,X1,X2) ) )
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(nnf_transformation,[],[f89]) ).
fof(f124,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f125,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f126,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f127,plain,
m2_filter_2(sK1,sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f128,plain,
r2_hidden(k6_lattices(sK0),sK1),
inference(cnf_transformation,[],[f108]) ).
fof(f129,plain,
v14_lattices(sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f130,plain,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0))
| sK1 != u1_struct_0(sK0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f141,plain,
! [X0] :
( ~ v10_lattices(X0)
| v3_struct_0(X0)
| u1_struct_0(X0) = k17_filter_2(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f142,plain,
! [X0] :
( m2_filter_2(k17_filter_2(X0),X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f149,plain,
! [X0,X1] :
( m2_lattice4(X1,X0)
| ~ m2_filter_2(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f151,plain,
! [X0,X1] :
( ~ v10_lattices(X0)
| ~ m2_lattice4(X1,X0)
| v3_struct_0(X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ r1_filter_2(X0,X1,X2)
| X1 = X2
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f175,plain,
! [X2,X0,X1] :
( r1_filter_2(X0,X1,X2)
| X1 != X2
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f181,plain,
! [X0,X1] :
( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ m2_filter_2(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f183,plain,
! [X0,X1] :
( u1_struct_0(X0) = k19_filter_2(X0,X1)
| ~ v14_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f188,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f190,plain,
! [X2,X0] :
( r1_filter_2(X0,X2,X2)
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(equality_resolution,[],[f175]) ).
fof(f191,plain,
! [X2,X0] :
( r1_filter_2(X0,X2,X2)
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(duplicate_literal_removal,[],[f190]) ).
fof(f193,definition,
( spl16_1
<=> sK1 = u1_struct_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f194,plain,
( sK1 = u1_struct_0(sK0)
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f197,definition,
( spl16_2
<=> r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f199,plain,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,k17_filter_2(sK0))
| spl16_2 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f130,f197,f193]) ).
fof(f220,plain,
! [X0] :
( ~ m1_subset_1(sK1,k1_zfmisc_1(X0))
| ~ v1_xboole_0(X0) ),
inference(resolution,[],[f186,f128]) ).
fof(f233,plain,
( v3_struct_0(sK0)
| u1_struct_0(sK0) = k17_filter_2(sK0)
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f141,f125]) ).
fof(f234,plain,
( u1_struct_0(sK0) = k17_filter_2(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f233,f126]) ).
fof(f235,plain,
u1_struct_0(sK0) = k17_filter_2(sK0),
inference(forward_subsumption_resolution,[],[f234,f124]) ).
fof(f236,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(superposition,[],[f142,f235]) ).
fof(f237,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f236,f126]) ).
fof(f238,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f237,f125]) ).
fof(f239,plain,
m2_filter_2(u1_struct_0(sK0),sK0),
inference(forward_subsumption_resolution,[],[f238,f124]) ).
fof(f248,plain,
! [X0] :
( ~ m2_lattice4(X0,sK0)
| v3_struct_0(sK0)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f151,f125]) ).
fof(f249,plain,
! [X0] :
( ~ m2_lattice4(X0,sK0)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f248,f126]) ).
fof(f250,plain,
! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_lattice4(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f249,f124]) ).
fof(f255,plain,
( ~ m2_lattice4(sK1,sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolution,[],[f250,f220]) ).
fof(f257,definition,
( spl16_3
<=> v1_xboole_0(u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f259,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| spl16_3 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl16_4
<=> m2_lattice4(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f263,plain,
( ~ m2_lattice4(sK1,sK0)
| spl16_4 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,plain,
( ~ spl16_3
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f255,f261,f257]) ).
fof(f284,plain,
! [X0,X1] :
( ~ v14_lattices(X0)
| u1_struct_0(X0) = k19_filter_2(X0,X1)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(forward_subsumption_resolution,[],[f183,f188]) ).
fof(f287,plain,
! [X0] :
( u1_struct_0(sK0) = k19_filter_2(sK0,X0)
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f284,f129]) ).
fof(f288,plain,
! [X0] :
( u1_struct_0(sK0) = k19_filter_2(sK0,X0)
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f287,f126]) ).
fof(f289,plain,
! [X0] :
( u1_struct_0(sK0) = k19_filter_2(sK0,X0)
| ~ r2_hidden(k6_lattices(sK0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f288,f125]) ).
fof(f290,plain,
! [X0] :
( ~ r2_hidden(k6_lattices(sK0),X0)
| u1_struct_0(sK0) = k19_filter_2(sK0,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f289,f124]) ).
fof(f310,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolution,[],[f290,f128]) ).
fof(f326,definition,
( spl16_10
<=> m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
fof(f327,plain,
( m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f328,plain,
( ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| spl16_10 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f330,definition,
( spl16_11
<=> u1_struct_0(sK0) = k19_filter_2(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
fof(f332,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f333,plain,
( ~ spl16_10
| spl16_11 ),
inference(avatar_split_clause,[],[f310,f330,f326]) ).
fof(f336,plain,
( ~ m2_lattice4(sK1,sK0)
| spl16_10 ),
inference(resolution,[],[f328,f250]) ).
fof(f339,plain,
( ~ spl16_4
| spl16_10 ),
inference(avatar_split_clause,[],[f336,f326,f261]) ).
fof(f342,plain,
( ~ m2_filter_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_4 ),
inference(resolution,[],[f263,f149]) ).
fof(f343,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_4 ),
inference(forward_subsumption_resolution,[],[f342,f127]) ).
fof(f344,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_4 ),
inference(forward_subsumption_resolution,[],[f343,f126]) ).
fof(f345,plain,
( ~ l3_lattices(sK0)
| spl16_4 ),
inference(forward_subsumption_resolution,[],[f344,f125]) ).
fof(f346,plain,
( $false
| spl16_4 ),
inference(forward_subsumption_resolution,[],[f345,f124]) ).
fof(f347,plain,
spl16_4,
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f388,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ m2_filter_2(sK1,sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ spl16_11 ),
inference(superposition,[],[f181,f332]) ).
fof(f389,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f388,f127]) ).
fof(f391,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f389,f126]) ).
fof(f393,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ l3_lattices(sK0)
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f391,f125]) ).
fof(f394,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f393,f124]) ).
fof(f405,definition,
( spl16_15
<=> m1_subset_1(u1_struct_0(sK0),k1_zfmisc_1(u1_struct_0(sK0))) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
fof(f407,plain,
( ~ m1_subset_1(u1_struct_0(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| spl16_15 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f438,plain,
( sK1 = u1_struct_0(sK0)
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_subset_1(u1_struct_0(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl16_11 ),
inference(resolution,[],[f394,f174]) ).
fof(f445,plain,
( ~ m2_lattice4(u1_struct_0(sK0),sK0)
| spl16_15 ),
inference(resolution,[],[f407,f250]) ).
fof(f448,plain,
( ~ m2_filter_2(u1_struct_0(sK0),sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(resolution,[],[f445,f149]) ).
fof(f449,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f448,f239]) ).
fof(f450,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f449,f126]) ).
fof(f451,plain,
( ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f450,f125]) ).
fof(f452,plain,
( $false
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f451,f124]) ).
fof(f453,plain,
spl16_15,
inference(avatar_contradiction_clause,[],[f452]) ).
fof(f454,plain,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,u1_struct_0(sK0))
| spl16_2 ),
inference(forward_demodulation,[],[f199,f235]) ).
fof(f456,plain,
( sK1 = u1_struct_0(sK0)
| ~ m1_subset_1(u1_struct_0(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| spl16_3
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f438,f259]) ).
fof(f457,plain,
( sK1 = u1_struct_0(sK0)
| ~ m1_subset_1(u1_struct_0(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| spl16_3
| ~ spl16_10
| ~ spl16_11 ),
inference(forward_subsumption_resolution,[],[f456,f327]) ).
fof(f458,plain,
( ~ spl16_15
| spl16_1
| spl16_3
| ~ spl16_10
| ~ spl16_11 ),
inference(avatar_split_clause,[],[f457,f330,f326,f257,f193,f405]) ).
fof(f469,plain,
( m1_subset_1(sK1,k1_zfmisc_1(sK1))
| ~ spl16_1
| ~ spl16_10 ),
inference(superposition,[],[f327,f194]) ).
fof(f526,plain,
( ~ r1_filter_2(sK1,sK1,sK1)
| ~ spl16_1
| spl16_2 ),
inference(forward_demodulation,[],[f454,f194]) ).
fof(f530,plain,
( v1_xboole_0(sK1)
| ~ m1_subset_1(sK1,k1_zfmisc_1(sK1))
| ~ spl16_1
| spl16_2 ),
inference(resolution,[],[f526,f191]) ).
fof(f533,plain,
( ~ m1_subset_1(sK1,k1_zfmisc_1(sK1))
| ~ spl16_1
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f530,f220]) ).
fof(f541,plain,
( $false
| ~ spl16_1
| spl16_2
| ~ spl16_10 ),
inference(forward_subsumption_resolution,[],[f469,f533]) ).
fof(f542,plain,
( ~ spl16_1
| spl16_2
| ~ spl16_10 ),
inference(avatar_contradiction_clause,[],[f541]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f200]) ).
cnf(s2,plain,
( ~ spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f264]) ).
cnf(s5,plain,
( ~ spl16_10
| spl16_11 ),
inference(sat_conversion,[],[f333]) ).
cnf(s6,plain,
( ~ spl16_4
| spl16_10 ),
inference(sat_conversion,[],[f339]) ).
cnf(s7,plain,
spl16_4,
inference(sat_conversion,[],[f347]) ).
cnf(s14,plain,
spl16_15,
inference(sat_conversion,[],[f453]) ).
cnf(s16,plain,
( spl16_1
| spl16_3
| ~ spl16_10
| ~ spl16_11
| ~ spl16_15 ),
inference(sat_conversion,[],[f458]) ).
cnf(s25,plain,
( ~ spl16_1
| spl16_2
| ~ spl16_10 ),
inference(sat_conversion,[],[f542]) ).
cnf(s35,plain,
spl16_10,
inference(rat,[],[s6,s7]) ).
cnf(s37,plain,
spl16_11,
inference(rat,[],[s5,s35]) ).
cnf(s38,plain,
~ spl16_3,
inference(rat,[],[s2,s7]) ).
cnf(s39,plain,
spl16_1,
inference(rat,[],[s16,s14,s37,s35,s38]) ).
cnf(s40,plain,
spl16_2,
inference(rat,[],[s25,s35,s39]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s1,s40,s39]) ).
fof(f543,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 % Computer : n012.cluster.edu
% 0.04/0.33 % Model : x86_64 x86_64
% 0.04/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.33 % Memory : 8046.5625MB
% 0.04/0.33 % OS : Linux 6.8.0-71-generic
% 0.04/0.33 % CPULimit : 300
% 0.04/0.33 % WCLimit : 300
% 0.04/0.33 % DateTime : Sun Sep 27 14:30:52 UTC 2026
% 0.04/0.33 % CPUTime :
% 0.04/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.35 Running first-order theorem proving
% 0.04/0.35 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
% 0.59/0.87 % (2437334)Detected formulas, will run a generic FOF schedule.
% 0.59/0.87 % (2437339)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=3896680873:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.59/0.87 % (2437340)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=2351118714:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.59/0.87 % (2437341)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=398191654:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.59/0.87 % (2437345)dis-21_1_sil=8000:lcm=predicate:random_seed=1586396958: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)
% 0.59/0.87 % (2437344)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2756742107:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.59/0.87 % (2437343)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4196967249:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.59/0.87 % (2437342)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1886708769:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.59/0.87 % (2437342)Refutation not found, incomplete strategy
% 0.59/0.87 % (2437342)------------------------------
% 0.59/0.87 % (2437342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.87 % (2437342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.87 % (2437342)CaDiCaL version: 2.1.3
% 0.59/0.87 % (2437342)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.87 % (2437342)Time elapsed: 0.002 s
% 0.59/0.87 % (2437342)Peak memory usage: 88 MB
% 0.59/0.87 % (2437342)Instructions burned: 4 (million)
% 0.59/0.87 % (2437344)First to succeed.
% 0.59/0.87 % (2437344)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2437334"
% 0.59/0.87 % (2437345)Instruction limit reached!
% 0.59/0.87 % (2437345)------------------------------
% 0.59/0.87 % (2437345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.87 % (2437345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.87 % (2437345)CaDiCaL version: 2.1.3
% 0.59/0.87 % (2437345)Termination reason: Instruction limit
% 0.59/0.87 % (2437345)Termination phase: Saturation
% 0.59/0.87 % (2437345)Time elapsed: 0.040 s
% 0.59/0.87 % (2437345)Peak memory usage: 91 MB
% 0.59/0.87 % (2437345)Instructions burned: 129 (million)
% 0.59/0.87 % (2437343)Instruction limit reached!
% 0.59/0.87 % (2437343)------------------------------
% 0.59/0.87 % (2437343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.87 % (2437343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.87 % (2437343)CaDiCaL version: 2.1.3
% 0.59/0.87 % (2437343)Termination reason: Instruction limit
% 0.59/0.87 % (2437343)Termination phase: Saturation
% 0.59/0.87 % (2437343)Time elapsed: 0.040 s
% 0.59/0.87 % (2437343)Peak memory usage: 88 MB
% 0.59/0.87 % (2437343)Instructions burned: 122 (million)
% 0.59/0.87 % (2437342)------------------------------
% 0.59/0.87 % (2437342)------------------------------
% 0.59/0.87 % (2437353)lrs+10_1_sil=8000:sp=occurrence:random_seed=2919248136:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.59/0.87 % (2437354)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3691914030:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.59/0.87 % (2437354)Refutation not found, incomplete strategy
% 0.59/0.87 % (2437354)------------------------------
% 0.59/0.87 % (2437354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.87 % (2437354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.87 % (2437354)CaDiCaL version: 2.1.3
% 0.59/0.87 % (2437354)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.87 % (2437354)Time elapsed: 0.002 s
% 0.59/0.87 % (2437354)Peak memory usage: 88 MB
% 0.59/0.87 % (2437354)Instructions burned: 3 (million)
% 0.59/0.87 % (2437353)Also succeeded, but the first one will report.
% 0.59/0.87 % (2437344)Refutation found. Thanks to Tanya!
% 0.59/0.87 % SZS status Theorem for theBenchmark
% 0.59/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/0.96 % (2437344)------------------------------
% 2.40/0.96 % (2437344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.96 % (2437344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.96 % (2437344)CaDiCaL version: 2.1.3
% 2.40/0.96 % (2437344)Termination reason: Refutation
% 2.40/0.96 % (2437344)Time elapsed: 0.007 s
% 2.40/0.96 % (2437344)Peak memory usage: 89 MB
% 2.40/0.96 % (2437344)Instructions burned: 16 (million)
% 2.40/0.96 % (2437344)------------------------------
% 2.40/0.96 % (2437344)------------------------------
% 2.40/0.96 % (2437334)Success in time 0.313 s
% 2.40/0.96 % Vampire exiting
%------------------------------------------------------------------------------