%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 11:48:22 AM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 14
% Syntax : Number of formulae : 127 ( 23 unt; 3 def)
% Number of atoms : 448 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 549 ( 228 ~; 245 |; 50 &)
% ( 7 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 1 sgn 100 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(f40,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
fof(f45,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
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/sandbox/benchmark/theBenchmark.p',t42_filter_2) ).
fof(f50,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f52,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f40]) ).
fof(f53,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
=> m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
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(f99,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
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(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] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| u1_struct_0(X0) = k17_filter_2(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_filter_2(X1,X0)
| m2_lattice4(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f150,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ v1_xboole_0(X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f151,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(cnf_transformation,[],[f76]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ r1_filter_2(X0,X1,X2)
| v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| X1 = X2 ),
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(f177,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f52]) ).
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(f182,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
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(f188,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(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] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0)
| r1_filter_2(X0,X2,X2) ),
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(f214,plain,
~ v1_xboole_0(sK1),
inference(resolution,[],[f188,f128]) ).
fof(f342,plain,
! [X0,X1] :
( r1_filter_2(X0,X1,X1)
| v1_xboole_0(X0)
| ~ r1_tarski(X1,X0) ),
inference(resolution,[],[f191,f182]) ).
fof(f351,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| u1_struct_0(sK0) = k17_filter_2(sK0) ),
inference(resolution,[],[f141,f124]) ).
fof(f353,plain,
( ~ v10_lattices(sK0)
| u1_struct_0(sK0) = k17_filter_2(sK0) ),
inference(forward_subsumption_resolution,[],[f351,f126]) ).
fof(f354,plain,
u1_struct_0(sK0) = k17_filter_2(sK0),
inference(forward_subsumption_resolution,[],[f353,f125]) ).
fof(f355,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(superposition,[],[f142,f354]) ).
fof(f356,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f355,f126]) ).
fof(f357,plain,
( m2_filter_2(u1_struct_0(sK0),sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f356,f125]) ).
fof(f358,plain,
m2_filter_2(u1_struct_0(sK0),sK0),
inference(forward_subsumption_resolution,[],[f357,f124]) ).
fof(f364,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f358,f150]) ).
fof(f365,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f364,f126]) ).
fof(f366,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f365,f125]) ).
fof(f367,plain,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f366,f124]) ).
fof(f368,plain,
( m2_lattice4(u1_struct_0(sK0),sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f149,f358]) ).
fof(f370,plain,
( m2_lattice4(sK1,sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f149,f127]) ).
fof(f374,plain,
( m2_lattice4(sK1,sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f370,f126]) ).
fof(f375,plain,
( m2_lattice4(u1_struct_0(sK0),sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f368,f126]) ).
fof(f376,plain,
( m2_lattice4(sK1,sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f374,f125]) ).
fof(f377,plain,
( m2_lattice4(u1_struct_0(sK0),sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f375,f125]) ).
fof(f378,plain,
m2_lattice4(sK1,sK0),
inference(forward_subsumption_resolution,[],[f376,f124]) ).
fof(f379,plain,
m2_lattice4(u1_struct_0(sK0),sK0),
inference(forward_subsumption_resolution,[],[f377,f124]) ).
fof(f423,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v14_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| u1_struct_0(X0) = k19_filter_2(X0,X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(forward_subsumption_resolution,[],[f183,f188]) ).
fof(f430,plain,
! [X0,X1] :
( ~ v14_lattices(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| u1_struct_0(X0) = k19_filter_2(X0,X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_lattice4(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(resolution,[],[f423,f151]) ).
fof(f438,plain,
! [X0,X1] :
( ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| u1_struct_0(X0) = k19_filter_2(X0,X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_lattice4(X1,X0) ),
inference(duplicate_literal_removal,[],[f430]) ).
fof(f752,plain,
( ~ v14_lattices(sK0)
| u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m2_lattice4(sK1,sK0) ),
inference(resolution,[],[f438,f128]) ).
fof(f759,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m2_lattice4(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f752,f129]) ).
fof(f760,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m2_lattice4(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f759,f126]) ).
fof(f761,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| ~ l3_lattices(sK0)
| ~ m2_lattice4(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f760,f125]) ).
fof(f762,plain,
( u1_struct_0(sK0) = k19_filter_2(sK0,sK1)
| ~ m2_lattice4(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f761,f124]) ).
fof(f763,plain,
u1_struct_0(sK0) = k19_filter_2(sK0,sK1),
inference(forward_subsumption_resolution,[],[f762,f378]) ).
fof(f768,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) ),
inference(superposition,[],[f181,f763]) ).
fof(f769,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f768,f127]) ).
fof(f772,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f769,f126]) ).
fof(f775,definition,
( spl16_15
<=> m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
fof(f776,plain,
( m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f777,plain,
( ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| spl16_15 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f783,plain,
( r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1)
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f772,f125]) ).
fof(f785,plain,
r1_filter_2(u1_struct_0(sK0),u1_struct_0(sK0),sK1),
inference(forward_subsumption_resolution,[],[f783,f124]) ).
fof(f791,plain,
( ~ m2_lattice4(sK1,sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(resolution,[],[f777,f151]) ).
fof(f793,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f791,f378]) ).
fof(f794,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f793,f126]) ).
fof(f795,plain,
( ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f794,f125]) ).
fof(f796,plain,
( $false
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f795,f124]) ).
fof(f797,plain,
spl16_15,
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f800,plain,
( ! [X0] :
( ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| sK1 = X0 )
| ~ spl16_15 ),
inference(resolution,[],[f776,f174]) ).
fof(f817,plain,
( ! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| sK1 = X0 )
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f800,f367]) ).
fof(f910,plain,
( ! [X0] :
( ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| sK1 = X0
| ~ m2_lattice4(X0,sK0)
| v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) )
| ~ spl16_15 ),
inference(resolution,[],[f817,f151]) ).
fof(f949,plain,
( ! [X0] :
( ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| sK1 = X0
| ~ m2_lattice4(X0,sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0) )
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f910,f126]) ).
fof(f979,plain,
( ! [X0] :
( ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| sK1 = X0
| ~ m2_lattice4(X0,sK0)
| ~ l3_lattices(sK0) )
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f949,f125]) ).
fof(f990,plain,
( ! [X0] :
( ~ r1_filter_2(u1_struct_0(sK0),X0,sK1)
| sK1 = X0
| ~ m2_lattice4(X0,sK0) )
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f979,f124]) ).
fof(f1018,plain,
( sK1 = u1_struct_0(sK0)
| ~ m2_lattice4(u1_struct_0(sK0),sK0)
| ~ spl16_15 ),
inference(resolution,[],[f990,f785]) ).
fof(f1035,plain,
( ~ r1_filter_2(u1_struct_0(sK0),sK1,u1_struct_0(sK0))
| spl16_2 ),
inference(forward_demodulation,[],[f199,f354]) ).
fof(f1036,plain,
( sK1 = u1_struct_0(sK0)
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f1018,f379]) ).
fof(f1038,plain,
( spl16_1
| ~ spl16_15 ),
inference(avatar_split_clause,[],[f1036,f775,f193]) ).
fof(f1192,plain,
( ~ r1_filter_2(sK1,sK1,sK1)
| ~ spl16_1
| spl16_2 ),
inference(forward_demodulation,[],[f1035,f194]) ).
fof(f1193,plain,
( v1_xboole_0(sK1)
| ~ r1_tarski(sK1,sK1)
| ~ spl16_1
| spl16_2 ),
inference(resolution,[],[f1192,f342]) ).
fof(f1194,plain,
( ~ r1_tarski(sK1,sK1)
| ~ spl16_1
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f1193,f214]) ).
fof(f1195,plain,
( $false
| ~ spl16_1
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f1194,f177]) ).
fof(f1196,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_contradiction_clause,[],[f1195]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f200]) ).
cnf(s18,plain,
spl16_15,
inference(sat_conversion,[],[f797]) ).
cnf(s31,plain,
( spl16_1
| ~ spl16_15 ),
inference(sat_conversion,[],[f1038]) ).
cnf(s36,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s37,plain,
spl16_1,
inference(rat,[],[s31,s18]) ).
cnf(s38,plain,
spl16_2,
inference(rat,[],[s36,s37]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s1,s38,s37]) ).
fof(f1197,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 % Computer : n005.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 14:31:03 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.50 % (4043475)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (4043483)dis+10_1_sil=32000:sp=arity:random_seed=1461018459:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (4043481)% WARNING: option uhcvi not known.
% 0.16/0.50 % (4043480)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2760594765_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (4043481)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3309584316:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (4043482)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2159362620:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (4043484)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1700014686:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (4043485)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1421247303:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (4043486)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=86333092:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % (4043483) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4043475-4043483"...
% 0.16/0.50 % (4043483)...printing done.
% 0.16/0.50 % TRYING [4]
% 0.16/0.50 % (4043483)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (4043483)------------------------------
% 0.16/0.50 % (4043483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (4043483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (4043483)CaDiCaL version: 2.1.3
% 0.16/0.50 % (4043483)Termination reason: Refutation
% 0.16/0.50 % (4043483)Time elapsed: 0.014 s
% 0.16/0.50 % (4043483)Peak memory usage: 12 MB
% 0.16/0.50 % (4043483)Instructions burned: 35 (million)
% 0.16/0.50 % (4043475)Success in time 0.044 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------