%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LAT301+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 : n018.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 11:48:17 AM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 139 ( 23 unt; 6 def)
% Number of atoms : 543 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 653 ( 249 ~; 274 |; 96 &)
% ( 11 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( v13_lattices(X0)
=> r2_hidden(k5_lattices(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( v13_lattices(X0)
=> r2_hidden(k5_lattices(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> k7_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_2) ).
fof(f15,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0)
& m2_filter_2(X1,X0) )
=> m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_filter_2) ).
fof(f16,axiom,
! [X0] :
( l3_lattices(X0)
=> ( v3_lattices(k1_lattice2(X0))
& l3_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(f31,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(f32,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(f49,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l3_lattices(X0) )
=> ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(f59,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(f75,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0)
& m2_filter_2(X1,X0) )
=> k15_filter_2(X0,X1) = k7_filter_2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
fof(f76,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(f79,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_filter_0(X1,X0)
=> ( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& v14_lattices(X0)
& l3_lattices(X0) )
=> r2_hidden(k6_lattices(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).
fof(f85,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
fof(f87,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& v13_lattices(X0)
& l3_lattices(X0) )
=> k5_lattices(X0) = k6_lattices(k1_lattice2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_lattice2) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k5_lattices(X0),X1)
& v13_lattices(X0)
& m2_filter_2(X1,X0) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f103,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k5_lattices(X0),X1)
& v13_lattices(X0)
& m2_filter_2(X1,X0) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(flattening,[],[f102]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( k7_filter_2(X0,X1) = 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,[],[f13]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( k7_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f120]) ).
fof(f124,plain,
! [X0,X1] :
( m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f125,plain,
! [X0,X1] :
( m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ( v3_lattices(k1_lattice2(X0))
& l3_lattices(k1_lattice2(X0)) )
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f140,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,[],[f31]) ).
fof(f141,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,[],[f140]) ).
fof(f142,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,[],[f32]) ).
fof(f143,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,[],[f142]) ).
fof(f157,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f158,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f157]) ).
fof(f173,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f174,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f173]) ).
fof(f182,plain,
! [X0,X1] :
( k15_filter_2(X0,X1) = k7_filter_2(X0,X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f183,plain,
! [X0,X1] :
( k15_filter_2(X0,X1) = k7_filter_2(X0,X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0) ),
inference(flattening,[],[f182]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f184]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( r2_hidden(k6_lattices(X0),X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_filter_0(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( r2_hidden(k6_lattices(X0),X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_filter_0(X1,X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f186]) ).
fof(f195,plain,
! [X0] :
( ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f196,plain,
! [X0] :
( ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f195]) ).
fof(f198,plain,
! [X0] :
( k5_lattices(X0) = k6_lattices(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f199,plain,
! [X0] :
( k5_lattices(X0) = k6_lattices(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f198]) ).
fof(f202,definition,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0)) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f203,plain,
! [X0] :
( sP0(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(definition_folding,[],[f174,f202]) ).
fof(f204,plain,
( ~ r2_hidden(k5_lattices(sK1),sK2)
& v13_lattices(sK1)
& m2_filter_2(sK2,sK1)
& ~ v3_struct_0(sK1)
& v10_lattices(sK1)
& l3_lattices(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f103]) ).
fof(f216,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( m1_filter_2(X1,X0)
| ~ m1_filter_0(X1,X0) )
& ( m1_filter_0(X1,X0)
| ~ m1_filter_2(X1,X0) ) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f233,plain,
! [X0] :
( ( ( v13_lattices(X0)
| ~ v14_lattices(k1_lattice2(X0)) )
& ( v14_lattices(k1_lattice2(X0))
| ~ v13_lattices(X0) ) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(nnf_transformation,[],[f196]) ).
fof(f234,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f235,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f236,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f237,plain,
m2_filter_2(sK2,sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f238,plain,
v13_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f239,plain,
~ r2_hidden(k5_lattices(sK1),sK2),
inference(cnf_transformation,[],[f204]) ).
fof(f261,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| k7_filter_2(X0,X1) = X1
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f264,plain,
! [X0,X1] :
( m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| ~ m2_filter_2(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f265,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f278,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,[],[f141]) ).
fof(f280,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,[],[f143]) ).
fof(f301,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f320,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f329,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f380,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| k7_filter_2(X0,X1) = k15_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f381,plain,
! [X0,X1] :
( ~ m1_filter_2(X1,X0)
| m1_filter_0(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f386,plain,
! [X0,X1] :
( r2_hidden(k6_lattices(X0),X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_filter_0(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f392,plain,
! [X0] :
( v14_lattices(k1_lattice2(X0))
| ~ v13_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f395,plain,
! [X0] :
( ~ v13_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| k5_lattices(X0) = k6_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f398,plain,
! [X0,X1] :
( r2_hidden(k6_lattices(X0),X1)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_filter_0(X1,X0) ),
inference(duplicate_literal_removal,[],[f386]) ).
fof(f630,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| sP0(sK1) ),
inference(resolution,[],[f329,f234]) ).
fof(f638,plain,
( ~ v10_lattices(sK1)
| sP0(sK1) ),
inference(forward_subsumption_resolution,[],[f630,f236]) ).
fof(f641,plain,
sP0(sK1),
inference(forward_subsumption_resolution,[],[f638,f235]) ).
fof(f756,plain,
( m2_lattice4(sK2,sK1)
| v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(resolution,[],[f278,f237]) ).
fof(f759,plain,
( m2_lattice4(sK2,sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f756,f236]) ).
fof(f760,plain,
( m2_lattice4(sK2,sK1)
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f759,f235]) ).
fof(f761,plain,
m2_lattice4(sK2,sK1),
inference(forward_subsumption_resolution,[],[f760,f234]) ).
fof(f793,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolution,[],[f395,f238]) ).
fof(f796,plain,
( ~ v10_lattices(sK1)
| k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f793,f236]) ).
fof(f798,plain,
( k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f796,f235]) ).
fof(f800,plain,
k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1)),
inference(forward_subsumption_resolution,[],[f798,f234]) ).
fof(f807,definition,
( spl28_27
<=> v3_struct_0(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl28_27])],[avatar_definition]) ).
fof(f808,plain,
( ~ v3_struct_0(k1_lattice2(sK1))
| spl28_27 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f809,plain,
( v3_struct_0(k1_lattice2(sK1))
| ~ spl28_27 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f834,plain,
! [X0] :
( r2_hidden(k5_lattices(sK1),X0)
| v3_struct_0(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ v14_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ m1_filter_0(X0,k1_lattice2(sK1)) ),
inference(superposition,[],[f398,f800]) ).
fof(f836,definition,
( spl28_29
<=> l3_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl28_29])],[avatar_definition]) ).
fof(f837,plain,
( l3_lattices(k1_lattice2(sK1))
| ~ spl28_29 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f838,plain,
( ~ l3_lattices(k1_lattice2(sK1))
| spl28_29 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f840,definition,
( spl28_30
<=> v14_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl28_30])],[avatar_definition]) ).
fof(f842,plain,
( ~ v14_lattices(k1_lattice2(sK1))
| spl28_30 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f844,definition,
( spl28_31
<=> v10_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl28_31])],[avatar_definition]) ).
fof(f845,plain,
( v10_lattices(k1_lattice2(sK1))
| ~ spl28_31 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f846,plain,
( ~ v10_lattices(k1_lattice2(sK1))
| spl28_31 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f848,definition,
( spl28_32
<=> ! [X0] :
( r2_hidden(k5_lattices(sK1),X0)
| ~ m1_filter_0(X0,k1_lattice2(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl28_32])],[avatar_definition]) ).
fof(f849,plain,
( ! [X0] :
( ~ m1_filter_0(X0,k1_lattice2(sK1))
| r2_hidden(k5_lattices(sK1),X0) )
| ~ spl28_32 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f850,plain,
( ~ spl28_29
| ~ spl28_30
| ~ spl28_31
| spl28_27
| spl28_32 ),
inference(avatar_split_clause,[],[f834,f848,f807,f844,f840,f836]) ).
fof(f852,plain,
! [X0,X1] :
( k7_filter_2(X0,X1) = 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,[],[f261,f280]) ).
fof(f862,plain,
! [X0,X1] :
( ~ m2_lattice4(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| k7_filter_2(X0,X1) = X1 ),
inference(duplicate_literal_removal,[],[f852]) ).
fof(f864,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ spl28_27 ),
inference(resolution,[],[f809,f301]) ).
fof(f868,plain,
( ~ l3_lattices(sK1)
| ~ spl28_27 ),
inference(forward_subsumption_resolution,[],[f864,f236]) ).
fof(f869,plain,
( $false
| ~ spl28_27 ),
inference(forward_subsumption_resolution,[],[f868,f234]) ).
fof(f870,plain,
~ spl28_27,
inference(avatar_contradiction_clause,[],[f869]) ).
fof(f871,plain,
( ~ l3_lattices(sK1)
| spl28_29 ),
inference(resolution,[],[f838,f265]) ).
fof(f872,plain,
( $false
| spl28_29 ),
inference(forward_subsumption_resolution,[],[f871,f234]) ).
fof(f873,plain,
spl28_29,
inference(avatar_contradiction_clause,[],[f872]) ).
fof(f926,plain,
( ~ v13_lattices(sK1)
| v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl28_30 ),
inference(resolution,[],[f842,f392]) ).
fof(f927,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl28_30 ),
inference(forward_subsumption_resolution,[],[f926,f238]) ).
fof(f928,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl28_30 ),
inference(forward_subsumption_resolution,[],[f927,f236]) ).
fof(f929,plain,
( ~ l3_lattices(sK1)
| spl28_30 ),
inference(forward_subsumption_resolution,[],[f928,f235]) ).
fof(f930,plain,
( $false
| spl28_30 ),
inference(forward_subsumption_resolution,[],[f929,f234]) ).
fof(f931,plain,
spl28_30,
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f932,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(resolution,[],[f380,f237]) ).
fof(f935,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f932,f236]) ).
fof(f936,plain,
( ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f935,f235]) ).
fof(f937,plain,
k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2),
inference(forward_subsumption_resolution,[],[f936,f234]) ).
fof(f965,plain,
( ~ sP0(sK1)
| spl28_31 ),
inference(resolution,[],[f846,f320]) ).
fof(f966,plain,
( $false
| spl28_31 ),
inference(forward_subsumption_resolution,[],[f965,f641]) ).
fof(f967,plain,
spl28_31,
inference(avatar_contradiction_clause,[],[f966]) ).
fof(f1034,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| ~ m2_filter_2(sK2,sK1) ),
inference(superposition,[],[f264,f937]) ).
fof(f1035,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| ~ m2_filter_2(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f1034,f236]) ).
fof(f1036,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ m2_filter_2(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f1035,f235]) ).
fof(f1037,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ m2_filter_2(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f1036,f234]) ).
fof(f1038,plain,
m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1)),
inference(forward_subsumption_resolution,[],[f1037,f237]) ).
fof(f1093,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolution,[],[f1038,f381]) ).
fof(f1098,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| spl28_27 ),
inference(forward_subsumption_resolution,[],[f1093,f808]) ).
fof(f1101,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| spl28_27
| ~ spl28_31 ),
inference(forward_subsumption_resolution,[],[f1098,f845]) ).
fof(f1104,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| spl28_27
| ~ spl28_29
| ~ spl28_31 ),
inference(forward_subsumption_resolution,[],[f1101,f837]) ).
fof(f1279,plain,
( r2_hidden(k5_lattices(sK1),k7_filter_2(sK1,sK2))
| spl28_27
| ~ spl28_29
| ~ spl28_31
| ~ spl28_32 ),
inference(resolution,[],[f849,f1104]) ).
fof(f1707,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(resolution,[],[f862,f761]) ).
fof(f1714,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f1707,f236]) ).
fof(f1716,plain,
( ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f1714,f235]) ).
fof(f1718,plain,
sK2 = k7_filter_2(sK1,sK2),
inference(forward_subsumption_resolution,[],[f1716,f234]) ).
fof(f1723,plain,
( r2_hidden(k5_lattices(sK1),sK2)
| spl28_27
| ~ spl28_29
| ~ spl28_31
| ~ spl28_32 ),
inference(superposition,[],[f1279,f1718]) ).
fof(f1729,plain,
( $false
| spl28_27
| ~ spl28_29
| ~ spl28_31
| ~ spl28_32 ),
inference(forward_subsumption_resolution,[],[f1723,f239]) ).
fof(f1730,plain,
( spl28_27
| ~ spl28_29
| ~ spl28_31
| ~ spl28_32 ),
inference(avatar_contradiction_clause,[],[f1729]) ).
cnf(s27,plain,
( spl28_27
| ~ spl28_29
| ~ spl28_30
| ~ spl28_31
| spl28_32 ),
inference(sat_conversion,[],[f850]) ).
cnf(s29,plain,
~ spl28_27,
inference(sat_conversion,[],[f870]) ).
cnf(s30,plain,
spl28_29,
inference(sat_conversion,[],[f873]) ).
cnf(s38,plain,
spl28_30,
inference(sat_conversion,[],[f931]) ).
cnf(s40,plain,
spl28_31,
inference(sat_conversion,[],[f967]) ).
cnf(s102,plain,
( spl28_27
| ~ spl28_29
| ~ spl28_31
| ~ spl28_32 ),
inference(sat_conversion,[],[f1730]) ).
cnf(s130,plain,
~ spl28_32,
inference(rat,[],[s102,s30,s40,s29]) ).
cnf(s138,plain,
$false,
inference(rat,[],[s27,s130,s40,s38,s30,s29]) ).
fof(f1742,plain,
$false,
inference(avatar_sat_refutation,[],[s138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 14:24:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.49 % (2406420)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2406431)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2929834024:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % (2406426)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2406425)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3363909166_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2406426)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=602010533:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2406427)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1184909978:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2406428)dis+10_1_sil=32000:sp=arity:random_seed=1654055684:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2406429)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1287424243:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2406430)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=943830130:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (2406428) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2406420-2406428"...
% 0.17/0.49 % (2406428)...printing done.
% 0.17/0.49 % (2406428)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (2406428)------------------------------
% 0.17/0.49 % (2406428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2406428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2406428)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2406428)Termination reason: Refutation
% 0.17/0.49 % (2406428)Time elapsed: 0.032 s
% 0.17/0.49 % (2406428)Peak memory usage: 13 MB
% 0.17/0.49 % (2406428)Instructions burned: 45 (million)
% 0.17/0.49 % (2406420)Success in time 0.071 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------