%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 11:46:41 AM UTC 2026
% Result : Theorem 2.84s 1.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 141 ( 23 unt; 6 def)
% Number of atoms : 551 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 663 ( 253 ~; 280 |; 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 : 100 ( 0 sgn 96 !; 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(f105,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(f106,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,[],[f105]) ).
fof(f107,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(f108,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,[],[f107]) ).
fof(f111,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(f112,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,[],[f111]) ).
fof(f115,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(f116,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,[],[f115]) ).
fof(f117,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(f118,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,[],[f117]) ).
fof(f119,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(f120,plain,
! [X0] :
( ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f119]) ).
fof(f132,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(f133,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,[],[f132]) ).
fof(f139,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(f140,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,[],[f139]) ).
fof(f144,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(f145,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,[],[f144]) ).
fof(f146,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(f147,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f146]) ).
fof(f150,plain,
! [X0] :
( ( v3_lattices(k1_lattice2(X0))
& l3_lattices(k1_lattice2(X0)) )
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f166,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(f167,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,[],[f166]) ).
fof(f170,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(f171,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,[],[f170]) ).
fof(f201,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(f202,plain,
! [X0] :
( sP0(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(definition_folding,[],[f145,f201]) ).
fof(f203,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)],[f106]) ).
fof(f206,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,[],[f120]) ).
fof(f208,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,[],[f201]) ).
fof(f215,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,[],[f171]) ).
fof(f232,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f233,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f234,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f235,plain,
m2_filter_2(sK2,sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f236,plain,
v13_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f237,plain,
~ r2_hidden(k5_lattices(sK1),sK2),
inference(cnf_transformation,[],[f203]) ).
fof(f238,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,[],[f108]) ).
fof(f241,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,[],[f112]) ).
fof(f243,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,[],[f116]) ).
fof(f245,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,[],[f118]) ).
fof(f246,plain,
! [X0] :
( v14_lattices(k1_lattice2(X0))
| ~ v13_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f271,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,[],[f133]) ).
fof(f278,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,[],[f140]) ).
fof(f281,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f290,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f292,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f294,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f315,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,[],[f167]) ).
fof(f318,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,[],[f215]) ).
fof(f383,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,[],[f271]) ).
fof(f447,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| sP0(sK1) ),
inference(resolution,[],[f290,f232]) ).
fof(f482,plain,
( ~ v10_lattices(sK1)
| sP0(sK1) ),
inference(forward_subsumption_resolution,[],[f447,f234]) ).
fof(f494,plain,
sP0(sK1),
inference(forward_subsumption_resolution,[],[f482,f233]) ).
fof(f636,plain,
( m2_lattice4(sK2,sK1)
| v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(resolution,[],[f243,f235]) ).
fof(f639,plain,
( m2_lattice4(sK2,sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f636,f234]) ).
fof(f640,plain,
( m2_lattice4(sK2,sK1)
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f639,f233]) ).
fof(f641,plain,
m2_lattice4(sK2,sK1),
inference(forward_subsumption_resolution,[],[f640,f232]) ).
fof(f696,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolution,[],[f238,f236]) ).
fof(f699,plain,
( ~ v10_lattices(sK1)
| k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f696,f234]) ).
fof(f701,plain,
( k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(forward_subsumption_resolution,[],[f699,f233]) ).
fof(f703,plain,
k5_lattices(sK1) = k6_lattices(k1_lattice2(sK1)),
inference(forward_subsumption_resolution,[],[f701,f232]) ).
fof(f710,definition,
( spl27_12
<=> v3_struct_0(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl27_12])],[avatar_definition]) ).
fof(f711,plain,
( ~ v3_struct_0(k1_lattice2(sK1))
| spl27_12 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f712,plain,
( v3_struct_0(k1_lattice2(sK1))
| ~ spl27_12 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f739,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ spl27_12 ),
inference(resolution,[],[f712,f292]) ).
fof(f743,plain,
( ~ l3_lattices(sK1)
| ~ spl27_12 ),
inference(forward_subsumption_resolution,[],[f739,f234]) ).
fof(f744,plain,
( $false
| ~ spl27_12 ),
inference(forward_subsumption_resolution,[],[f743,f232]) ).
fof(f745,plain,
~ spl27_12,
inference(avatar_contradiction_clause,[],[f744]) ).
fof(f756,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,[],[f383,f703]) ).
fof(f757,plain,
( ! [X0] :
( r2_hidden(k5_lattices(sK1),X0)
| ~ v10_lattices(k1_lattice2(sK1))
| ~ v14_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ m1_filter_0(X0,k1_lattice2(sK1)) )
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f756,f711]) ).
fof(f759,definition,
( spl27_14
<=> l3_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl27_14])],[avatar_definition]) ).
fof(f760,plain,
( l3_lattices(k1_lattice2(sK1))
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f761,plain,
( ~ l3_lattices(k1_lattice2(sK1))
| spl27_14 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f763,definition,
( spl27_15
<=> v14_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl27_15])],[avatar_definition]) ).
fof(f765,plain,
( ~ v14_lattices(k1_lattice2(sK1))
| spl27_15 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f767,definition,
( spl27_16
<=> v10_lattices(k1_lattice2(sK1)) ),
introduced(definition,[new_symbols(definition,[spl27_16])],[avatar_definition]) ).
fof(f768,plain,
( v10_lattices(k1_lattice2(sK1))
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f769,plain,
( ~ v10_lattices(k1_lattice2(sK1))
| spl27_16 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f771,definition,
( spl27_17
<=> ! [X0] :
( r2_hidden(k5_lattices(sK1),X0)
| ~ m1_filter_0(X0,k1_lattice2(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl27_17])],[avatar_definition]) ).
fof(f772,plain,
( ! [X0] :
( ~ m1_filter_0(X0,k1_lattice2(sK1))
| r2_hidden(k5_lattices(sK1),X0) )
| ~ spl27_17 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f773,plain,
( ~ spl27_14
| ~ spl27_15
| ~ spl27_16
| spl27_17
| spl27_12 ),
inference(avatar_split_clause,[],[f757,f710,f771,f767,f763,f759]) ).
fof(f774,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(resolution,[],[f241,f235]) ).
fof(f777,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f774,f234]) ).
fof(f778,plain,
( ~ l3_lattices(sK1)
| k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f777,f233]) ).
fof(f779,plain,
k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2),
inference(forward_subsumption_resolution,[],[f778,f232]) ).
fof(f780,plain,
( ~ l3_lattices(sK1)
| spl27_14 ),
inference(resolution,[],[f761,f294]) ).
fof(f781,plain,
( $false
| spl27_14 ),
inference(forward_subsumption_resolution,[],[f780,f232]) ).
fof(f782,plain,
spl27_14,
inference(avatar_contradiction_clause,[],[f781]) ).
fof(f784,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,[],[f278,f315]) ).
fof(f793,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,[],[f784]) ).
fof(f867,plain,
( ~ v13_lattices(sK1)
| v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl27_15 ),
inference(resolution,[],[f765,f246]) ).
fof(f868,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f867,f236]) ).
fof(f869,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f868,f234]) ).
fof(f870,plain,
( ~ l3_lattices(sK1)
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f869,f233]) ).
fof(f871,plain,
( $false
| spl27_15 ),
inference(forward_subsumption_resolution,[],[f870,f232]) ).
fof(f872,plain,
spl27_15,
inference(avatar_contradiction_clause,[],[f871]) ).
fof(f900,plain,
( ~ sP0(sK1)
| spl27_16 ),
inference(resolution,[],[f769,f281]) ).
fof(f901,plain,
( $false
| spl27_16 ),
inference(forward_subsumption_resolution,[],[f900,f494]) ).
fof(f902,plain,
spl27_16,
inference(avatar_contradiction_clause,[],[f901]) ).
fof(f947,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,[],[f245,f779]) ).
fof(f948,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,[],[f947,f234]) ).
fof(f949,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ m2_filter_2(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f948,f233]) ).
fof(f950,plain,
( m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ m2_filter_2(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f949,f232]) ).
fof(f951,plain,
m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1)),
inference(forward_subsumption_resolution,[],[f950,f235]) ).
fof(f1172,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,[],[f951,f318]) ).
fof(f1177,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| spl27_12 ),
inference(forward_subsumption_resolution,[],[f1172,f711]) ).
fof(f1180,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| spl27_12
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f1177,f768]) ).
fof(f1183,plain,
( m1_filter_0(k7_filter_2(sK1,sK2),k1_lattice2(sK1))
| spl27_12
| ~ spl27_14
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f1180,f760]) ).
fof(f1250,plain,
( r2_hidden(k5_lattices(sK1),k7_filter_2(sK1,sK2))
| spl27_12
| ~ spl27_14
| ~ spl27_16
| ~ spl27_17 ),
inference(resolution,[],[f772,f1183]) ).
fof(f1455,plain,
( v3_struct_0(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(resolution,[],[f793,f641]) ).
fof(f1462,plain,
( ~ v10_lattices(sK1)
| ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f1455,f234]) ).
fof(f1464,plain,
( ~ l3_lattices(sK1)
| sK2 = k7_filter_2(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f1462,f233]) ).
fof(f1466,plain,
sK2 = k7_filter_2(sK1,sK2),
inference(forward_subsumption_resolution,[],[f1464,f232]) ).
fof(f1471,plain,
( r2_hidden(k5_lattices(sK1),sK2)
| spl27_12
| ~ spl27_14
| ~ spl27_16
| ~ spl27_17 ),
inference(superposition,[],[f1250,f1466]) ).
fof(f1477,plain,
( $false
| spl27_12
| ~ spl27_14
| ~ spl27_16
| ~ spl27_17 ),
inference(forward_subsumption_resolution,[],[f1471,f237]) ).
fof(f1478,plain,
( spl27_12
| ~ spl27_14
| ~ spl27_16
| ~ spl27_17 ),
inference(avatar_contradiction_clause,[],[f1477]) ).
cnf(s13,plain,
~ spl27_12,
inference(sat_conversion,[],[f745]) ).
cnf(s14,plain,
( spl27_12
| ~ spl27_14
| ~ spl27_15
| ~ spl27_16
| spl27_17 ),
inference(sat_conversion,[],[f773]) ).
cnf(s15,plain,
spl27_14,
inference(sat_conversion,[],[f782]) ).
cnf(s23,plain,
spl27_15,
inference(sat_conversion,[],[f872]) ).
cnf(s25,plain,
spl27_16,
inference(sat_conversion,[],[f902]) ).
cnf(s59,plain,
( spl27_12
| ~ spl27_14
| ~ spl27_16
| ~ spl27_17 ),
inference(sat_conversion,[],[f1478]) ).
cnf(s71,plain,
( spl27_12
| spl27_17 ),
inference(rat,[],[s14,s25,s23,s15]) ).
cnf(s72,plain,
~ spl27_17,
inference(rat,[],[s59,s15,s25,s13]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s71,s72,s13]) ).
fof(f1490,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 14:25:26 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/1.31 % (2894331)Detected formulas, will run a generic FOF schedule.
% 2.84/1.31 % (2894598)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1083030296:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.31 % (2894593)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=1024987133:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.31 % (2894596)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2254978653:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.31 % (2894600)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3255995747:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.31 % (2894594)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=962948865:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.31 % (2894591)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=4097996464:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.31 % (2894598)Instruction limit reached!
% 2.84/1.31 % (2894598)------------------------------
% 2.84/1.31 % (2894598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.31 % (2894598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.31 % (2894598)CaDiCaL version: 2.1.3
% 2.84/1.31 % (2894598)Termination reason: Instruction limit
% 2.84/1.31 % (2894598)Termination phase: Saturation
% 2.84/1.31 % (2894598)Time elapsed: 0.039 s
% 2.84/1.31 % (2894598)Peak memory usage: 88 MB
% 2.84/1.31 % (2894598)Instructions burned: 119 (million)
% 2.84/1.31 % (2894596)Refutation not found, incomplete strategy
% 2.84/1.31 % (2894596)------------------------------
% 2.84/1.31 % (2894596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.31 % (2894596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.31 % (2894596)CaDiCaL version: 2.1.3
% 2.84/1.31 % (2894596)Termination reason: Refutation not found, incomplete strategy
% 2.84/1.31 % (2894596)Time elapsed: 0.002 s
% 2.84/1.31 % (2894596)Peak memory usage: 88 MB
% 2.84/1.31 % (2894596)Instructions burned: 1 (million)
% 2.84/1.31 % (2894602)dis-21_1_sil=8000:lcm=predicate:random_seed=3838960590: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)
% 2.84/1.31 % (2894602)Instruction limit reached!
% 2.84/1.31 % (2894602)------------------------------
% 2.84/1.31 % (2894602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.31 % (2894602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.31 % (2894602)CaDiCaL version: 2.1.3
% 2.84/1.31 % (2894602)Termination reason: Instruction limit
% 2.84/1.31 % (2894602)Termination phase: Saturation
% 2.84/1.31 % (2894602)Time elapsed: 0.070 s
% 2.84/1.31 % (2894602)Peak memory usage: 91 MB
% 2.84/1.31 % (2894602)Instructions burned: 129 (million)
% 2.84/1.31 % (2894600)Instruction limit reached!
% 2.84/1.31 % (2894600)------------------------------
% 2.84/1.31 % (2894600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.31 % (2894600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.31 % (2894600)CaDiCaL version: 2.1.3
% 2.84/1.31 % (2894600)Termination reason: Instruction limit
% 2.84/1.31 % (2894600)Termination phase: Saturation
% 2.84/1.31 % (2894600)Time elapsed: 0.097 s
% 2.84/1.31 % (2894600)Peak memory usage: 90 MB
% 2.84/1.31 % (2894600)Instructions burned: 140 (million)
% 2.84/1.31 % (2894683)lrs+10_1_sil=8000:sp=occurrence:random_seed=1416037337:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.84/1.31 % (2894683)First to succeed.
% 2.84/1.31 % (2894683)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2894331"
% 2.84/1.31 % (2894596)------------------------------
% 2.84/1.31 % (2894596)------------------------------
% 2.84/1.31 % (2894741)lrs+1011_1_sil=32000:sp=occurrence:random_seed=664189522:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.84/1.31 % (2894736)lrs+10_1_sil=32000:urr=on:br=off:random_seed=195499815:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.84/1.31 % (2894736)Refutation not found, incomplete strategy
% 2.84/1.31 % (2894736)------------------------------
% 2.84/1.31 % (2894736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.31 % (2894736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.31 % (2894736)CaDiCaL version: 2.1.3
% 2.84/1.31 % (2894736)Termination reason: Refutation not found, incomplete strategy
% 2.84/1.31 % (2894736)Time elapsed: 0.003 s
% 2.84/1.31 % (2894736)Peak memory usage: 88 MB
% 2.84/1.31 % (2894736)Instructions burned: 3 (million)
% 2.84/1.31 % (2894683)Refutation found. Thanks to Tanya!
% 2.84/1.31 % SZS status Theorem for theBenchmark
% 2.84/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (2894683)------------------------------
% 0.18/1.51 % (2894683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (2894683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (2894683)CaDiCaL version: 2.1.3
% 0.18/1.51 % (2894683)Termination reason: Refutation
% 0.18/1.51 % (2894683)Time elapsed: 0.016 s
% 0.18/1.51 % (2894683)Peak memory usage: 90 MB
% 0.18/1.51 % (2894683)Instructions burned: 42 (million)
% 0.18/1.51 % (2894683)------------------------------
% 0.18/1.51 % (2894683)------------------------------
% 0.18/1.51 % (2894331)Success in time 0.441 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------