%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT301+2 : 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 : n017.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 7.47s 2.08s
% Output : Refutation 8.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 22 unt; 8 def)
% Number of atoms : 479 ( 8 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 594 ( 229 ~; 256 |; 75 &)
% ( 17 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 59 ( 0 sgn 55 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2452,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(f2564,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(f2569,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(f2644,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(f2659,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(f2669,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(f2872,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(f2941,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
fof(f2949,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(f2950,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)],[f2949]) ).
fof(f2974,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ( ~ v3_struct_0(k1_lattice2(X0))
& v3_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)) ) ),
inference(pure_predicate_removal,[],[f2569]) ).
fof(f2996,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,[],[f2872]) ).
fof(f2997,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,[],[f2996]) ).
fof(f3131,plain,
! [X0] :
( ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f2941]) ).
fof(f3132,plain,
! [X0] :
( ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f3131]) ).
fof(f3147,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,[],[f2950]) ).
fof(f3148,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,[],[f3147]) ).
fof(f3271,plain,
! [X0] :
( ( v3_lattices(k1_lattice2(X0))
& l3_lattices(k1_lattice2(X0)) )
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f2669]) ).
fof(f3274,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_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,[],[f2974]) ).
fof(f3275,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_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,[],[f3274]) ).
fof(f3276,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f2564]) ).
fof(f3277,plain,
! [X0] :
( ( ~ v3_struct_0(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f3276]) ).
fof(f3441,plain,
! [X0] :
( ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f2644]) ).
fof(f3442,plain,
! [X0] :
( ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f3441]) ).
fof(f3445,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,[],[f2659]) ).
fof(f3446,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,[],[f3445]) ).
fof(f3449,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,[],[f2452]) ).
fof(f3450,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,[],[f3449]) ).
fof(f3524,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,[],[f2997]) ).
fof(f3544,plain,
! [X0] :
( ! [X1] :
( ( m2_filter_2(X1,X0)
| ~ m1_filter_2(X1,k1_lattice2(X0)) )
& ( m1_filter_2(X1,k1_lattice2(X0))
| ~ m2_filter_2(X1,X0) ) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(nnf_transformation,[],[f3132]) ).
fof(f3550,plain,
( ~ r2_hidden(k5_lattices(sK16),sK17)
& v13_lattices(sK16)
& m2_filter_2(sK17,sK16)
& ~ v3_struct_0(sK16)
& v10_lattices(sK16)
& l3_lattices(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f3148]) ).
fof(f3693,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,[],[f3442]) ).
fof(f3724,plain,
! [X0,X1] :
( m1_filter_0(X1,X0)
| ~ m1_filter_2(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3524]) ).
fof(f3837,plain,
! [X0,X1] :
( m1_filter_2(X1,k1_lattice2(X0))
| ~ m2_filter_2(X1,X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3544]) ).
fof(f3874,plain,
l3_lattices(sK16),
inference(cnf_transformation,[],[f3550]) ).
fof(f3875,plain,
v10_lattices(sK16),
inference(cnf_transformation,[],[f3550]) ).
fof(f3876,plain,
~ v3_struct_0(sK16),
inference(cnf_transformation,[],[f3550]) ).
fof(f3877,plain,
m2_filter_2(sK17,sK16),
inference(cnf_transformation,[],[f3550]) ).
fof(f3878,plain,
v13_lattices(sK16),
inference(cnf_transformation,[],[f3550]) ).
fof(f3879,plain,
~ r2_hidden(k5_lattices(sK16),sK17),
inference(cnf_transformation,[],[f3550]) ).
fof(f4028,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3271]) ).
fof(f4031,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3275]) ).
fof(f4040,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3277]) ).
fof(f4274,plain,
! [X0] :
( v14_lattices(k1_lattice2(X0))
| ~ v13_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3693]) ).
fof(f4277,plain,
! [X0] :
( k5_lattices(X0) = k6_lattices(k1_lattice2(X0))
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f3446]) ).
fof(f4280,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,[],[f3450]) ).
fof(f4555,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,[],[f4280]) ).
fof(f4561,definition,
( spl157_1
<=> v3_struct_0(sK16) ),
introduced(definition,[new_symbols(definition,[spl157_1])],[avatar_definition]) ).
fof(f4563,plain,
( ~ v3_struct_0(sK16)
| spl157_1 ),
inference(avatar_component_clause,[],[f4561]) ).
fof(f4564,plain,
~ spl157_1,
inference(avatar_split_clause,[],[f3876,f4561]) ).
fof(f4566,definition,
( spl157_2
<=> r2_hidden(k5_lattices(sK16),sK17) ),
introduced(definition,[new_symbols(definition,[spl157_2])],[avatar_definition]) ).
fof(f4568,plain,
( ~ r2_hidden(k5_lattices(sK16),sK17)
| spl157_2 ),
inference(avatar_component_clause,[],[f4566]) ).
fof(f4569,plain,
~ spl157_2,
inference(avatar_split_clause,[],[f3879,f4566]) ).
fof(f4614,definition,
( spl157_3
<=> l3_lattices(sK16) ),
introduced(definition,[new_symbols(definition,[spl157_3])],[avatar_definition]) ).
fof(f4616,plain,
( l3_lattices(sK16)
| ~ spl157_3 ),
inference(avatar_component_clause,[],[f4614]) ).
fof(f4617,plain,
spl157_3,
inference(avatar_split_clause,[],[f3874,f4614]) ).
fof(f4619,definition,
( spl157_4
<=> v10_lattices(sK16) ),
introduced(definition,[new_symbols(definition,[spl157_4])],[avatar_definition]) ).
fof(f4621,plain,
( v10_lattices(sK16)
| ~ spl157_4 ),
inference(avatar_component_clause,[],[f4619]) ).
fof(f4622,plain,
spl157_4,
inference(avatar_split_clause,[],[f3875,f4619]) ).
fof(f4624,definition,
( spl157_5
<=> v13_lattices(sK16) ),
introduced(definition,[new_symbols(definition,[spl157_5])],[avatar_definition]) ).
fof(f4626,plain,
( v13_lattices(sK16)
| ~ spl157_5 ),
inference(avatar_component_clause,[],[f4624]) ).
fof(f4627,plain,
spl157_5,
inference(avatar_split_clause,[],[f3878,f4624]) ).
fof(f4833,plain,
( v10_lattices(k1_lattice2(sK16))
| ~ v10_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1 ),
inference(resolution,[],[f4563,f4031]) ).
fof(f4842,plain,
( ~ v3_struct_0(k1_lattice2(sK16))
| ~ l3_lattices(sK16)
| spl157_1 ),
inference(resolution,[],[f4563,f4040]) ).
fof(f4894,plain,
( v14_lattices(k1_lattice2(sK16))
| ~ v13_lattices(sK16)
| ~ v10_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1 ),
inference(resolution,[],[f4563,f4274]) ).
fof(f4897,plain,
( k5_lattices(sK16) = k6_lattices(k1_lattice2(sK16))
| ~ v10_lattices(sK16)
| ~ v13_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1 ),
inference(resolution,[],[f4563,f4277]) ).
fof(f5198,plain,
( k5_lattices(sK16) = k6_lattices(k1_lattice2(sK16))
| ~ v13_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_4 ),
inference(forward_subsumption_resolution,[],[f4897,f4621]) ).
fof(f5200,plain,
( v14_lattices(k1_lattice2(sK16))
| ~ v10_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_5 ),
inference(forward_subsumption_resolution,[],[f4894,f4626]) ).
fof(f5251,plain,
( ~ v3_struct_0(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3 ),
inference(forward_subsumption_resolution,[],[f4842,f4616]) ).
fof(f5258,plain,
( v10_lattices(k1_lattice2(sK16))
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_4 ),
inference(forward_subsumption_resolution,[],[f4833,f4621]) ).
fof(f5583,plain,
( k5_lattices(sK16) = k6_lattices(k1_lattice2(sK16))
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_4
| ~ spl157_5 ),
inference(forward_subsumption_resolution,[],[f5198,f4626]) ).
fof(f5585,plain,
( v14_lattices(k1_lattice2(sK16))
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_4
| ~ spl157_5 ),
inference(forward_subsumption_resolution,[],[f5200,f4621]) ).
fof(f5609,plain,
( v10_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4 ),
inference(forward_subsumption_resolution,[],[f5258,f4616]) ).
fof(f5848,plain,
( k5_lattices(sK16) = k6_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5 ),
inference(forward_subsumption_resolution,[],[f5583,f4616]) ).
fof(f5849,plain,
( v14_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5 ),
inference(forward_subsumption_resolution,[],[f5585,f4616]) ).
fof(f5945,definition,
( spl157_6
<=> m2_filter_2(sK17,sK16) ),
introduced(definition,[new_symbols(definition,[spl157_6])],[avatar_definition]) ).
fof(f5947,plain,
( m2_filter_2(sK17,sK16)
| ~ spl157_6 ),
inference(avatar_component_clause,[],[f5945]) ).
fof(f5948,plain,
spl157_6,
inference(avatar_split_clause,[],[f3877,f5945]) ).
fof(f5961,plain,
( m1_filter_2(sK17,k1_lattice2(sK16))
| v3_struct_0(sK16)
| ~ v10_lattices(sK16)
| ~ l3_lattices(sK16)
| ~ spl157_6 ),
inference(resolution,[],[f5947,f3837]) ).
fof(f5974,plain,
( m1_filter_2(sK17,k1_lattice2(sK16))
| ~ v10_lattices(sK16)
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_6 ),
inference(forward_subsumption_resolution,[],[f5961,f4563]) ).
fof(f5992,plain,
( m1_filter_2(sK17,k1_lattice2(sK16))
| ~ l3_lattices(sK16)
| spl157_1
| ~ spl157_4
| ~ spl157_6 ),
inference(forward_subsumption_resolution,[],[f5974,f4621]) ).
fof(f6010,plain,
( m1_filter_2(sK17,k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_6 ),
inference(forward_subsumption_resolution,[],[f5992,f4616]) ).
fof(f6240,plain,
( l3_lattices(k1_lattice2(sK16))
| ~ spl157_3 ),
inference(resolution,[],[f4616,f4028]) ).
fof(f7339,definition,
( spl157_9
<=> m1_filter_2(sK17,k1_lattice2(sK16)) ),
introduced(definition,[new_symbols(definition,[spl157_9])],[avatar_definition]) ).
fof(f7341,plain,
( m1_filter_2(sK17,k1_lattice2(sK16))
| ~ spl157_9 ),
inference(avatar_component_clause,[],[f7339]) ).
fof(f7342,plain,
( spl157_9
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_6 ),
inference(avatar_split_clause,[],[f6010,f5945,f4619,f4614,f4561,f7339]) ).
fof(f7345,plain,
( m1_filter_0(sK17,k1_lattice2(sK16))
| v3_struct_0(k1_lattice2(sK16))
| ~ v10_lattices(k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| ~ spl157_9 ),
inference(resolution,[],[f7341,f3724]) ).
fof(f7353,plain,
( m1_filter_0(sK17,k1_lattice2(sK16))
| ~ v10_lattices(k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_9 ),
inference(forward_subsumption_resolution,[],[f7345,f5251]) ).
fof(f7358,plain,
( m1_filter_0(sK17,k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_9 ),
inference(forward_subsumption_resolution,[],[f7353,f5609]) ).
fof(f7361,plain,
( m1_filter_0(sK17,k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_9 ),
inference(forward_subsumption_resolution,[],[f7358,f6240]) ).
fof(f8015,definition,
( spl157_17
<=> m1_filter_0(sK17,k1_lattice2(sK16)) ),
introduced(definition,[new_symbols(definition,[spl157_17])],[avatar_definition]) ).
fof(f8017,plain,
( m1_filter_0(sK17,k1_lattice2(sK16))
| ~ spl157_17 ),
inference(avatar_component_clause,[],[f8015]) ).
fof(f8018,plain,
( spl157_17
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_9 ),
inference(avatar_split_clause,[],[f7361,f7339,f4619,f4614,f4561,f8015]) ).
fof(f8431,plain,
( r2_hidden(k6_lattices(k1_lattice2(sK16)),sK17)
| v3_struct_0(k1_lattice2(sK16))
| ~ v10_lattices(k1_lattice2(sK16))
| ~ v14_lattices(k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| ~ spl157_17 ),
inference(resolution,[],[f8017,f4555]) ).
fof(f8436,plain,
( r2_hidden(k6_lattices(k1_lattice2(sK16)),sK17)
| ~ v10_lattices(k1_lattice2(sK16))
| ~ v14_lattices(k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_17 ),
inference(forward_subsumption_resolution,[],[f8431,f5251]) ).
fof(f8470,plain,
( r2_hidden(k6_lattices(k1_lattice2(sK16)),sK17)
| ~ v14_lattices(k1_lattice2(sK16))
| ~ l3_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_17 ),
inference(forward_subsumption_resolution,[],[f8436,f5609]) ).
fof(f8502,plain,
( r2_hidden(k6_lattices(k1_lattice2(sK16)),sK17)
| ~ l3_lattices(k1_lattice2(sK16))
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(forward_subsumption_resolution,[],[f8470,f5849]) ).
fof(f8534,plain,
( r2_hidden(k6_lattices(k1_lattice2(sK16)),sK17)
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(forward_subsumption_resolution,[],[f8502,f6240]) ).
fof(f8552,plain,
( r2_hidden(k5_lattices(sK16),sK17)
| spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(forward_demodulation,[],[f8534,f5848]) ).
fof(f8561,plain,
( $false
| spl157_1
| spl157_2
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(forward_subsumption_resolution,[],[f8552,f4568]) ).
fof(f8562,plain,
( spl157_1
| spl157_2
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(avatar_contradiction_clause,[],[f8561]) ).
cnf(s1,plain,
~ spl157_1,
inference(sat_conversion,[],[f4564]) ).
cnf(s2,plain,
~ spl157_2,
inference(sat_conversion,[],[f4569]) ).
cnf(s3,plain,
spl157_3,
inference(sat_conversion,[],[f4617]) ).
cnf(s4,plain,
spl157_4,
inference(sat_conversion,[],[f4622]) ).
cnf(s5,plain,
spl157_5,
inference(sat_conversion,[],[f4627]) ).
cnf(s6,plain,
spl157_6,
inference(sat_conversion,[],[f5948]) ).
cnf(s9,plain,
( spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_6
| spl157_9 ),
inference(sat_conversion,[],[f7342]) ).
cnf(s17,plain,
( spl157_1
| ~ spl157_3
| ~ spl157_4
| ~ spl157_9
| spl157_17 ),
inference(sat_conversion,[],[f8018]) ).
cnf(s20,plain,
( spl157_1
| spl157_2
| ~ spl157_3
| ~ spl157_4
| ~ spl157_5
| ~ spl157_17 ),
inference(sat_conversion,[],[f8562]) ).
cnf(s21,plain,
~ spl157_17,
inference(rat,[],[s20,s2,s5,s4,s3,s1]) ).
cnf(s24,plain,
~ spl157_9,
inference(rat,[],[s17,s21,s3,s4,s1]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s9,s3,s6,s4,s24,s1]) ).
fof(f8578,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT301+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n017.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 14:17:53 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 7.47/2.07 % (2608413)Detected formulas, will run a generic FOF schedule.
% 7.47/2.07 % (2608420)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=2124139640:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 7.47/2.07 % (2608423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3508835043:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 7.47/2.07 % (2608422)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2282754698:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 7.47/2.07 % (2608418)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=3338509361:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 7.47/2.07 % (2608421)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1746559581:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 7.47/2.07 % (2608424)dis-21_1_sil=8000:lcm=predicate:random_seed=2604305908:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 7.47/2.07 % (2608419)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=2322448978:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 7.47/2.07 % (2608421)Refutation not found, incomplete strategy
% 7.47/2.07 % (2608421)------------------------------
% 7.47/2.07 % (2608421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608421)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608421)Termination reason: Refutation not found, incomplete strategy
% 7.47/2.07 % (2608421)Time elapsed: 0.015 s
% 7.47/2.07 % (2608421)Peak memory usage: 91 MB
% 7.47/2.07 % (2608421)Instructions burned: 18 (million)
% 7.47/2.07 % (2608424)Instruction limit reached!
% 7.47/2.07 % (2608424)------------------------------
% 7.47/2.07 % (2608424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608424)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608424)Termination reason: Instruction limit
% 7.47/2.07 % (2608424)Termination phase: Function definition elimination
% 7.47/2.07 % (2608424)Time elapsed: 0.076 s
% 7.47/2.07 % (2608424)Peak memory usage: 93 MB
% 7.47/2.07 % (2608424)Instructions burned: 130 (million)
% 7.47/2.07 % (2608422)Instruction limit reached!
% 7.47/2.07 % (2608422)------------------------------
% 7.47/2.07 % (2608422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608422)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608422)Termination reason: Instruction limit
% 7.47/2.07 % (2608422)Termination phase: Saturation
% 7.47/2.07 % (2608422)Time elapsed: 0.080 s
% 7.47/2.07 % (2608422)Peak memory usage: 91 MB
% 7.47/2.07 % (2608422)Instructions burned: 119 (million)
% 7.47/2.07 % (2608423)Instruction limit reached!
% 7.47/2.07 % (2608423)------------------------------
% 7.47/2.07 % (2608423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608423)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608423)Termination reason: Instruction limit
% 7.47/2.07 % (2608423)Termination phase: Property scanning
% 7.47/2.07 % (2608423)Time elapsed: 0.087 s
% 7.47/2.07 % (2608423)Peak memory usage: 94 MB
% 7.47/2.07 % (2608423)Instructions burned: 141 (million)
% 7.47/2.07 % (2608432)lrs+10_1_sil=8000:sp=occurrence:random_seed=775356976:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 7.47/2.07 % (2608433)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2215714171:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 7.47/2.07 % (2608434)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3674026691:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 7.47/2.07 % (2608421)------------------------------
% 7.47/2.07 % (2608421)------------------------------
% 7.47/2.07 % (2608433)Refutation not found, incomplete strategy
% 7.47/2.07 % (2608433)------------------------------
% 7.47/2.07 % (2608433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608433)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608433)Termination reason: Refutation not found, incomplete strategy
% 7.47/2.07 % (2608433)Time elapsed: 0.032 s
% 7.47/2.07 % (2608433)Peak memory usage: 92 MB
% 7.47/2.07 % (2608433)Instructions burned: 57 (million)
% 7.47/2.07 % (2608432)Instruction limit reached!
% 7.47/2.07 % (2608432)------------------------------
% 7.47/2.07 % (2608432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608432)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608432)Termination reason: Instruction limit
% 7.47/2.07 % (2608432)Termination phase: Saturation
% 7.47/2.07 % (2608432)Time elapsed: 0.173 s
% 7.47/2.07 % (2608432)Peak memory usage: 94 MB
% 7.47/2.07 % (2608432)Instructions burned: 286 (million)
% 7.47/2.07 % (2608438)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2248906796:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 7.47/2.07 % (2608434)Instruction limit reached!
% 7.47/2.07 % (2608434)------------------------------
% 7.47/2.07 % (2608434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608434)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608434)Termination reason: Instruction limit
% 7.47/2.07 % (2608434)Termination phase: Saturation
% 7.47/2.07 % (2608434)Time elapsed: 0.221 s
% 7.47/2.07 % (2608434)Peak memory usage: 94 MB
% 7.47/2.07 % (2608434)Instructions burned: 326 (million)
% 7.47/2.07 % (2608433)------------------------------
% 7.47/2.07 % (2608433)------------------------------
% 7.47/2.07 % (2608439)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2820339541:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 7.47/2.07 % (2608438)Instruction limit reached!
% 7.47/2.07 % (2608438)------------------------------
% 7.47/2.07 % (2608438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608438)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608438)Termination reason: Instruction limit
% 7.47/2.07 % (2608438)Termination phase: Saturation
% 7.47/2.07 % (2608438)Time elapsed: 0.143 s
% 7.47/2.07 % (2608438)Peak memory usage: 97 MB
% 7.47/2.07 % (2608438)Instructions burned: 248 (million)
% 7.47/2.07 % (2608441)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1916613032:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 7.47/2.07 % (2608439)Refutation not found, incomplete strategy
% 7.47/2.07 % (2608439)------------------------------
% 7.47/2.07 % (2608439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608439)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608439)Termination reason: Refutation not found, incomplete strategy
% 7.47/2.07 % (2608439)Time elapsed: 0.076 s
% 7.47/2.07 % (2608439)Peak memory usage: 94 MB
% 7.47/2.07 % (2608439)Instructions burned: 131 (million)
% 7.47/2.07 % (2608442)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=242561486:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 7.47/2.07 % (2608442)Instruction limit reached!
% 7.47/2.07 % (2608442)------------------------------
% 7.47/2.07 % (2608442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.07 % (2608442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.07 % (2608442)CaDiCaL version: 2.1.3
% 7.47/2.07 % (2608442)Termination reason: Instruction limit
% 7.47/2.07 % (2608442)Termination phase: Saturation
% 7.47/2.07 % (2608442)Time elapsed: 0.065 s
% 7.47/2.07 % (2608442)Peak memory usage: 93 MB
% 7.47/2.07 % (2608442)Instructions burned: 114 (million)
% 7.47/2.07 % (2608444)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2944217458:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 7.47/2.07 % (2608420)First to succeed.
% 7.47/2.07 % (2608420)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2608413"
% 7.47/2.07 % (2608444)Instruction limit reached!
% 7.47/2.07 % (2608444)------------------------------
% 7.47/2.08 % (2608444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.47/2.08 % (2608444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.47/2.08 % (2608444)CaDiCaL version: 2.1.3
% 7.47/2.08 % (2608444)Termination reason: Instruction limit
% 7.47/2.08 % (2608444)Termination phase: Property scanning
% 7.47/2.08 % (2608444)Time elapsed: 0.079 s
% 7.47/2.08 % (2608444)Peak memory usage: 94 MB
% 7.47/2.08 % (2608444)Instructions burned: 129 (million)
% 7.47/2.08 % (2608439)------------------------------
% 7.47/2.08 % (2608439)------------------------------
% 7.47/2.08 % (2608447)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1040801735:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 7.47/2.08 % (2608420)Refutation found. Thanks to Tanya!
% 7.47/2.08 % SZS status Theorem for theBenchmark
% 7.47/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 8.34/2.24 % (2608420)------------------------------
% 8.34/2.24 % (2608420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.34/2.24 % (2608420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.34/2.24 % (2608420)CaDiCaL version: 2.1.3
% 8.34/2.24 % (2608420)Termination reason: Refutation
% 8.34/2.24 % (2608420)Time elapsed: 0.787 s
% 8.34/2.24 % (2608420)Peak memory usage: 143 MB
% 8.34/2.24 % (2608420)Instructions burned: 1766 (million)
% 8.34/2.24 % (2608420)------------------------------
% 8.34/2.24 % (2608420)------------------------------
% 8.34/2.24 % (2608413)Success in time 1.194 s
% 8.34/2.24 % Vampire exiting
%------------------------------------------------------------------------------