%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT327+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 : n020.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 11:46:58 AM UTC 2026
% Result : Theorem 1.70s 1.31s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 119 ( 21 unt; 9 def)
% Number of atoms : 485 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 642 ( 276 ~; 280 |; 58 &)
% ( 12 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 10 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 81 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X1,k22_filter_2(X0,X1,X2))
& r2_hidden(X2,k22_filter_2(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X1,k22_filter_2(X0,X1,X2))
& r2_hidden(X2,k22_filter_2(X0,X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v6_lattices(X0)
& v8_lattices(X0)
& v9_lattices(X0)
& l3_lattices(X0)
& m1_subset_1(X1,u1_struct_0(X0))
& m1_subset_1(X2,u1_struct_0(X0)) )
=> r3_lattices(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(f41,axiom,
! [X0] :
( l3_lattices(X0)
=> ( ( ~ v3_struct_0(X0)
& v10_lattices(X0) )
=> ( ~ v3_struct_0(X0)
& v4_lattices(X0)
& v5_lattices(X0)
& v6_lattices(X0)
& v7_lattices(X0)
& v8_lattices(X0)
& v9_lattices(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f44,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X1,X3)
& r3_lattices(X0,X3,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ r2_hidden(X1,k22_filter_2(X0,X1,X2))
| ~ r2_hidden(X2,k22_filter_2(X0,X1,X2)) )
& r3_lattices(X0,X1,X2)
& m1_subset_1(X2,u1_struct_0(X0)) )
& m1_subset_1(X1,u1_struct_0(X0)) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ r2_hidden(X1,k22_filter_2(X0,X1,X2))
| ~ r2_hidden(X2,k22_filter_2(X0,X1,X2)) )
& r3_lattices(X0,X1,X2)
& m1_subset_1(X2,u1_struct_0(X0)) )
& m1_subset_1(X1,u1_struct_0(X0)) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(flattening,[],[f48]) ).
fof(f74,plain,
! [X0,X1,X2] :
( r3_lattices(X0,X1,X1)
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f75,plain,
! [X0,X1,X2] :
( r3_lattices(X0,X1,X1)
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(flattening,[],[f74]) ).
fof(f81,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v4_lattices(X0)
& v5_lattices(X0)
& v6_lattices(X0)
& v7_lattices(X0)
& v8_lattices(X0)
& v9_lattices(X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v4_lattices(X0)
& v5_lattices(X0)
& v6_lattices(X0)
& v7_lattices(X0)
& v8_lattices(X0)
& v9_lattices(X0) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f81]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X1,X3)
& r3_lattices(X0,X3,X2) ) )
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X1,X3)
& r3_lattices(X0,X3,X2) ) )
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
( ( ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2))
| ~ r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2)) )
& r3_lattices(sK0,sK1,sK2)
& m1_subset_1(sK2,u1_struct_0(sK0))
& m1_subset_1(sK1,u1_struct_0(sK0))
& ~ v3_struct_0(sK0)
& v10_lattices(sK0)
& l3_lattices(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X3,X2) )
& ( ( r3_lattices(X0,X1,X3)
& r3_lattices(X0,X3,X2) )
| ~ r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) )
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X3,X2) )
& ( ( r3_lattices(X0,X1,X3)
& r3_lattices(X0,X3,X2) )
| ~ r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) )
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f105,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f106,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f107,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f87]) ).
fof(f109,plain,
r3_lattices(sK0,sK1,sK2),
inference(cnf_transformation,[],[f87]) ).
fof(f110,plain,
( ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2))
| ~ r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f143,plain,
! [X2,X0,X1] :
( r3_lattices(X0,X1,X1)
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f152,plain,
! [X0] :
( v9_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f153,plain,
! [X0] :
( v8_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f155,plain,
! [X0] :
( v6_lattices(X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ v10_lattices(X0)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f165,definition,
( spl16_1
<=> r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f169,definition,
( spl16_2
<=> r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f171,plain,
( ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2))
| spl16_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f110,f169,f165]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ r3_lattices(sK0,X0,X1)
| ~ r3_lattices(sK0,X1,X2)
| ~ r3_lattices(sK0,X0,X2)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| v3_struct_0(sK0)
| r2_hidden(X1,k22_filter_2(sK0,X0,X2))
| ~ l3_lattices(sK0) ),
inference(resolution,[],[f163,f105]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ r3_lattices(sK0,X0,X1)
| ~ r3_lattices(sK0,X1,X2)
| ~ r3_lattices(sK0,X0,X2)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(X1,k22_filter_2(sK0,X0,X2))
| ~ l3_lattices(sK0) ),
inference(forward_subsumption_resolution,[],[f240,f106]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r3_lattices(sK0,X0,X2)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(X1,k22_filter_2(sK0,X0,X2)) ),
inference(forward_subsumption_resolution,[],[f241,f104]) ).
fof(f244,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,sK2)
| ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| r2_hidden(X0,k22_filter_2(sK0,X1,sK2)) ),
inference(resolution,[],[f242,f108]) ).
fof(f269,definition,
( spl16_9
<=> ! [X0] :
( ~ r3_lattices(sK0,X0,sK2)
| r2_hidden(sK2,k22_filter_2(sK0,X0,sK2))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
fof(f270,plain,
( ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(sK2,k22_filter_2(sK0,X0,sK2))
| ~ r3_lattices(sK0,X0,sK2) )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,definition,
( spl16_10
<=> r3_lattices(sK0,sK2,sK2) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
fof(f274,plain,
( ~ r3_lattices(sK0,sK2,sK2)
| spl16_10 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f280,definition,
( spl16_12
<=> r3_lattices(sK0,sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
fof(f281,plain,
( r3_lattices(sK0,sK1,sK1)
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( ~ r3_lattices(sK0,sK1,sK1)
| spl16_12 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f314,definition,
( spl16_13
<=> v9_lattices(sK0) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
fof(f315,plain,
( v9_lattices(sK0)
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( ~ v9_lattices(sK0)
| spl16_13 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f318,definition,
( spl16_14
<=> v8_lattices(sK0) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
fof(f319,plain,
( v8_lattices(sK0)
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f320,plain,
( ~ v8_lattices(sK0)
| spl16_14 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f322,definition,
( spl16_15
<=> v6_lattices(sK0) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
fof(f323,plain,
( v6_lattices(sK0)
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f324,plain,
( ~ v6_lattices(sK0)
| spl16_15 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f333,definition,
( spl16_17
<=> ! [X0] : ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
fof(f334,plain,
( ! [X0] : ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f358,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_13 ),
inference(resolution,[],[f316,f152]) ).
fof(f359,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_13 ),
inference(forward_subsumption_resolution,[],[f358,f106]) ).
fof(f360,plain,
( ~ l3_lattices(sK0)
| spl16_13 ),
inference(forward_subsumption_resolution,[],[f359,f105]) ).
fof(f361,plain,
( $false
| spl16_13 ),
inference(forward_subsumption_resolution,[],[f360,f104]) ).
fof(f362,plain,
spl16_13,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f388,plain,
! [X0] :
( ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,sK2,sK2)
| ~ r3_lattices(sK0,X0,sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(sK2,k22_filter_2(sK0,X0,sK2)) ),
inference(resolution,[],[f244,f108]) ).
fof(f390,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,X0,X0)
| r2_hidden(X0,k22_filter_2(sK0,X0,sK2)) ),
inference(factoring,[],[f244]) ).
fof(f391,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,X0,X0)
| r2_hidden(X0,k22_filter_2(sK0,X0,sK2)) ),
inference(duplicate_literal_removal,[],[f390]) ).
fof(f392,plain,
! [X0] :
( ~ r3_lattices(sK0,X0,sK2)
| ~ r3_lattices(sK0,sK2,sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(sK2,k22_filter_2(sK0,X0,sK2)) ),
inference(duplicate_literal_removal,[],[f388]) ).
fof(f402,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_14 ),
inference(resolution,[],[f320,f153]) ).
fof(f403,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_14 ),
inference(forward_subsumption_resolution,[],[f402,f106]) ).
fof(f404,plain,
( ~ l3_lattices(sK0)
| spl16_14 ),
inference(forward_subsumption_resolution,[],[f403,f105]) ).
fof(f405,plain,
( $false
| spl16_14 ),
inference(forward_subsumption_resolution,[],[f404,f104]) ).
fof(f406,plain,
spl16_14,
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f443,plain,
( v3_struct_0(sK0)
| ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(resolution,[],[f324,f155]) ).
fof(f444,plain,
( ~ v10_lattices(sK0)
| ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f443,f106]) ).
fof(f445,plain,
( ~ l3_lattices(sK0)
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f444,f105]) ).
fof(f446,plain,
( $false
| spl16_15 ),
inference(forward_subsumption_resolution,[],[f445,f104]) ).
fof(f447,plain,
spl16_15,
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f448,plain,
( ~ spl16_10
| spl16_9 ),
inference(avatar_split_clause,[],[f392,f269,f272]) ).
fof(f468,plain,
( ! [X0] :
( v3_struct_0(sK0)
| ~ v6_lattices(sK0)
| ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10 ),
inference(resolution,[],[f274,f143]) ).
fof(f478,plain,
( ! [X0] :
( ~ v6_lattices(sK0)
| ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10 ),
inference(forward_subsumption_resolution,[],[f468,f106]) ).
fof(f482,plain,
( ! [X0] :
( ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f478,f323]) ).
fof(f486,plain,
( ! [X0] :
( ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f482,f319]) ).
fof(f490,plain,
( ! [X0] :
( ~ l3_lattices(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f486,f315]) ).
fof(f492,plain,
( ! [X0] :
( ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f490,f104]) ).
fof(f494,plain,
( ! [X0] : ~ m1_subset_1(X0,u1_struct_0(sK0))
| spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f492,f108]) ).
fof(f496,plain,
( spl16_17
| spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(avatar_split_clause,[],[f494,f322,f318,f314,f272,f333]) ).
fof(f497,plain,
( ! [X0] :
( v3_struct_0(sK0)
| ~ v6_lattices(sK0)
| ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12 ),
inference(resolution,[],[f282,f143]) ).
fof(f507,plain,
( ! [X0] :
( ~ v6_lattices(sK0)
| ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12 ),
inference(forward_subsumption_resolution,[],[f497,f106]) ).
fof(f511,plain,
( ! [X0] :
( ~ v8_lattices(sK0)
| ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f507,f323]) ).
fof(f515,plain,
( ! [X0] :
( ~ v9_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f511,f319]) ).
fof(f519,plain,
( ! [X0] :
( ~ l3_lattices(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f515,f315]) ).
fof(f521,plain,
( ! [X0] :
( ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) )
| spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f519,f104]) ).
fof(f523,plain,
( ! [X0] : ~ m1_subset_1(X0,u1_struct_0(sK0))
| spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(forward_subsumption_resolution,[],[f521,f107]) ).
fof(f524,plain,
( spl16_17
| spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(avatar_split_clause,[],[f523,f322,f318,f314,f280,f333]) ).
fof(f550,plain,
( $false
| ~ spl16_17 ),
inference(resolution,[],[f334,f107]) ).
fof(f555,plain,
~ spl16_17,
inference(avatar_contradiction_clause,[],[f550]) ).
fof(f781,plain,
( r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2))
| ~ r3_lattices(sK0,sK1,sK2)
| ~ spl16_9 ),
inference(resolution,[],[f270,f107]) ).
fof(f800,plain,
( r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2))
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f781,f109]) ).
fof(f801,plain,
( spl16_1
| ~ spl16_9 ),
inference(avatar_split_clause,[],[f800,f269,f165]) ).
fof(f1035,plain,
( ~ r3_lattices(sK0,sK1,sK2)
| ~ r3_lattices(sK0,sK1,sK1)
| r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ),
inference(resolution,[],[f391,f107]) ).
fof(f1041,plain,
( ~ r3_lattices(sK0,sK1,sK1)
| r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ),
inference(forward_subsumption_resolution,[],[f1035,f109]) ).
fof(f1042,plain,
( r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2))
| ~ spl16_12 ),
inference(forward_subsumption_resolution,[],[f1041,f281]) ).
fof(f1043,plain,
( $false
| spl16_2
| ~ spl16_12 ),
inference(forward_subsumption_resolution,[],[f1042,f171]) ).
fof(f1044,plain,
( spl16_2
| ~ spl16_12 ),
inference(avatar_contradiction_clause,[],[f1043]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
spl16_13,
inference(sat_conversion,[],[f362]) ).
cnf(s15,plain,
spl16_14,
inference(sat_conversion,[],[f406]) ).
cnf(s21,plain,
spl16_15,
inference(sat_conversion,[],[f447]) ).
cnf(s22,plain,
( spl16_9
| ~ spl16_10 ),
inference(sat_conversion,[],[f448]) ).
cnf(s26,plain,
( spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15
| spl16_17 ),
inference(sat_conversion,[],[f496]) ).
cnf(s27,plain,
( spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15
| spl16_17 ),
inference(sat_conversion,[],[f524]) ).
cnf(s30,plain,
~ spl16_17,
inference(sat_conversion,[],[f555]) ).
cnf(s48,plain,
( spl16_1
| ~ spl16_9 ),
inference(sat_conversion,[],[f801]) ).
cnf(s60,plain,
( spl16_2
| ~ spl16_12 ),
inference(sat_conversion,[],[f1044]) ).
cnf(s62,plain,
( spl16_12
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(rat,[],[s27,s30]) ).
cnf(s63,plain,
( spl16_10
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(rat,[],[s26,s30]) ).
cnf(s65,plain,
spl16_12,
inference(rat,[],[s62,s21,s15,s10]) ).
cnf(s66,plain,
spl16_10,
inference(rat,[],[s63,s21,s15,s10]) ).
cnf(s69,plain,
spl16_2,
inference(rat,[],[s60,s65]) ).
cnf(s74,plain,
spl16_9,
inference(rat,[],[s22,s66]) ).
cnf(s75,plain,
spl16_1,
inference(rat,[],[s48,s74]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s1,s69,s75]) ).
fof(f1045,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 14:40:32 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 1.70/1.31 % (3450614)Detected formulas, will run a generic FOF schedule.
% 1.70/1.31 % (3450622)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=215555590:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.70/1.31 % (3450622)Refutation not found, incomplete strategy
% 1.70/1.31 % (3450622)------------------------------
% 1.70/1.31 % (3450622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.70/1.31 % (3450622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/1.31 % (3450622)CaDiCaL version: 2.1.3
% 1.70/1.31 % (3450622)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.31 % (3450622)Time elapsed: 0.001 s
% 1.70/1.31 % (3450622)Peak memory usage: 88 MB
% 1.70/1.31 % (3450622)Instructions burned: 2 (million)
% 1.70/1.31 % (3450621)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=1237683341:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.70/1.31 % (3450619)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=2864369780:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.70/1.31 % (3450620)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=3577424039:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.70/1.31 % (3450625)dis-21_1_sil=8000:lcm=predicate:random_seed=1937953522: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)
% 1.70/1.31 % (3450623)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3362718613:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.70/1.31 % (3450624)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2963511556:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.70/1.31 % (3450624)First to succeed.
% 1.70/1.31 % (3450624)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3450614"
% 1.70/1.31 % (3450623)Instruction limit reached!
% 1.70/1.31 % (3450623)------------------------------
% 1.70/1.31 % (3450623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.70/1.31 % (3450623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/1.31 % (3450623)CaDiCaL version: 2.1.3
% 1.70/1.31 % (3450623)Termination reason: Instruction limit
% 1.70/1.31 % (3450623)Termination phase: Saturation
% 1.70/1.31 % (3450623)Time elapsed: 0.067 s
% 1.70/1.31 % (3450623)Peak memory usage: 88 MB
% 1.70/1.31 % (3450623)Instructions burned: 121 (million)
% 1.70/1.31 % (3450625)Instruction limit reached!
% 1.70/1.31 % (3450625)------------------------------
% 1.70/1.31 % (3450625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.70/1.31 % (3450625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/1.31 % (3450625)CaDiCaL version: 2.1.3
% 1.70/1.31 % (3450625)Termination reason: Instruction limit
% 1.70/1.31 % (3450625)Termination phase: Saturation
% 1.70/1.31 % (3450625)Time elapsed: 0.075 s
% 1.70/1.31 % (3450625)Peak memory usage: 90 MB
% 1.70/1.31 % (3450625)Instructions burned: 129 (million)
% 1.70/1.31 % (3450622)------------------------------
% 1.70/1.31 % (3450622)------------------------------
% 1.70/1.31 % (3450634)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3913608212:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.70/1.31 % (3450635)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1728251538:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.70/1.31 % (3450633)lrs+10_1_sil=8000:sp=occurrence:random_seed=4209151212:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.70/1.31 % (3450634)Also succeeded, but the first one will report.
% 1.70/1.31 % (3450635)Also succeeded, but the first one will report.
% 1.70/1.31 % (3450633)Also succeeded, but the first one will report.
% 1.70/1.31 % (3450624)Refutation found. Thanks to Tanya!
% 1.70/1.31 % SZS status Theorem for theBenchmark
% 1.70/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.51 % (3450624)------------------------------
% 0.15/1.51 % (3450624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (3450624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (3450624)CaDiCaL version: 2.1.3
% 0.15/1.51 % (3450624)Termination reason: Refutation
% 0.15/1.51 % (3450624)Time elapsed: 0.022 s
% 0.15/1.51 % (3450624)Peak memory usage: 90 MB
% 0.15/1.51 % (3450624)Instructions burned: 30 (million)
% 0.15/1.51 % (3450624)------------------------------
% 0.15/1.51 % (3450624)------------------------------
% 0.15/1.51 % (3450614)Success in time 0.444 s
% 0.15/1.51 % Vampire exiting
%------------------------------------------------------------------------------