%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:21 AM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 150 ( 29 unt; 8 def)
% Number of atoms : 528 ( 9 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 616 ( 238 ~; 295 |; 50 &)
% ( 11 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 120 ( 1 sgn 112 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( ( r1_tarski(X2,X3)
=> r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) )
& r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( ( r1_tarski(X2,X3)
=> r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3)) )
& r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ! [X2] :
( m2_filter_2(X2,X0)
=> ( X2 = k19_filter_2(X0,X1)
<=> ( r1_tarski(X1,X2)
& ! [X3] :
( m2_filter_2(X3,X0)
=> ( r1_tarski(X1,X3)
=> r1_tarski(X2,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_2) ).
fof(f8,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0)
& ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> m2_filter_2(k19_filter_2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).
fof(f16,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(f17,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(f28,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f36,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( r1_tarski(X0,X1)
& r1_tarski(X1,X2) )
=> r1_tarski(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f43,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f46,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f36]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3))
& r1_tarski(X2,X3) )
| ~ r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1)) )
& ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ r1_tarski(k19_filter_2(X0,X2),k19_filter_2(X0,X3))
& r1_tarski(X2,X3) )
| ~ r1_tarski(k19_filter_2(X0,k19_filter_2(X0,X1)),k19_filter_2(X0,X1)) )
& ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v10_lattices(X0)
& l3_lattices(X0) ),
inference(flattening,[],[f48]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k19_filter_2(X0,X1)
<=> ( r1_tarski(X1,X2)
& ! [X3] :
( r1_tarski(X2,X3)
| ~ r1_tarski(X1,X3)
| ~ m2_filter_2(X3,X0) ) ) )
| ~ m2_filter_2(X2,X0) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = k19_filter_2(X0,X1)
<=> ( r1_tarski(X1,X2)
& ! [X3] :
( r1_tarski(X2,X3)
| ~ r1_tarski(X1,X3)
| ~ m2_filter_2(X3,X0) ) ) )
| ~ m2_filter_2(X2,X0) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( m2_filter_2(k19_filter_2(X0,X1),X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( m2_filter_2(k19_filter_2(X0,X1),X0)
| v3_struct_0(X0)
| ~ v10_lattices(X0)
| ~ l3_lattices(X0)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f57]) ).
fof(f62,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,[],[f16]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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,[],[f17]) ).
fof(f65,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,[],[f64]) ).
fof(f78,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(flattening,[],[f78]) ).
fof(f85,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f88,plain,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| r1_tarski(sK2,sK3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f89,plain,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f90,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f49]) ).
fof(f91,plain,
~ v1_xboole_0(sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f49]) ).
fof(f93,plain,
~ v1_xboole_0(sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f94,plain,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f49]) ).
fof(f95,plain,
~ v1_xboole_0(sK1),
inference(cnf_transformation,[],[f49]) ).
fof(f96,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f97,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f98,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ m2_filter_2(X2,X0)
| ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(X2,X3)
| k19_filter_2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f56]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ m2_filter_2(X2,X0)
| r1_tarski(X1,X2)
| k19_filter_2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f56]) ).
fof(f112,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f117,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| m2_lattice4(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f118,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f119,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f129,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f28]) ).
fof(f142,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1)
| r1_tarski(X0,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f150,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f85]) ).
fof(f153,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| r1_tarski(X1,k19_filter_2(X0,X1)) ),
inference(equality_resolution,[],[f111]) ).
fof(f154,plain,
! [X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ m2_filter_2(X3,X0)
| ~ r1_tarski(X1,X3)
| r1_tarski(k19_filter_2(X0,X1),X3) ),
inference(equality_resolution,[],[f110]) ).
fof(f155,plain,
~ v10_lattices(sK0),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f156,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f157,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(sK2,sK3) ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f165,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ r1_tarski(X1,k19_filter_2(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f153]) ).
fof(f166,plain,
! [X3,X0,X1] :
( ~ l3_lattices(X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| m2_filter_2(k19_filter_2(X0,X1),X0)
| m2_filter_2(X3,X0)
| r1_tarski(X1,X3)
| ~ r1_tarski(k19_filter_2(X0,X1),X3) ),
inference(consistent_polarity_flipping,[],[f154]) ).
fof(f170,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f173,plain,
! [X0,X1] :
( m2_filter_2(X1,X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(X1) ),
inference(consistent_polarity_flipping,[],[f118]) ).
fof(f174,plain,
! [X0,X1] :
( ~ m2_lattice4(X1,X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(X1,X0)
| ~ l3_lattices(X0) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f175,plain,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v10_lattices(X0)
| v3_struct_0(X0)
| m2_lattice4(X1,X0)
| ~ l3_lattices(X0) ),
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f181,plain,
! [X0] : ~ r1_tarski(X0,X0),
inference(consistent_polarity_flipping,[],[f142]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ r1_tarski(X0,X2)
| r1_tarski(X0,X1)
| r1_tarski(X1,X2) ),
inference(consistent_polarity_flipping,[],[f144]) ).
fof(f186,definition,
( spl19_1
<=> r1_tarski(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f188,plain,
( ~ r1_tarski(sK2,sK3)
| spl19_1 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl19_2
<=> r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f192,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( ~ spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f157,f190,f186]) ).
fof(f195,definition,
( spl19_3
<=> r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f197,plain,
( r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl19_3
| spl19_2 ),
inference(avatar_split_clause,[],[f156,f190,f195]) ).
fof(f248,definition,
( spl19_4
<=> v1_xboole_0(k19_filter_2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f249,plain,
( ~ v1_xboole_0(k19_filter_2(sK0,sK1))
| spl19_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( v1_xboole_0(k19_filter_2(sK0,sK1))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f258,plain,
( k1_xboole_0 = k19_filter_2(sK0,sK1)
| ~ spl19_4 ),
inference(resolution,[],[f250,f150]) ).
fof(f269,plain,
! [X0] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v10_lattices(sK0)
| v3_struct_0(sK0)
| ~ m2_filter_2(k19_filter_2(sK0,X0),sK0) ),
inference(resolution,[],[f170,f96]) ).
fof(f283,plain,
! [X0] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ m2_filter_2(k19_filter_2(sK0,X0),sK0) ),
inference(forward_subsumption_resolution,[],[f269,f155]) ).
fof(f284,plain,
! [X0] :
( ~ m2_filter_2(k19_filter_2(sK0,X0),sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(X0) ),
inference(forward_subsumption_resolution,[],[f283,f98]) ).
fof(f290,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ r1_tarski(X1,k19_filter_2(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f165,f170]) ).
fof(f291,plain,
! [X0] :
( v10_lattices(sK0)
| v3_struct_0(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(X0)
| ~ r1_tarski(X0,k19_filter_2(sK0,X0)) ),
inference(resolution,[],[f290,f96]) ).
fof(f297,plain,
! [X0] :
( v3_struct_0(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(X0)
| ~ r1_tarski(X0,k19_filter_2(sK0,X0)) ),
inference(forward_subsumption_resolution,[],[f291,f155]) ).
fof(f298,plain,
! [X0] :
( ~ r1_tarski(X0,k19_filter_2(sK0,X0))
| v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f297,f98]) ).
fof(f299,plain,
! [X3,X0,X1] :
( ~ l3_lattices(X0)
| v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| m2_filter_2(X3,X0)
| r1_tarski(X1,X3)
| ~ r1_tarski(k19_filter_2(X0,X1),X3) ),
inference(forward_subsumption_resolution,[],[f166,f170]) ).
fof(f302,plain,
! [X0,X1] :
( v10_lattices(sK0)
| v3_struct_0(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(X0)
| m2_filter_2(X1,sK0)
| r1_tarski(X0,X1)
| ~ r1_tarski(k19_filter_2(sK0,X0),X1) ),
inference(resolution,[],[f299,f96]) ).
fof(f308,plain,
! [X0,X1] :
( v3_struct_0(sK0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(X0)
| m2_filter_2(X1,sK0)
| r1_tarski(X0,X1)
| ~ r1_tarski(k19_filter_2(sK0,X0),X1) ),
inference(forward_subsumption_resolution,[],[f302,f155]) ).
fof(f309,plain,
! [X0,X1] :
( ~ r1_tarski(k19_filter_2(sK0,X0),X1)
| v1_xboole_0(X0)
| m2_filter_2(X1,sK0)
| r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(forward_subsumption_resolution,[],[f308,f98]) ).
fof(f341,plain,
( ~ m2_filter_2(k1_xboole_0,sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(sK1)
| ~ spl19_4 ),
inference(superposition,[],[f284,f258]) ).
fof(f342,plain,
( ~ m2_filter_2(k1_xboole_0,sK0)
| v1_xboole_0(sK1)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f341,f94]) ).
fof(f344,plain,
( ~ m2_filter_2(k1_xboole_0,sK0)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f342,f95]) ).
fof(f384,plain,
( v10_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| ~ v1_xboole_0(k1_xboole_0)
| ~ spl19_4 ),
inference(resolution,[],[f344,f173]) ).
fof(f385,plain,
( v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| ~ v1_xboole_0(k1_xboole_0)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f384,f155]) ).
fof(f386,plain,
( ~ l3_lattices(sK0)
| ~ v1_xboole_0(k1_xboole_0)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f385,f98]) ).
fof(f387,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f386,f96]) ).
fof(f388,plain,
( $false
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f387,f129]) ).
fof(f389,plain,
~ spl19_4,
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f398,plain,
( v1_xboole_0(sK2)
| m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| r1_tarski(sK2,k19_filter_2(sK0,sK3))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_3 ),
inference(resolution,[],[f309,f197]) ).
fof(f402,definition,
( spl19_17
<=> m2_filter_2(k19_filter_2(sK0,sK3),sK0) ),
introduced(definition,[new_symbols(definition,[spl19_17])],[avatar_definition]) ).
fof(f403,plain,
( ~ m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| spl19_17 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| ~ spl19_17 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f410,plain,
( m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| r1_tarski(sK2,k19_filter_2(sK0,sK3))
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f398,f93]) ).
fof(f412,plain,
( m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| r1_tarski(sK2,k19_filter_2(sK0,sK3))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f410,f92]) ).
fof(f414,definition,
( spl19_19
<=> r1_tarski(sK2,k19_filter_2(sK0,sK3)) ),
introduced(definition,[new_symbols(definition,[spl19_19])],[avatar_definition]) ).
fof(f416,plain,
( r1_tarski(sK2,k19_filter_2(sK0,sK3))
| ~ spl19_19 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f418,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(sK3)
| ~ spl19_17 ),
inference(resolution,[],[f404,f284]) ).
fof(f419,plain,
( v1_xboole_0(sK3)
| ~ spl19_17 ),
inference(forward_subsumption_resolution,[],[f418,f90]) ).
fof(f420,plain,
( $false
| ~ spl19_17 ),
inference(forward_subsumption_resolution,[],[f419,f91]) ).
fof(f421,plain,
~ spl19_17,
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f441,plain,
( v1_xboole_0(k19_filter_2(sK0,sK1))
| m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| r1_tarski(k19_filter_2(sK0,sK1),k19_filter_2(sK0,sK1))
| ~ m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_2 ),
inference(resolution,[],[f192,f309]) ).
fof(f444,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| r1_tarski(k19_filter_2(sK0,sK1),k19_filter_2(sK0,sK1))
| ~ m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_2
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f441,f249]) ).
fof(f445,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_2
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f444,f181]) ).
fof(f447,definition,
( spl19_24
<=> m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0))) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
fof(f448,plain,
( m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f449,plain,
( ~ m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0)))
| spl19_24 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f451,definition,
( spl19_25
<=> m2_filter_2(k19_filter_2(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition]) ).
fof(f453,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f471,plain,
( v10_lattices(sK0)
| v3_struct_0(sK0)
| m2_lattice4(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(resolution,[],[f449,f175]) ).
fof(f473,plain,
( v3_struct_0(sK0)
| m2_lattice4(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f471,f155]) ).
fof(f474,plain,
( m2_lattice4(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f473,f98]) ).
fof(f475,plain,
( m2_lattice4(k19_filter_2(sK0,sK1),sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f474,f96]) ).
fof(f488,plain,
( v10_lattices(sK0)
| v3_struct_0(sK0)
| m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(resolution,[],[f475,f174]) ).
fof(f489,plain,
( v3_struct_0(sK0)
| m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f488,f155]) ).
fof(f490,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ l3_lattices(sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f489,f98]) ).
fof(f491,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f490,f96]) ).
fof(f492,plain,
( spl19_25
| spl19_24 ),
inference(avatar_split_clause,[],[f491,f447,f451]) ).
fof(f493,plain,
( r1_tarski(sK2,k19_filter_2(sK0,sK3))
| ~ spl19_3
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f412,f403]) ).
fof(f495,plain,
( spl19_19
| ~ spl19_3
| spl19_17 ),
inference(avatar_split_clause,[],[f493,f402,f195,f414]) ).
fof(f504,plain,
( ! [X0] :
( r1_tarski(X0,k19_filter_2(sK0,sK3))
| r1_tarski(sK2,X0) )
| ~ spl19_19 ),
inference(resolution,[],[f416,f182]) ).
fof(f552,plain,
( r1_tarski(sK2,sK3)
| v1_xboole_0(sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ spl19_19 ),
inference(resolution,[],[f504,f298]) ).
fof(f558,plain,
( v1_xboole_0(sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
| spl19_1
| ~ spl19_19 ),
inference(forward_subsumption_resolution,[],[f552,f188]) ).
fof(f559,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
| spl19_1
| ~ spl19_19 ),
inference(forward_subsumption_resolution,[],[f558,f91]) ).
fof(f560,plain,
( $false
| spl19_1
| ~ spl19_19 ),
inference(forward_subsumption_resolution,[],[f559,f90]) ).
fof(f561,plain,
( spl19_1
| ~ spl19_19 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f567,plain,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| ~ spl19_2
| spl19_4
| ~ spl19_24 ),
inference(forward_subsumption_resolution,[],[f445,f448]) ).
fof(f572,plain,
( spl19_25
| ~ spl19_2
| spl19_4
| ~ spl19_24 ),
inference(avatar_split_clause,[],[f567,f447,f248,f190,f451]) ).
fof(f593,plain,
( ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(sK1)
| ~ spl19_25 ),
inference(resolution,[],[f453,f284]) ).
fof(f594,plain,
( v1_xboole_0(sK1)
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f593,f94]) ).
fof(f595,plain,
( $false
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f594,f95]) ).
fof(f596,plain,
~ spl19_25,
inference(avatar_contradiction_clause,[],[f595]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f193]) ).
cnf(s2,plain,
( spl19_2
| spl19_3 ),
inference(sat_conversion,[],[f198]) ).
cnf(s13,plain,
~ spl19_4,
inference(sat_conversion,[],[f389]) ).
cnf(s16,plain,
~ spl19_17,
inference(sat_conversion,[],[f421]) ).
cnf(s24,plain,
( spl19_24
| spl19_25 ),
inference(sat_conversion,[],[f492]) ).
cnf(s25,plain,
( ~ spl19_3
| spl19_17
| spl19_19 ),
inference(sat_conversion,[],[f495]) ).
cnf(s29,plain,
( spl19_1
| ~ spl19_19 ),
inference(sat_conversion,[],[f561]) ).
cnf(s36,plain,
( ~ spl19_2
| spl19_4
| ~ spl19_24
| spl19_25 ),
inference(sat_conversion,[],[f572]) ).
cnf(s44,plain,
~ spl19_25,
inference(sat_conversion,[],[f596]) ).
cnf(s45,plain,
( ~ spl19_2
| spl19_4
| ~ spl19_24 ),
inference(rat,[],[s36,s44]) ).
cnf(s46,plain,
spl19_24,
inference(rat,[],[s24,s44]) ).
cnf(s51,plain,
~ spl19_2,
inference(rat,[],[s45,s46,s13]) ).
cnf(s52,plain,
spl19_3,
inference(rat,[],[s2,s51]) ).
cnf(s54,plain,
spl19_19,
inference(rat,[],[s25,s16,s52]) ).
cnf(s55,plain,
spl19_1,
inference(rat,[],[s29,s54]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s1,s51,s55]) ).
fof(f597,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n016.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 14:33:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.48 % (2698454)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2698463)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3644058884:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (2698460)% WARNING: option uhcvi not known.
% 0.15/0.48 % (2698459)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3621669197_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (2698460)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2725936425:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2698464)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=629796885:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (2698461)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3630230828:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (2698462)dis+10_1_sil=32000:sp=arity:random_seed=2718179240:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (2698465)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1013834511:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % TRYING [5]
% 0.15/0.48 % (2698460) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2698454-2698460"...
% 0.15/0.48 % (2698462) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2698454-2698462"...
% 0.15/0.48 % (2698460)...printing done.
% 0.15/0.48 % (2698460)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2698460)------------------------------
% 0.15/0.48 % (2698460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2698460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2698460)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2698460)Termination reason: Refutation
% 0.15/0.48 % (2698460)Time elapsed: 0.017 s
% 0.15/0.48 % (2698460)Peak memory usage: 13 MB
% 0.15/0.48 % (2698460)Instructions burned: 23 (million)
% 0.15/0.48 % (2698454)Success in time 0.053 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------