TSTP Solution File: SEU369+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:58:32 EDT 2023
% Result : Theorem 3.04s 0.84s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 25
% Syntax : Number of formulae : 191 ( 35 unt; 0 def)
% Number of atoms : 794 ( 42 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1039 ( 436 ~; 482 |; 85 &)
% ( 13 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 3 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 243 (; 229 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14921,plain,
$false,
inference(avatar_sat_refutation,[],[f780,f781,f3970,f14913]) ).
fof(f14913,plain,
( ~ spl46_1
| spl46_2 ),
inference(avatar_contradiction_clause,[],[f14912]) ).
fof(f14912,plain,
( $false
| ~ spl46_1
| spl46_2 ),
inference(subsumption_resolution,[],[f14911,f779]) ).
fof(f779,plain,
( ~ subset(sK13,sK14)
| spl46_2 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f777,plain,
( spl46_2
<=> subset(sK13,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl46_2])]) ).
fof(f14911,plain,
( subset(sK13,sK14)
| ~ spl46_1 ),
inference(subsumption_resolution,[],[f14910,f771]) ).
fof(f771,plain,
element(sK13,sF45),
inference(definition_folding,[],[f744,f769,f766,f765]) ).
fof(f765,plain,
boole_lattice(sK12) = sF43,
introduced(function_definition,[]) ).
fof(f766,plain,
poset_of_lattice(sF43) = sF44,
introduced(function_definition,[]) ).
fof(f769,plain,
the_carrier(sF44) = sF45,
introduced(function_definition,[]) ).
fof(f744,plain,
element(sK13,the_carrier(poset_of_lattice(boole_lattice(sK12)))),
inference(definition_unfolding,[],[f345,f352]) ).
fof(f352,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',d2_yellow_1) ).
fof(f345,plain,
element(sK13,the_carrier(boole_POSet(sK12))),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
( ( ~ subset(sK13,sK14)
| ~ related_reflexive(boole_POSet(sK12),sK13,sK14) )
& ( subset(sK13,sK14)
| related_reflexive(boole_POSet(sK12),sK13,sK14) )
& element(sK14,the_carrier(boole_POSet(sK12)))
& element(sK13,the_carrier(boole_POSet(sK12))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f266,f268,f267]) ).
fof(f267,plain,
( ? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) )
=> ( ? [X2] :
( ( ~ subset(sK13,X2)
| ~ related_reflexive(boole_POSet(sK12),sK13,X2) )
& ( subset(sK13,X2)
| related_reflexive(boole_POSet(sK12),sK13,X2) )
& element(X2,the_carrier(boole_POSet(sK12))) )
& element(sK13,the_carrier(boole_POSet(sK12))) ) ),
introduced(choice_axiom,[]) ).
fof(f268,plain,
( ? [X2] :
( ( ~ subset(sK13,X2)
| ~ related_reflexive(boole_POSet(sK12),sK13,X2) )
& ( subset(sK13,X2)
| related_reflexive(boole_POSet(sK12),sK13,X2) )
& element(X2,the_carrier(boole_POSet(sK12))) )
=> ( ( ~ subset(sK13,sK14)
| ~ related_reflexive(boole_POSet(sK12),sK13,sK14) )
& ( subset(sK13,sK14)
| related_reflexive(boole_POSet(sK12),sK13,sK14) )
& element(sK14,the_carrier(boole_POSet(sK12))) ) ),
introduced(choice_axiom,[]) ).
fof(f266,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(flattening,[],[f265]) ).
fof(f265,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(nnf_transformation,[],[f132]) ).
fof(f132,plain,
? [X0,X1] :
( ? [X2] :
( ( related_reflexive(boole_POSet(X0),X1,X2)
<~> subset(X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,negated_conjecture,
~ ! [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
=> ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
inference(negated_conjecture,[],[f114]) ).
fof(f114,conjecture,
! [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
=> ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',t2_yellow_1) ).
fof(f14910,plain,
( ~ element(sK13,sF45)
| subset(sK13,sK14)
| ~ spl46_1 ),
inference(subsumption_resolution,[],[f14897,f770]) ).
fof(f770,plain,
element(sK14,sF45),
inference(definition_folding,[],[f743,f769,f766,f765]) ).
fof(f743,plain,
element(sK14,the_carrier(poset_of_lattice(boole_lattice(sK12)))),
inference(definition_unfolding,[],[f346,f352]) ).
fof(f346,plain,
element(sK14,the_carrier(boole_POSet(sK12))),
inference(cnf_transformation,[],[f269]) ).
fof(f14897,plain,
( ~ element(sK14,sF45)
| ~ element(sK13,sF45)
| subset(sK13,sK14)
| ~ spl46_1 ),
inference(resolution,[],[f5137,f774]) ).
fof(f774,plain,
( related_reflexive(sF44,sK13,sK14)
| ~ spl46_1 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f773,plain,
( spl46_1
<=> related_reflexive(sF44,sK13,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl46_1])]) ).
fof(f5137,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X1,X0)
| ~ element(X0,sF45)
| ~ element(X1,sF45)
| subset(X1,X0) ),
inference(duplicate_literal_removal,[],[f5136]) ).
fof(f5136,plain,
! [X0,X1] :
( ~ element(X0,sF45)
| ~ related_reflexive(sF44,X1,X0)
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X1,X0) ),
inference(forward_demodulation,[],[f5135,f2844]) ).
fof(f2844,plain,
sF45 = the_carrier(sF43),
inference(subsumption_resolution,[],[f2843,f784]) ).
fof(f784,plain,
~ empty_carrier(sF43),
inference(superposition,[],[f369,f765]) ).
fof(f369,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',fc1_lattice3) ).
fof(f2843,plain,
( sF45 = the_carrier(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f2842,f792]) ).
fof(f792,plain,
lattice(sF43),
inference(superposition,[],[f379,f765]) ).
fof(f379,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',fc2_lattice3) ).
fof(f2842,plain,
( sF45 = the_carrier(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f2841,f800]) ).
fof(f800,plain,
latt_str(sF43),
inference(superposition,[],[f412,f765]) ).
fof(f412,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( latt_str(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',dt_k1_lattice3) ).
fof(f2841,plain,
( sF45 = the_carrier(sF43)
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(trivial_inequality_removal,[],[f2840]) ).
fof(f2840,plain,
( sF44 != sF44
| sF45 = the_carrier(sF43)
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(superposition,[],[f1790,f766]) ).
fof(f1790,plain,
! [X1] :
( sF44 != poset_of_lattice(X1)
| sF45 = the_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(superposition,[],[f1787,f529]) ).
fof(f529,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',d2_lattice3) ).
fof(f1787,plain,
! [X8,X7] :
( sF44 != rel_str_of(X7,X8)
| sF45 = X7 ),
inference(forward_demodulation,[],[f1784,f1271]) ).
fof(f1271,plain,
sF44 = rel_str_of(sF45,the_InternalRel(sF44)),
inference(subsumption_resolution,[],[f1270,f824]) ).
fof(f824,plain,
rel_str(sF44),
inference(forward_demodulation,[],[f812,f766]) ).
fof(f812,plain,
rel_str(poset_of_lattice(sF43)),
inference(superposition,[],[f761,f765]) ).
fof(f761,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f414,f352]) ).
fof(f414,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',dt_k3_yellow_1) ).
fof(f1270,plain,
( sF44 = rel_str_of(sF45,the_InternalRel(sF44))
| ~ rel_str(sF44) ),
inference(subsumption_resolution,[],[f1266,f816]) ).
fof(f816,plain,
strict_rel_str(sF44),
inference(forward_demodulation,[],[f804,f766]) ).
fof(f804,plain,
strict_rel_str(poset_of_lattice(sF43)),
inference(superposition,[],[f748,f765]) ).
fof(f748,plain,
! [X0] : strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f354,f352]) ).
fof(f354,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',fc7_yellow_1) ).
fof(f1266,plain,
( sF44 = rel_str_of(sF45,the_InternalRel(sF44))
| ~ strict_rel_str(sF44)
| ~ rel_str(sF44) ),
inference(superposition,[],[f432,f769]) ).
fof(f432,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',abstractness_v1_orders_2) ).
fof(f1784,plain,
! [X8,X7] :
( sF45 = X7
| rel_str_of(sF45,the_InternalRel(sF44)) != rel_str_of(X7,X8) ),
inference(resolution,[],[f1416,f905]) ).
fof(f905,plain,
relation_of2_as_subset(the_InternalRel(sF44),sF45,sF45),
inference(subsumption_resolution,[],[f904,f824]) ).
fof(f904,plain,
( relation_of2_as_subset(the_InternalRel(sF44),sF45,sF45)
| ~ rel_str(sF44) ),
inference(superposition,[],[f427,f769]) ).
fof(f427,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',dt_u1_orders_2) ).
fof(f1416,plain,
! [X8,X6,X9,X7] :
( ~ relation_of2_as_subset(X7,X6,X6)
| X6 = X8
| rel_str_of(X6,X7) != rel_str_of(X8,X9) ),
inference(resolution,[],[f575,f613]) ).
fof(f613,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',redefinition_m2_relset_1) ).
fof(f575,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',free_g1_orders_2) ).
fof(f5135,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X1,X0)
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X1,X0)
| ~ element(X0,the_carrier(sF43)) ),
inference(subsumption_resolution,[],[f5134,f784]) ).
fof(f5134,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X1,X0)
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X1,X0)
| ~ element(X0,the_carrier(sF43))
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f5133,f792]) ).
fof(f5133,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X1,X0)
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X1,X0)
| ~ element(X0,the_carrier(sF43))
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f5116,f800]) ).
fof(f5116,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X1,X0)
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X1,X0)
| ~ element(X0,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(superposition,[],[f3504,f556]) ).
fof(f556,plain,
! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',d3_lattice3) ).
fof(f3504,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X0,sF45)
| ~ element(X1,sF45)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f3503]) ).
fof(f3503,plain,
! [X0,X1] :
( ~ element(X0,sF45)
| ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X0,X1) ),
inference(forward_demodulation,[],[f3502,f2844]) ).
fof(f3502,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X0,X1)
| ~ element(X0,the_carrier(sF43)) ),
inference(subsumption_resolution,[],[f3501,f784]) ).
fof(f3501,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X0,X1)
| ~ element(X0,the_carrier(sF43))
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f3500,f792]) ).
fof(f3500,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X0,X1)
| ~ element(X0,the_carrier(sF43))
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f3483,f800]) ).
fof(f3483,plain,
! [X0,X1] :
( ~ related_reflexive(sF44,X0,cast_to_el_of_LattPOSet(sF43,X1))
| ~ element(X1,sF45)
| ~ element(X0,sF45)
| subset(X0,X1)
| ~ element(X0,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(superposition,[],[f3252,f556]) ).
fof(f3252,plain,
! [X2,X3] :
( ~ related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X3,sF45)
| ~ element(X2,sF45)
| subset(X2,X3) ),
inference(duplicate_literal_removal,[],[f3251]) ).
fof(f3251,plain,
! [X2,X3] :
( ~ element(X2,sF45)
| ~ element(X3,sF45)
| ~ related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X2,sF45)
| subset(X2,X3) ),
inference(forward_demodulation,[],[f3250,f2844]) ).
fof(f3250,plain,
! [X2,X3] :
( ~ element(X3,sF45)
| ~ related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X2,the_carrier(sF43)) ),
inference(duplicate_literal_removal,[],[f3249]) ).
fof(f3249,plain,
! [X2,X3] :
( ~ element(X3,sF45)
| ~ related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ element(X2,the_carrier(sF43)) ),
inference(forward_demodulation,[],[f3248,f2844]) ).
fof(f3248,plain,
! [X2,X3] :
( ~ related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ element(X3,the_carrier(sF43))
| ~ element(X2,the_carrier(sF43)) ),
inference(forward_demodulation,[],[f3247,f766]) ).
fof(f3247,plain,
! [X2,X3] :
( ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X3,the_carrier(sF43))
| ~ element(X2,the_carrier(sF43)) ),
inference(subsumption_resolution,[],[f3246,f784]) ).
fof(f3246,plain,
! [X2,X3] :
( ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X3,the_carrier(sF43))
| ~ element(X2,the_carrier(sF43))
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f3245,f792]) ).
fof(f3245,plain,
! [X2,X3] :
( ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X3,the_carrier(sF43))
| ~ element(X2,the_carrier(sF43))
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f3242,f800]) ).
fof(f3242,plain,
! [X2,X3] :
( ~ element(X2,sF45)
| subset(X2,X3)
| ~ element(X3,sF45)
| ~ related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,X2),cast_to_el_of_LattPOSet(sF43,X3))
| ~ element(X3,the_carrier(sF43))
| ~ element(X2,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43) ),
inference(resolution,[],[f2946,f558]) ).
fof(f558,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',t7_lattice3) ).
fof(f2946,plain,
! [X0,X1] :
( ~ below_refl(sF43,X0,X1)
| ~ element(X0,sF45)
| subset(X0,X1)
| ~ element(X1,sF45) ),
inference(forward_demodulation,[],[f2870,f2844]) ).
fof(f2870,plain,
! [X0,X1] :
( ~ element(X0,sF45)
| ~ element(X1,the_carrier(sF43))
| subset(X0,X1)
| ~ below_refl(sF43,X0,X1) ),
inference(backward_demodulation,[],[f1858,f2844]) ).
fof(f1858,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sF43))
| subset(X0,X1)
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1) ),
inference(subsumption_resolution,[],[f1857,f784]) ).
fof(f1857,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f1856,f788]) ).
fof(f788,plain,
meet_commutative(sF43),
inference(superposition,[],[f375,f765]) ).
fof(f375,plain,
! [X0] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f1856,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| ~ meet_commutative(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f1855,f790]) ).
fof(f790,plain,
meet_absorbing(sF43),
inference(superposition,[],[f377,f765]) ).
fof(f377,plain,
! [X0] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f1855,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| ~ meet_absorbing(sF43)
| ~ meet_commutative(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f1854,f791]) ).
fof(f791,plain,
join_absorbing(sF43),
inference(superposition,[],[f378,f765]) ).
fof(f378,plain,
! [X0] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f1854,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| ~ join_absorbing(sF43)
| ~ meet_absorbing(sF43)
| ~ meet_commutative(sF43)
| empty_carrier(sF43) ),
inference(subsumption_resolution,[],[f1853,f800]) ).
fof(f1853,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| ~ latt_str(sF43)
| ~ join_absorbing(sF43)
| ~ meet_absorbing(sF43)
| ~ meet_commutative(sF43)
| empty_carrier(sF43) ),
inference(duplicate_literal_removal,[],[f1852]) ).
fof(f1852,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ below_refl(sF43,X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ join_absorbing(sF43)
| ~ meet_absorbing(sF43)
| ~ meet_commutative(sF43)
| empty_carrier(sF43) ),
inference(resolution,[],[f1497,f602]) ).
fof(f602,plain,
! [X2,X0,X1] :
( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0,X1,X2] :
( ( ( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f228]) ).
fof(f228,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& latt_str(X0)
& join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',redefinition_r3_lattices) ).
fof(f1497,plain,
! [X0,X1] :
( ~ below(sF43,X0,X1)
| subset(X0,X1)
| ~ element(X1,the_carrier(sF43))
| ~ element(X0,the_carrier(sF43)) ),
inference(superposition,[],[f577,f765]) ).
fof(f577,plain,
! [X2,X0,X1] :
( ~ below(boole_lattice(X0),X1,X2)
| subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0,X1] :
( ! [X2] :
( ( ( below(boole_lattice(X0),X1,X2)
| ~ subset(X1,X2) )
& ( subset(X1,X2)
| ~ below(boole_lattice(X0),X1,X2) ) )
| ~ element(X2,the_carrier(boole_lattice(X0))) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(nnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ! [X2] :
( ( below(boole_lattice(X0),X1,X2)
<=> subset(X1,X2) )
| ~ element(X2,the_carrier(boole_lattice(X0))) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( below(boole_lattice(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',t2_lattice3) ).
fof(f3970,plain,
( spl46_1
| ~ spl46_2 ),
inference(avatar_contradiction_clause,[],[f3969]) ).
fof(f3969,plain,
( $false
| spl46_1
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3968,f770]) ).
fof(f3968,plain,
( ~ element(sK14,sF45)
| spl46_1
| ~ spl46_2 ),
inference(forward_demodulation,[],[f3967,f2844]) ).
fof(f3967,plain,
( ~ element(sK14,the_carrier(sF43))
| spl46_1
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3966,f784]) ).
fof(f3966,plain,
( ~ element(sK14,the_carrier(sF43))
| empty_carrier(sF43)
| spl46_1
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3965,f792]) ).
fof(f3965,plain,
( ~ element(sK14,the_carrier(sF43))
| ~ lattice(sF43)
| empty_carrier(sF43)
| spl46_1
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3964,f800]) ).
fof(f3964,plain,
( ~ element(sK14,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43)
| spl46_1
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3956,f775]) ).
fof(f775,plain,
( ~ related_reflexive(sF44,sK13,sK14)
| spl46_1 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f3956,plain,
( related_reflexive(sF44,sK13,sK14)
| ~ element(sK14,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43)
| ~ spl46_2 ),
inference(superposition,[],[f3869,f556]) ).
fof(f3869,plain,
( related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3868,f771]) ).
fof(f3868,plain,
( ~ element(sK13,sF45)
| related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ spl46_2 ),
inference(forward_demodulation,[],[f3867,f2844]) ).
fof(f3867,plain,
( related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3866,f784]) ).
fof(f3866,plain,
( related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| empty_carrier(sF43)
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3865,f792]) ).
fof(f3865,plain,
( related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ lattice(sF43)
| empty_carrier(sF43)
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3845,f800]) ).
fof(f3845,plain,
( related_reflexive(sF44,sK13,cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ latt_str(sF43)
| ~ lattice(sF43)
| empty_carrier(sF43)
| ~ spl46_2 ),
inference(superposition,[],[f3842,f556]) ).
fof(f3842,plain,
( related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3841,f771]) ).
fof(f3841,plain,
( ~ element(sK13,sF45)
| related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ spl46_2 ),
inference(forward_demodulation,[],[f3840,f2844]) ).
fof(f3840,plain,
( related_reflexive(sF44,cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ spl46_2 ),
inference(forward_demodulation,[],[f3839,f766]) ).
fof(f3839,plain,
( related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ spl46_2 ),
inference(subsumption_resolution,[],[f3838,f770]) ).
fof(f3838,plain,
( ~ element(sK14,sF45)
| related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ spl46_2 ),
inference(forward_demodulation,[],[f3837,f2844]) ).
fof(f3837,plain,
( ~ element(sK14,the_carrier(sF43))
| related_reflexive(poset_of_lattice(sF43),cast_to_el_of_LattPOSet(sF43,sK13),cast_to_el_of_LattPOSet(sF43,sK14))
| ~ element(sK13,the_carrier(sF43))
| ~ spl46_2 ),
inference(superposition,[],[f2743,f765]) ).
fof(f2743,plain,
( ! [X0] :
( ~ element(sK14,the_carrier(boole_lattice(X0)))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),cast_to_el_of_LattPOSet(boole_lattice(X0),sK13),cast_to_el_of_LattPOSet(boole_lattice(X0),sK14))
| ~ element(sK13,the_carrier(boole_lattice(X0))) )
| ~ spl46_2 ),
inference(resolution,[],[f2168,f778]) ).
fof(f778,plain,
( subset(sK13,sK14)
| ~ spl46_2 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f2168,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X0))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(subsumption_resolution,[],[f2167,f369]) ).
fof(f2167,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X0))
| ~ subset(X2,X0) ),
inference(subsumption_resolution,[],[f2166,f379]) ).
fof(f2166,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ lattice(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X0))
| ~ subset(X2,X0) ),
inference(subsumption_resolution,[],[f2165,f412]) ).
fof(f2165,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ lattice(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X0))
| ~ subset(X2,X0) ),
inference(duplicate_literal_removal,[],[f2160]) ).
fof(f2160,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ lattice(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X2),cast_to_el_of_LattPOSet(boole_lattice(X1),X0))
| ~ subset(X2,X0)
| ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(resolution,[],[f1665,f578]) ).
fof(f578,plain,
! [X2,X0,X1] :
( below(boole_lattice(X0),X1,X2)
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f292]) ).
fof(f1665,plain,
! [X3,X4,X5] :
( ~ below(X3,X4,X5)
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ lattice(X3)
| empty_carrier(X3)
| related_reflexive(poset_of_lattice(X3),cast_to_el_of_LattPOSet(X3,X4),cast_to_el_of_LattPOSet(X3,X5)) ),
inference(subsumption_resolution,[],[f1664,f881]) ).
fof(f881,plain,
! [X3] :
( meet_commutative(X3)
| empty_carrier(X3)
| ~ latt_str(X3)
| ~ lattice(X3) ),
inference(resolution,[],[f494,f490]) ).
fof(f490,plain,
! [X0] :
( ~ sP4(X0)
| meet_commutative(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f494,plain,
! [X0] :
( sP4(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP4(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(definition_folding,[],[f176,f249]) ).
fof(f176,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833',cc1_lattices) ).
fof(f1664,plain,
! [X3,X4,X5] :
( related_reflexive(poset_of_lattice(X3),cast_to_el_of_LattPOSet(X3,X4),cast_to_el_of_LattPOSet(X3,X5))
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ lattice(X3)
| empty_carrier(X3)
| ~ below(X3,X4,X5)
| ~ meet_commutative(X3) ),
inference(subsumption_resolution,[],[f1663,f883]) ).
fof(f883,plain,
! [X5] :
( meet_absorbing(X5)
| empty_carrier(X5)
| ~ latt_str(X5)
| ~ lattice(X5) ),
inference(resolution,[],[f494,f492]) ).
fof(f492,plain,
! [X0] :
( ~ sP4(X0)
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f1663,plain,
! [X3,X4,X5] :
( related_reflexive(poset_of_lattice(X3),cast_to_el_of_LattPOSet(X3,X4),cast_to_el_of_LattPOSet(X3,X5))
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ lattice(X3)
| empty_carrier(X3)
| ~ below(X3,X4,X5)
| ~ meet_absorbing(X3)
| ~ meet_commutative(X3) ),
inference(subsumption_resolution,[],[f1658,f884]) ).
fof(f884,plain,
! [X6] :
( join_absorbing(X6)
| empty_carrier(X6)
| ~ latt_str(X6)
| ~ lattice(X6) ),
inference(resolution,[],[f494,f493]) ).
fof(f493,plain,
! [X0] :
( ~ sP4(X0)
| join_absorbing(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f1658,plain,
! [X3,X4,X5] :
( related_reflexive(poset_of_lattice(X3),cast_to_el_of_LattPOSet(X3,X4),cast_to_el_of_LattPOSet(X3,X5))
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ lattice(X3)
| empty_carrier(X3)
| ~ below(X3,X4,X5)
| ~ join_absorbing(X3)
| ~ meet_absorbing(X3)
| ~ meet_commutative(X3) ),
inference(duplicate_literal_removal,[],[f1657]) ).
fof(f1657,plain,
! [X3,X4,X5] :
( related_reflexive(poset_of_lattice(X3),cast_to_el_of_LattPOSet(X3,X4),cast_to_el_of_LattPOSet(X3,X5))
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ lattice(X3)
| empty_carrier(X3)
| ~ below(X3,X4,X5)
| ~ element(X5,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ latt_str(X3)
| ~ join_absorbing(X3)
| ~ meet_absorbing(X3)
| ~ meet_commutative(X3)
| empty_carrier(X3) ),
inference(resolution,[],[f557,f603]) ).
fof(f603,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f557,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f781,plain,
( spl46_1
| spl46_2 ),
inference(avatar_split_clause,[],[f768,f777,f773]) ).
fof(f768,plain,
( subset(sK13,sK14)
| related_reflexive(sF44,sK13,sK14) ),
inference(definition_folding,[],[f742,f766,f765]) ).
fof(f742,plain,
( subset(sK13,sK14)
| related_reflexive(poset_of_lattice(boole_lattice(sK12)),sK13,sK14) ),
inference(definition_unfolding,[],[f347,f352]) ).
fof(f347,plain,
( subset(sK13,sK14)
| related_reflexive(boole_POSet(sK12),sK13,sK14) ),
inference(cnf_transformation,[],[f269]) ).
fof(f780,plain,
( ~ spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f767,f777,f773]) ).
fof(f767,plain,
( ~ subset(sK13,sK14)
| ~ related_reflexive(sF44,sK13,sK14) ),
inference(definition_folding,[],[f741,f766,f765]) ).
fof(f741,plain,
( ~ subset(sK13,sK14)
| ~ related_reflexive(poset_of_lattice(boole_lattice(sK12)),sK13,sK14) ),
inference(definition_unfolding,[],[f348,f352]) ).
fof(f348,plain,
( ~ subset(sK13,sK14)
| ~ related_reflexive(boole_POSet(sK12),sK13,sK14) ),
inference(cnf_transformation,[],[f269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.37 % Computer : n014.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Wed Aug 23 18:16:49 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.oUYXwER5Ui/Vampire---4.8_13833
% 0.17/0.38 % (14023)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (14033)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.23/0.45 % (14036)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.23/0.45 % (14035)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.23/0.45 % (14028)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.23/0.45 % (14030)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.23/0.45 % (14027)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.23/0.45 % (14031)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.23/0.45 % (14036)Refutation not found, incomplete strategy% (14036)------------------------------
% 0.23/0.45 % (14036)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45 % (14036)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45 % (14036)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.45
% 0.23/0.45 % (14036)Memory used [KB]: 5884
% 0.23/0.45 % (14036)Time elapsed: 0.008 s
% 0.23/0.45 % (14036)------------------------------
% 0.23/0.45 % (14036)------------------------------
% 0.23/0.46 % (14027)Refutation not found, incomplete strategy% (14027)------------------------------
% 0.23/0.46 % (14027)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46 % (14027)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46 % (14027)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.46
% 0.23/0.46 % (14027)Memory used [KB]: 6140
% 0.23/0.46 % (14027)Time elapsed: 0.011 s
% 0.23/0.46 % (14027)------------------------------
% 0.23/0.46 % (14027)------------------------------
% 0.23/0.49 % (14037)lrs-11_32_amm=off:bce=on:cond=on:er=filter:fsd=off:fde=none:gs=on:gsem=on:lcm=reverse:nm=4:nwc=1.1:sos=all:sac=on:sp=frequency:urr=on:stl=125_403 on Vampire---4 for (403ds/0Mi)
% 0.23/0.50 % (14039)lrs+1010_5:1_bd=off:fsd=off:fde=unused:lcm=predicate:nm=64:nwc=1.7:sac=on:sp=frequency:tgt=ground:stl=62_333 on Vampire---4 for (333ds/0Mi)
% 3.04/0.84 % (14031)First to succeed.
% 3.04/0.84 % (14031)Refutation found. Thanks to Tanya!
% 3.04/0.84 % SZS status Theorem for Vampire---4
% 3.04/0.84 % SZS output start Proof for Vampire---4
% See solution above
% 3.04/0.84 % (14031)------------------------------
% 3.04/0.84 % (14031)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 3.04/0.84 % (14031)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 3.04/0.84 % (14031)Termination reason: Refutation
% 3.04/0.84
% 3.04/0.84 % (14031)Memory used [KB]: 13688
% 3.04/0.84 % (14031)Time elapsed: 0.384 s
% 3.04/0.84 % (14031)------------------------------
% 3.04/0.84 % (14031)------------------------------
% 3.04/0.84 % (14023)Success in time 0.459 s
% 3.04/0.84 % Vampire---4.8 exiting
%------------------------------------------------------------------------------