TSTP Solution File: SEU343+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU343+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 : n026.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 17:58:21 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 72
% Syntax : Number of formulae : 321 ( 26 unt; 0 def)
% Number of atoms : 1193 ( 200 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1466 ( 594 ~; 701 |; 94 &)
% ( 47 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 57 ( 55 usr; 44 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 6 con; 0-6 aty)
% Number of variables : 373 (; 349 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3975,plain,
$false,
inference(avatar_sat_refutation,[],[f403,f455,f508,f580,f598,f604,f639,f664,f670,f706,f728,f750,f772,f794,f876,f898,f928,f950,f972,f994,f1016,f1039,f1061,f1067,f1073,f1079,f1086,f1092,f1098,f1104,f1123,f3371,f3384,f3401,f3694,f3703,f3965,f3974]) ).
fof(f3974,plain,
( spl20_2
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(avatar_contradiction_clause,[],[f3973]) ).
fof(f3973,plain,
( $false
| spl20_2
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3972,f402]) ).
fof(f402,plain,
( set_intersection2(sK1,sK2) != meet(boole_lattice(sK0),sK1,sK2)
| spl20_2 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f400,plain,
( spl20_2
<=> set_intersection2(sK1,sK2) = meet(boole_lattice(sK0),sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f3972,plain,
( set_intersection2(sK1,sK2) = meet(boole_lattice(sK0),sK1,sK2)
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(forward_demodulation,[],[f3971,f2962]) ).
fof(f2962,plain,
set_intersection2(sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2),
inference(forward_demodulation,[],[f2952,f2102]) ).
fof(f2102,plain,
set_intersection2(sK1,sK2) = subset_intersection2(sK0,sK1,sK2),
inference(resolution,[],[f338,f394]) ).
fof(f394,plain,
element(sK2,powerset(sK0)),
inference(subsumption_resolution,[],[f393,f210]) ).
fof(f210,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( latt_str(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_k1_lattice3) ).
fof(f393,plain,
( element(sK2,powerset(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f384,f211]) ).
fof(f211,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f384,plain,
( element(sK2,powerset(sK0))
| ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(superposition,[],[f201,f300]) ).
fof(f300,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f249]) ).
fof(f249,plain,
! [X0,X1] :
( powerset(X0) = the_carrier(X1)
| boole_lattice(X0) != X1
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( ( ( boole_lattice(X0) = X1
| ( ( apply_binary(the_L_meet(X1),sK7(X0,X1),sK8(X0,X1)) != subset_intersection2(X0,sK7(X0,X1),sK8(X0,X1))
| apply_binary(the_L_join(X1),sK7(X0,X1),sK8(X0,X1)) != subset_union2(X0,sK7(X0,X1),sK8(X0,X1)) )
& element(sK8(X0,X1),powerset(X0))
& element(sK7(X0,X1),powerset(X0)) )
| powerset(X0) != the_carrier(X1) )
& ( ( ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5)
& apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) )
& powerset(X0) = the_carrier(X1) )
| boole_lattice(X0) != X1 ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f173,f175,f174]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3)
| apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) )
=> ( ? [X3] :
( ( apply_binary(the_L_meet(X1),sK7(X0,X1),X3) != subset_intersection2(X0,sK7(X0,X1),X3)
| apply_binary(the_L_join(X1),sK7(X0,X1),X3) != subset_union2(X0,sK7(X0,X1),X3) )
& element(X3,powerset(X0)) )
& element(sK7(X0,X1),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f175,plain,
! [X0,X1] :
( ? [X3] :
( ( apply_binary(the_L_meet(X1),sK7(X0,X1),X3) != subset_intersection2(X0,sK7(X0,X1),X3)
| apply_binary(the_L_join(X1),sK7(X0,X1),X3) != subset_union2(X0,sK7(X0,X1),X3) )
& element(X3,powerset(X0)) )
=> ( ( apply_binary(the_L_meet(X1),sK7(X0,X1),sK8(X0,X1)) != subset_intersection2(X0,sK7(X0,X1),sK8(X0,X1))
| apply_binary(the_L_join(X1),sK7(X0,X1),sK8(X0,X1)) != subset_union2(X0,sK7(X0,X1),sK8(X0,X1)) )
& element(sK8(X0,X1),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f173,plain,
! [X0,X1] :
( ( ( boole_lattice(X0) = X1
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3)
| apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) )
| powerset(X0) != the_carrier(X1) )
& ( ( ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5)
& apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) )
& powerset(X0) = the_carrier(X1) )
| boole_lattice(X0) != X1 ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(rectify,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( ( ( boole_lattice(X0) = X1
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3)
| apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) )
| powerset(X0) != the_carrier(X1) )
& ( ( ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3)
& apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) )
& powerset(X0) = the_carrier(X1) )
| boole_lattice(X0) != X1 ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ( ( boole_lattice(X0) = X1
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3)
| apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) )
| powerset(X0) != the_carrier(X1) )
& ( ( ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3)
& apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) )
& powerset(X0) = the_carrier(X1) )
| boole_lattice(X0) != X1 ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(nnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ( boole_lattice(X0) = X1
<=> ( ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3)
& apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) )
& powerset(X0) = the_carrier(X1) ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ( boole_lattice(X0) = X1
<=> ( ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3)
& apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) )
& powerset(X0) = the_carrier(X1) ) )
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( latt_str(X1)
& strict_latt_str(X1) )
=> ( boole_lattice(X0) = X1
<=> ( ! [X2] :
( element(X2,powerset(X0))
=> ! [X3] :
( element(X3,powerset(X0))
=> ( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3)
& apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3) ) ) )
& powerset(X0) = the_carrier(X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',d1_lattice3) ).
fof(f201,plain,
element(sK2,the_carrier(boole_lattice(sK0))),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
( ( set_intersection2(sK1,sK2) != meet(boole_lattice(sK0),sK1,sK2)
| set_union2(sK1,sK2) != join(boole_lattice(sK0),sK1,sK2) )
& element(sK2,the_carrier(boole_lattice(sK0)))
& element(sK1,the_carrier(boole_lattice(sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f92,f161,f160]) ).
fof(f160,plain,
( ? [X0,X1] :
( ? [X2] :
( ( set_intersection2(X1,X2) != meet(boole_lattice(X0),X1,X2)
| set_union2(X1,X2) != join(boole_lattice(X0),X1,X2) )
& element(X2,the_carrier(boole_lattice(X0))) )
& element(X1,the_carrier(boole_lattice(X0))) )
=> ( ? [X2] :
( ( set_intersection2(sK1,X2) != meet(boole_lattice(sK0),sK1,X2)
| set_union2(sK1,X2) != join(boole_lattice(sK0),sK1,X2) )
& element(X2,the_carrier(boole_lattice(sK0))) )
& element(sK1,the_carrier(boole_lattice(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
( ? [X2] :
( ( set_intersection2(sK1,X2) != meet(boole_lattice(sK0),sK1,X2)
| set_union2(sK1,X2) != join(boole_lattice(sK0),sK1,X2) )
& element(X2,the_carrier(boole_lattice(sK0))) )
=> ( ( set_intersection2(sK1,sK2) != meet(boole_lattice(sK0),sK1,sK2)
| set_union2(sK1,sK2) != join(boole_lattice(sK0),sK1,sK2) )
& element(sK2,the_carrier(boole_lattice(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
? [X0,X1] :
( ? [X2] :
( ( set_intersection2(X1,X2) != meet(boole_lattice(X0),X1,X2)
| set_union2(X1,X2) != join(boole_lattice(X0),X1,X2) )
& element(X2,the_carrier(boole_lattice(X0))) )
& element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,negated_conjecture,
~ ! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( set_intersection2(X1,X2) = meet(boole_lattice(X0),X1,X2)
& set_union2(X1,X2) = join(boole_lattice(X0),X1,X2) ) ) ),
inference(negated_conjecture,[],[f77]) ).
fof(f77,conjecture,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( set_intersection2(X1,X2) = meet(boole_lattice(X0),X1,X2)
& set_union2(X1,X2) = join(boole_lattice(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',t1_lattice3) ).
fof(f338,plain,
! [X10] :
( ~ element(X10,powerset(sK0))
| subset_intersection2(sK0,sK1,X10) = set_intersection2(sK1,X10) ),
inference(resolution,[],[f327,f276]) ).
fof(f276,plain,
! [X2,X0,X1] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',redefinition_k5_subset_1) ).
fof(f327,plain,
element(sK1,powerset(sK0)),
inference(subsumption_resolution,[],[f326,f210]) ).
fof(f326,plain,
( element(sK1,powerset(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f317,f211]) ).
fof(f317,plain,
( element(sK1,powerset(sK0))
| ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(superposition,[],[f200,f300]) ).
fof(f200,plain,
element(sK1,the_carrier(boole_lattice(sK0))),
inference(cnf_transformation,[],[f162]) ).
fof(f2952,plain,
subset_intersection2(sK0,sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2),
inference(resolution,[],[f358,f394]) ).
fof(f358,plain,
! [X19] :
( ~ element(X19,powerset(sK0))
| subset_intersection2(sK0,sK1,X19) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,X19) ),
inference(subsumption_resolution,[],[f357,f210]) ).
fof(f357,plain,
! [X19] :
( subset_intersection2(sK0,sK1,X19) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,X19)
| ~ element(X19,powerset(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f347,f211]) ).
fof(f347,plain,
! [X19] :
( subset_intersection2(sK0,sK1,X19) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,X19)
| ~ element(X19,powerset(sK0))
| ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(resolution,[],[f327,f298]) ).
fof(f298,plain,
! [X0,X4,X5] :
( subset_intersection2(X0,X4,X5) = apply_binary(the_L_meet(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ latt_str(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X4,X5] :
( apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| boole_lattice(X0) != X1
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f3971,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3970,f449]) ).
fof(f449,plain,
( ~ empty(the_carrier(boole_lattice(sK0)))
| spl20_3 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f448,plain,
( spl20_3
<=> empty(the_carrier(boole_lattice(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
fof(f3970,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3969,f610]) ).
fof(f610,plain,
( function(the_L_meet(boole_lattice(sK0)))
| ~ spl20_6 ),
inference(resolution,[],[f593,f219]) ).
fof(f219,plain,
! [X0] :
( function(the_L_meet(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_meet(X0)) )
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> ( relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_meet(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_u1_lattices) ).
fof(f593,plain,
( meet_semilatt_str(boole_lattice(sK0))
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f592,plain,
( spl20_6
<=> meet_semilatt_str(boole_lattice(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_6])]) ).
fof(f3969,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3968,f611]) ).
fof(f611,plain,
( quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_6 ),
inference(resolution,[],[f593,f220]) ).
fof(f220,plain,
! [X0] :
( quasi_total(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f3968,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3967,f3227]) ).
fof(f3227,plain,
( relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_6 ),
inference(resolution,[],[f612,f280]) ).
fof(f280,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,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,[],[f74]) ).
fof(f74,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',redefinition_m2_relset_1) ).
fof(f612,plain,
( relation_of2_as_subset(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_6 ),
inference(resolution,[],[f593,f221]) ).
fof(f221,plain,
! [X0] :
( relation_of2_as_subset(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f3967,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3966,f200]) ).
fof(f3966,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3953,f201]) ).
fof(f3953,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(duplicate_literal_removal,[],[f3950]) ).
fof(f3950,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(superposition,[],[f284,f930]) ).
fof(f930,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ spl20_18 ),
inference(resolution,[],[f927,f201]) ).
fof(f927,plain,
( ! [X2] :
( ~ element(X2,the_carrier(boole_lattice(sK0)))
| meet(boole_lattice(sK0),sK1,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK1,X2) )
| ~ spl20_18 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f926,plain,
( spl20_18
<=> ! [X2] :
( meet(boole_lattice(sK0),sK1,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK1,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_18])]) ).
fof(f284,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( element(X5,X1)
& element(X4,X0)
& relation_of2(X3,cartesian_product2(X0,X1),X2)
& quasi_total(X3,cartesian_product2(X0,X1),X2)
& function(X3)
& ~ empty(X1)
& ~ empty(X0) )
=> apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',redefinition_k2_binop_1) ).
fof(f3965,plain,
( spl20_2
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(avatar_contradiction_clause,[],[f3964]) ).
fof(f3964,plain,
( $false
| spl20_2
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3963,f402]) ).
fof(f3963,plain,
( set_intersection2(sK1,sK2) = meet(boole_lattice(sK0),sK1,sK2)
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(forward_demodulation,[],[f3962,f2962]) ).
fof(f3962,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| spl20_3
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3961,f449]) ).
fof(f3961,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3960,f610]) ).
fof(f3960,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3959,f611]) ).
fof(f3959,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_6
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3958,f3227]) ).
fof(f3958,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3957,f200]) ).
fof(f3957,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(subsumption_resolution,[],[f3954,f201]) ).
fof(f3954,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(duplicate_literal_removal,[],[f3949]) ).
fof(f3949,plain,
( meet(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_meet(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_meet(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_meet(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_18 ),
inference(superposition,[],[f930,f284]) ).
fof(f3703,plain,
( spl20_1
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(avatar_contradiction_clause,[],[f3702]) ).
fof(f3702,plain,
( $false
| spl20_1
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3701,f398]) ).
fof(f398,plain,
( set_union2(sK1,sK2) != join(boole_lattice(sK0),sK1,sK2)
| spl20_1 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f396,plain,
( spl20_1
<=> set_union2(sK1,sK2) = join(boole_lattice(sK0),sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f3701,plain,
( set_union2(sK1,sK2) = join(boole_lattice(sK0),sK1,sK2)
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(forward_demodulation,[],[f3700,f3000]) ).
fof(f3000,plain,
set_union2(sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2),
inference(forward_demodulation,[],[f2990,f2166]) ).
fof(f2166,plain,
set_union2(sK1,sK2) = subset_union2(sK0,sK1,sK2),
inference(resolution,[],[f340,f394]) ).
fof(f340,plain,
! [X12] :
( ~ element(X12,powerset(sK0))
| subset_union2(sK0,sK1,X12) = set_union2(sK1,X12) ),
inference(resolution,[],[f327,f277]) ).
fof(f277,plain,
! [X2,X0,X1] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_union2(X0,X1,X2) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',redefinition_k4_subset_1) ).
fof(f2990,plain,
subset_union2(sK0,sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2),
inference(resolution,[],[f362,f394]) ).
fof(f362,plain,
! [X21] :
( ~ element(X21,powerset(sK0))
| subset_union2(sK0,sK1,X21) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,X21) ),
inference(subsumption_resolution,[],[f361,f210]) ).
fof(f361,plain,
! [X21] :
( subset_union2(sK0,sK1,X21) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,X21)
| ~ element(X21,powerset(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f349,f211]) ).
fof(f349,plain,
! [X21] :
( subset_union2(sK0,sK1,X21) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,X21)
| ~ element(X21,powerset(sK0))
| ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0)) ),
inference(resolution,[],[f327,f299]) ).
fof(f299,plain,
! [X0,X4,X5] :
( subset_union2(X0,X4,X5) = apply_binary(the_L_join(boole_lattice(X0)),X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| ~ latt_str(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X4,X5] :
( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
| ~ element(X5,powerset(X0))
| ~ element(X4,powerset(X0))
| boole_lattice(X0) != X1
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f3700,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3699,f449]) ).
fof(f3699,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3698,f676]) ).
fof(f676,plain,
( function(the_L_join(boole_lattice(sK0)))
| ~ spl20_9 ),
inference(resolution,[],[f659,f216]) ).
fof(f216,plain,
! [X0] :
( function(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_join(X0)) )
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( join_semilatt_str(X0)
=> ( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_join(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_u2_lattices) ).
fof(f659,plain,
( join_semilatt_str(boole_lattice(sK0))
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f658,plain,
( spl20_9
<=> join_semilatt_str(boole_lattice(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_9])]) ).
fof(f3698,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3697,f677]) ).
fof(f677,plain,
( quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_9 ),
inference(resolution,[],[f659,f217]) ).
fof(f217,plain,
! [X0] :
( quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f3697,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3696,f3293]) ).
fof(f3293,plain,
( relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_9 ),
inference(resolution,[],[f678,f280]) ).
fof(f678,plain,
( relation_of2_as_subset(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ spl20_9 ),
inference(resolution,[],[f659,f218]) ).
fof(f218,plain,
! [X0] :
( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f3696,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3695,f200]) ).
fof(f3695,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3682,f201]) ).
fof(f3682,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(duplicate_literal_removal,[],[f3679]) ).
fof(f3679,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(superposition,[],[f284,f878]) ).
fof(f878,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ spl20_16 ),
inference(resolution,[],[f875,f201]) ).
fof(f875,plain,
( ! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| join(boole_lattice(sK0),sK1,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK1,X0) )
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f874,plain,
( spl20_16
<=> ! [X0] :
( join(boole_lattice(sK0),sK1,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK1,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_16])]) ).
fof(f3694,plain,
( spl20_1
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(avatar_contradiction_clause,[],[f3693]) ).
fof(f3693,plain,
( $false
| spl20_1
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3692,f398]) ).
fof(f3692,plain,
( set_union2(sK1,sK2) = join(boole_lattice(sK0),sK1,sK2)
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(forward_demodulation,[],[f3691,f3000]) ).
fof(f3691,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| spl20_3
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3690,f449]) ).
fof(f3690,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3689,f676]) ).
fof(f3689,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3688,f677]) ).
fof(f3688,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_9
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3687,f3293]) ).
fof(f3687,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3686,f200]) ).
fof(f3686,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(subsumption_resolution,[],[f3683,f201]) ).
fof(f3683,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(duplicate_literal_removal,[],[f3678]) ).
fof(f3678,plain,
( join(boole_lattice(sK0),sK1,sK2) = apply_binary(the_L_join(boole_lattice(sK0)),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ relation_of2(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(the_L_join(boole_lattice(sK0)),cartesian_product2(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0))),the_carrier(boole_lattice(sK0)))
| ~ function(the_L_join(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_16 ),
inference(superposition,[],[f878,f284]) ).
fof(f3401,plain,
( ~ spl20_40
| spl20_41
| ~ spl20_42
| spl20_43 ),
inference(avatar_split_clause,[],[f821,f3398,f3394,f3390,f3386]) ).
fof(f3386,plain,
( spl20_40
<=> strict_latt_str(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_40])]) ).
fof(f3390,plain,
( spl20_41
<=> element(sK1,the_carrier(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_41])]) ).
fof(f3394,plain,
( spl20_42
<=> powerset(sK0) = the_carrier(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_42])]) ).
fof(f3398,plain,
( spl20_43
<=> element(sK7(sK0,sK15),powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_43])]) ).
fof(f821,plain,
( element(sK7(sK0,sK15),powerset(sK0))
| powerset(sK0) != the_carrier(sK15)
| element(sK1,the_carrier(sK15))
| ~ strict_latt_str(sK15) ),
inference(resolution,[],[f314,f289]) ).
fof(f289,plain,
latt_str(sK15),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
latt_str(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f44,f190]) ).
fof(f190,plain,
( ? [X0] : latt_str(X0)
=> latt_str(sK15) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',existence_l3_lattices) ).
fof(f314,plain,
! [X0] :
( ~ latt_str(X0)
| element(sK7(sK0,X0),powerset(sK0))
| the_carrier(X0) != powerset(sK0)
| element(sK1,the_carrier(X0))
| ~ strict_latt_str(X0) ),
inference(superposition,[],[f200,f252]) ).
fof(f252,plain,
! [X0,X1] :
( boole_lattice(X0) = X1
| element(sK7(X0,X1),powerset(X0))
| powerset(X0) != the_carrier(X1)
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f3384,plain,
( spl20_37
| ~ spl20_38
| spl20_39 ),
inference(avatar_split_clause,[],[f827,f3381,f3377,f3373]) ).
fof(f3373,plain,
( spl20_37
<=> element(sK1,the_carrier(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_37])]) ).
fof(f3377,plain,
( spl20_38
<=> powerset(sK0) = the_carrier(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_38])]) ).
fof(f3381,plain,
( spl20_39
<=> element(sK7(sK0,sK19),powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_39])]) ).
fof(f827,plain,
( element(sK7(sK0,sK19),powerset(sK0))
| powerset(sK0) != the_carrier(sK19)
| element(sK1,the_carrier(sK19)) ),
inference(subsumption_resolution,[],[f823,f297]) ).
fof(f297,plain,
strict_latt_str(sK19),
inference(cnf_transformation,[],[f199]) ).
fof(f199,plain,
( strict_latt_str(sK19)
& latt_str(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f67,f198]) ).
fof(f198,plain,
( ? [X0] :
( strict_latt_str(X0)
& latt_str(X0) )
=> ( strict_latt_str(sK19)
& latt_str(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f67,axiom,
? [X0] :
( strict_latt_str(X0)
& latt_str(X0) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',rc3_lattices) ).
fof(f823,plain,
( element(sK7(sK0,sK19),powerset(sK0))
| powerset(sK0) != the_carrier(sK19)
| element(sK1,the_carrier(sK19))
| ~ strict_latt_str(sK19) ),
inference(resolution,[],[f314,f296]) ).
fof(f296,plain,
latt_str(sK19),
inference(cnf_transformation,[],[f199]) ).
fof(f3371,plain,
( spl20_34
| ~ spl20_35
| spl20_36 ),
inference(avatar_split_clause,[],[f826,f3368,f3364,f3360]) ).
fof(f3360,plain,
( spl20_34
<=> element(sK1,the_carrier(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_34])]) ).
fof(f3364,plain,
( spl20_35
<=> powerset(sK0) = the_carrier(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_35])]) ).
fof(f3368,plain,
( spl20_36
<=> element(sK7(sK0,sK18),powerset(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_36])]) ).
fof(f826,plain,
( element(sK7(sK0,sK18),powerset(sK0))
| powerset(sK0) != the_carrier(sK18)
| element(sK1,the_carrier(sK18)) ),
inference(subsumption_resolution,[],[f822,f295]) ).
fof(f295,plain,
strict_latt_str(sK18),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
( strict_latt_str(sK18)
& ~ empty_carrier(sK18)
& latt_str(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f70,f196]) ).
fof(f196,plain,
( ? [X0] :
( strict_latt_str(X0)
& ~ empty_carrier(X0)
& latt_str(X0) )
=> ( strict_latt_str(sK18)
& ~ empty_carrier(sK18)
& latt_str(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f70,axiom,
? [X0] :
( strict_latt_str(X0)
& ~ empty_carrier(X0)
& latt_str(X0) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',rc6_lattices) ).
fof(f822,plain,
( element(sK7(sK0,sK18),powerset(sK0))
| powerset(sK0) != the_carrier(sK18)
| element(sK1,the_carrier(sK18))
| ~ strict_latt_str(sK18) ),
inference(resolution,[],[f314,f293]) ).
fof(f293,plain,
latt_str(sK18),
inference(cnf_transformation,[],[f197]) ).
fof(f1123,plain,
( spl20_32
| ~ spl20_33 ),
inference(avatar_split_clause,[],[f345,f1120,f1117]) ).
fof(f1117,plain,
( spl20_32
<=> ! [X17] : ~ in(X17,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_32])]) ).
fof(f1120,plain,
( spl20_33
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_33])]) ).
fof(f345,plain,
! [X17] :
( ~ empty(sK0)
| ~ in(X17,sK1) ),
inference(resolution,[],[f327,f282]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',t5_subset) ).
fof(f1104,plain,
( spl20_3
| spl20_31 ),
inference(avatar_split_clause,[],[f377,f1102,f448]) ).
fof(f1102,plain,
( spl20_31
<=> ! [X13,X14,X12,X15] :
( apply_binary_as_element(X12,the_carrier(boole_lattice(sK0)),X13,X14,X15,sK2) = apply_binary(X14,X15,sK2)
| empty(X12)
| ~ function(X14)
| ~ quasi_total(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ relation_of2(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ element(X15,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_31])]) ).
fof(f377,plain,
! [X14,X15,X12,X13] :
( apply_binary_as_element(X12,the_carrier(boole_lattice(sK0)),X13,X14,X15,sK2) = apply_binary(X14,X15,sK2)
| ~ element(X15,X12)
| ~ relation_of2(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ quasi_total(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ function(X14)
| empty(the_carrier(boole_lattice(sK0)))
| empty(X12) ),
inference(resolution,[],[f201,f284]) ).
fof(f1098,plain,
( spl20_3
| spl20_30 ),
inference(avatar_split_clause,[],[f376,f1096,f448]) ).
fof(f1096,plain,
( spl20_30
<=> ! [X10,X11,X9,X8] :
( apply_binary_as_element(the_carrier(boole_lattice(sK0)),X8,X9,X10,sK2,X11) = apply_binary(X10,sK2,X11)
| empty(X8)
| ~ function(X10)
| ~ quasi_total(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ relation_of2(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ element(X11,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_30])]) ).
fof(f376,plain,
! [X10,X11,X8,X9] :
( apply_binary_as_element(the_carrier(boole_lattice(sK0)),X8,X9,X10,sK2,X11) = apply_binary(X10,sK2,X11)
| ~ element(X11,X8)
| ~ relation_of2(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ quasi_total(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ function(X10)
| empty(X8)
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f201,f284]) ).
fof(f1092,plain,
( spl20_3
| spl20_29 ),
inference(avatar_split_clause,[],[f310,f1090,f448]) ).
fof(f1090,plain,
( spl20_29
<=> ! [X13,X14,X12,X15] :
( apply_binary_as_element(X12,the_carrier(boole_lattice(sK0)),X13,X14,X15,sK1) = apply_binary(X14,X15,sK1)
| empty(X12)
| ~ function(X14)
| ~ quasi_total(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ relation_of2(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ element(X15,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_29])]) ).
fof(f310,plain,
! [X14,X15,X12,X13] :
( apply_binary_as_element(X12,the_carrier(boole_lattice(sK0)),X13,X14,X15,sK1) = apply_binary(X14,X15,sK1)
| ~ element(X15,X12)
| ~ relation_of2(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ quasi_total(X14,cartesian_product2(X12,the_carrier(boole_lattice(sK0))),X13)
| ~ function(X14)
| empty(the_carrier(boole_lattice(sK0)))
| empty(X12) ),
inference(resolution,[],[f200,f284]) ).
fof(f1086,plain,
( spl20_3
| spl20_28 ),
inference(avatar_split_clause,[],[f309,f1084,f448]) ).
fof(f1084,plain,
( spl20_28
<=> ! [X10,X11,X9,X8] :
( apply_binary_as_element(the_carrier(boole_lattice(sK0)),X8,X9,X10,sK1,X11) = apply_binary(X10,sK1,X11)
| empty(X8)
| ~ function(X10)
| ~ quasi_total(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ relation_of2(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ element(X11,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_28])]) ).
fof(f309,plain,
! [X10,X11,X8,X9] :
( apply_binary_as_element(the_carrier(boole_lattice(sK0)),X8,X9,X10,sK1,X11) = apply_binary(X10,sK1,X11)
| ~ element(X11,X8)
| ~ relation_of2(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ quasi_total(X10,cartesian_product2(the_carrier(boole_lattice(sK0)),X8),X9)
| ~ function(X10)
| empty(X8)
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f200,f284]) ).
fof(f1079,plain,
( spl20_3
| spl20_27 ),
inference(avatar_split_clause,[],[f379,f1077,f448]) ).
fof(f1077,plain,
( spl20_27
<=> ! [X20,X21,X23,X22] :
( element(apply_binary_as_element(X20,the_carrier(boole_lattice(sK0)),X21,X22,X23,sK2),X21)
| empty(X20)
| ~ function(X22)
| ~ quasi_total(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ relation_of2(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ element(X23,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_27])]) ).
fof(f379,plain,
! [X21,X22,X23,X20] :
( element(apply_binary_as_element(X20,the_carrier(boole_lattice(sK0)),X21,X22,X23,sK2),X21)
| ~ element(X23,X20)
| ~ relation_of2(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ quasi_total(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ function(X22)
| empty(the_carrier(boole_lattice(sK0)))
| empty(X20) ),
inference(resolution,[],[f201,f283]) ).
fof(f283,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( element(X5,X1)
& element(X4,X0)
& relation_of2(X3,cartesian_product2(X0,X1),X2)
& quasi_total(X3,cartesian_product2(X0,X1),X2)
& function(X3)
& ~ empty(X1)
& ~ empty(X0) )
=> element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_k2_binop_1) ).
fof(f1073,plain,
( spl20_3
| spl20_26 ),
inference(avatar_split_clause,[],[f378,f1071,f448]) ).
fof(f1071,plain,
( spl20_26
<=> ! [X18,X17,X16,X19] :
( element(apply_binary_as_element(the_carrier(boole_lattice(sK0)),X16,X17,X18,sK2,X19),X17)
| empty(X16)
| ~ function(X18)
| ~ quasi_total(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ relation_of2(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ element(X19,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_26])]) ).
fof(f378,plain,
! [X18,X19,X16,X17] :
( element(apply_binary_as_element(the_carrier(boole_lattice(sK0)),X16,X17,X18,sK2,X19),X17)
| ~ element(X19,X16)
| ~ relation_of2(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ quasi_total(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ function(X18)
| empty(X16)
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f201,f283]) ).
fof(f1067,plain,
( spl20_3
| spl20_25 ),
inference(avatar_split_clause,[],[f312,f1065,f448]) ).
fof(f1065,plain,
( spl20_25
<=> ! [X20,X21,X23,X22] :
( element(apply_binary_as_element(X20,the_carrier(boole_lattice(sK0)),X21,X22,X23,sK1),X21)
| empty(X20)
| ~ function(X22)
| ~ quasi_total(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ relation_of2(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ element(X23,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_25])]) ).
fof(f312,plain,
! [X21,X22,X23,X20] :
( element(apply_binary_as_element(X20,the_carrier(boole_lattice(sK0)),X21,X22,X23,sK1),X21)
| ~ element(X23,X20)
| ~ relation_of2(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ quasi_total(X22,cartesian_product2(X20,the_carrier(boole_lattice(sK0))),X21)
| ~ function(X22)
| empty(the_carrier(boole_lattice(sK0)))
| empty(X20) ),
inference(resolution,[],[f200,f283]) ).
fof(f1061,plain,
( spl20_3
| spl20_24 ),
inference(avatar_split_clause,[],[f311,f1059,f448]) ).
fof(f1059,plain,
( spl20_24
<=> ! [X18,X17,X16,X19] :
( element(apply_binary_as_element(the_carrier(boole_lattice(sK0)),X16,X17,X18,sK1,X19),X17)
| empty(X16)
| ~ function(X18)
| ~ quasi_total(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ relation_of2(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ element(X19,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_24])]) ).
fof(f311,plain,
! [X18,X19,X16,X17] :
( element(apply_binary_as_element(the_carrier(boole_lattice(sK0)),X16,X17,X18,sK1,X19),X17)
| ~ element(X19,X16)
| ~ relation_of2(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ quasi_total(X18,cartesian_product2(the_carrier(boole_lattice(sK0)),X16),X17)
| ~ function(X18)
| empty(X16)
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f200,f283]) ).
fof(f1039,plain,
( ~ spl20_6
| spl20_23 ),
inference(avatar_split_clause,[],[f388,f1037,f592]) ).
fof(f1037,plain,
( spl20_23
<=> ! [X3] :
( meet(boole_lattice(sK0),X3,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK2)
| ~ element(X3,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_23])]) ).
fof(f388,plain,
! [X3] :
( meet(boole_lattice(sK0),X3,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK2)
| ~ element(X3,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f371,f208]) ).
fof(f208,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',fc1_lattice3) ).
fof(f371,plain,
! [X3] :
( meet(boole_lattice(sK0),X3,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK2)
| ~ element(X3,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f227]) ).
fof(f227,plain,
! [X2,X0,X1] :
( meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ( meet_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> meet(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',d2_lattices) ).
fof(f1016,plain,
( ~ spl20_6
| spl20_22 ),
inference(avatar_split_clause,[],[f387,f1014,f592]) ).
fof(f1014,plain,
( spl20_22
<=> ! [X2] :
( meet(boole_lattice(sK0),sK2,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK2,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_22])]) ).
fof(f387,plain,
! [X2] :
( meet(boole_lattice(sK0),sK2,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK2,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f370,f208]) ).
fof(f370,plain,
! [X2] :
( meet(boole_lattice(sK0),sK2,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK2,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f227]) ).
fof(f994,plain,
( ~ spl20_9
| spl20_21 ),
inference(avatar_split_clause,[],[f386,f992,f658]) ).
fof(f992,plain,
( spl20_21
<=> ! [X1] :
( join(boole_lattice(sK0),X1,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK2)
| ~ element(X1,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_21])]) ).
fof(f386,plain,
! [X1] :
( join(boole_lattice(sK0),X1,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK2)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f369,f208]) ).
fof(f369,plain,
! [X1] :
( join(boole_lattice(sK0),X1,sK2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK2)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f226]) ).
fof(f226,plain,
! [X2,X0,X1] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',d1_lattices) ).
fof(f972,plain,
( ~ spl20_9
| spl20_20 ),
inference(avatar_split_clause,[],[f385,f970,f658]) ).
fof(f970,plain,
( spl20_20
<=> ! [X0] :
( join(boole_lattice(sK0),sK2,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK2,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_20])]) ).
fof(f385,plain,
! [X0] :
( join(boole_lattice(sK0),sK2,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK2,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f368,f208]) ).
fof(f368,plain,
! [X0] :
( join(boole_lattice(sK0),sK2,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK2,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f226]) ).
fof(f950,plain,
( ~ spl20_6
| spl20_19 ),
inference(avatar_split_clause,[],[f321,f948,f592]) ).
fof(f948,plain,
( spl20_19
<=> ! [X3] :
( meet(boole_lattice(sK0),X3,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK1)
| ~ element(X3,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_19])]) ).
fof(f321,plain,
! [X3] :
( meet(boole_lattice(sK0),X3,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK1)
| ~ element(X3,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f304,f208]) ).
fof(f304,plain,
! [X3] :
( meet(boole_lattice(sK0),X3,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),X3,sK1)
| ~ element(X3,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f227]) ).
fof(f928,plain,
( ~ spl20_6
| spl20_18 ),
inference(avatar_split_clause,[],[f320,f926,f592]) ).
fof(f320,plain,
! [X2] :
( meet(boole_lattice(sK0),sK1,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK1,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f303,f208]) ).
fof(f303,plain,
! [X2] :
( meet(boole_lattice(sK0),sK1,X2) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_meet(boole_lattice(sK0)),sK1,X2)
| ~ element(X2,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f227]) ).
fof(f898,plain,
( ~ spl20_9
| spl20_17 ),
inference(avatar_split_clause,[],[f319,f896,f658]) ).
fof(f896,plain,
( spl20_17
<=> ! [X1] :
( join(boole_lattice(sK0),X1,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_17])]) ).
fof(f319,plain,
! [X1] :
( join(boole_lattice(sK0),X1,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f302,f208]) ).
fof(f302,plain,
! [X1] :
( join(boole_lattice(sK0),X1,sK1) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),X1,sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f226]) ).
fof(f876,plain,
( ~ spl20_9
| spl20_16 ),
inference(avatar_split_clause,[],[f318,f874,f658]) ).
fof(f318,plain,
! [X0] :
( join(boole_lattice(sK0),sK1,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK1,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f301,f208]) ).
fof(f301,plain,
! [X0] :
( join(boole_lattice(sK0),sK1,X0) = apply_binary_as_element(the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_carrier(boole_lattice(sK0)),the_L_join(boole_lattice(sK0)),sK1,X0)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f226]) ).
fof(f794,plain,
( ~ spl20_9
| spl20_15 ),
inference(avatar_split_clause,[],[f392,f792,f658]) ).
fof(f792,plain,
( spl20_15
<=> ! [X7] :
( element(join(boole_lattice(sK0),X7,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_15])]) ).
fof(f392,plain,
! [X7] :
( element(join(boole_lattice(sK0),X7,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f375,f208]) ).
fof(f375,plain,
! [X7] :
( element(join(boole_lattice(sK0),X7,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f263]) ).
fof(f263,plain,
! [X2,X0,X1] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> element(join(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_k1_lattices) ).
fof(f772,plain,
( ~ spl20_9
| spl20_14 ),
inference(avatar_split_clause,[],[f391,f770,f658]) ).
fof(f770,plain,
( spl20_14
<=> ! [X6] :
( element(join(boole_lattice(sK0),sK2,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_14])]) ).
fof(f391,plain,
! [X6] :
( element(join(boole_lattice(sK0),sK2,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f374,f208]) ).
fof(f374,plain,
! [X6] :
( element(join(boole_lattice(sK0),sK2,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f263]) ).
fof(f750,plain,
( ~ spl20_6
| spl20_13 ),
inference(avatar_split_clause,[],[f390,f748,f592]) ).
fof(f748,plain,
( spl20_13
<=> ! [X5] :
( element(meet(boole_lattice(sK0),X5,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_13])]) ).
fof(f390,plain,
! [X5] :
( element(meet(boole_lattice(sK0),X5,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f373,f208]) ).
fof(f373,plain,
! [X5] :
( element(meet(boole_lattice(sK0),X5,sK2),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f262]) ).
fof(f262,plain,
! [X2,X0,X1] :
( element(meet(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( element(meet(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( element(meet(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& meet_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> element(meet(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_k2_lattices) ).
fof(f728,plain,
( ~ spl20_6
| spl20_12 ),
inference(avatar_split_clause,[],[f389,f726,f592]) ).
fof(f726,plain,
( spl20_12
<=> ! [X4] :
( element(meet(boole_lattice(sK0),sK2,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
fof(f389,plain,
! [X4] :
( element(meet(boole_lattice(sK0),sK2,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f372,f208]) ).
fof(f372,plain,
! [X4] :
( element(meet(boole_lattice(sK0),sK2,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f201,f262]) ).
fof(f706,plain,
( ~ spl20_9
| spl20_11 ),
inference(avatar_split_clause,[],[f325,f704,f658]) ).
fof(f704,plain,
( spl20_11
<=> ! [X7] :
( element(join(boole_lattice(sK0),X7,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
fof(f325,plain,
! [X7] :
( element(join(boole_lattice(sK0),X7,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f308,f208]) ).
fof(f308,plain,
! [X7] :
( element(join(boole_lattice(sK0),X7,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X7,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f263]) ).
fof(f670,plain,
spl20_9,
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f669,plain,
( $false
| spl20_9 ),
inference(subsumption_resolution,[],[f665,f211]) ).
fof(f665,plain,
( ~ latt_str(boole_lattice(sK0))
| spl20_9 ),
inference(resolution,[],[f660,f223]) ).
fof(f223,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( join_semilatt_str(X0)
& meet_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',dt_l3_lattices) ).
fof(f660,plain,
( ~ join_semilatt_str(boole_lattice(sK0))
| spl20_9 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f664,plain,
( ~ spl20_9
| spl20_10 ),
inference(avatar_split_clause,[],[f324,f662,f658]) ).
fof(f662,plain,
( spl20_10
<=> ! [X6] :
( element(join(boole_lattice(sK0),sK1,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
fof(f324,plain,
! [X6] :
( element(join(boole_lattice(sK0),sK1,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f307,f208]) ).
fof(f307,plain,
! [X6] :
( element(join(boole_lattice(sK0),sK1,X6),the_carrier(boole_lattice(sK0)))
| ~ element(X6,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f263]) ).
fof(f639,plain,
( ~ spl20_6
| spl20_8 ),
inference(avatar_split_clause,[],[f323,f637,f592]) ).
fof(f637,plain,
( spl20_8
<=> ! [X5] :
( element(meet(boole_lattice(sK0),X5,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_8])]) ).
fof(f323,plain,
! [X5] :
( element(meet(boole_lattice(sK0),X5,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f306,f208]) ).
fof(f306,plain,
! [X5] :
( element(meet(boole_lattice(sK0),X5,sK1),the_carrier(boole_lattice(sK0)))
| ~ element(X5,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f262]) ).
fof(f604,plain,
spl20_6,
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f603,plain,
( $false
| spl20_6 ),
inference(subsumption_resolution,[],[f599,f211]) ).
fof(f599,plain,
( ~ latt_str(boole_lattice(sK0))
| spl20_6 ),
inference(resolution,[],[f594,f222]) ).
fof(f222,plain,
! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f594,plain,
( ~ meet_semilatt_str(boole_lattice(sK0))
| spl20_6 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f598,plain,
( ~ spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f322,f596,f592]) ).
fof(f596,plain,
( spl20_7
<=> ! [X4] :
( element(meet(boole_lattice(sK0),sK1,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_7])]) ).
fof(f322,plain,
! [X4] :
( element(meet(boole_lattice(sK0),sK1,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f305,f208]) ).
fof(f305,plain,
! [X4] :
( element(meet(boole_lattice(sK0),sK1,X4),the_carrier(boole_lattice(sK0)))
| ~ element(X4,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f200,f262]) ).
fof(f580,plain,
( spl20_3
| spl20_5 ),
inference(avatar_split_clause,[],[f380,f577,f448]) ).
fof(f577,plain,
( spl20_5
<=> in(sK2,the_carrier(boole_lattice(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_5])]) ).
fof(f380,plain,
( in(sK2,the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f201,f247]) ).
fof(f247,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',t2_subset) ).
fof(f508,plain,
~ spl20_3,
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f507,plain,
( $false
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f506,f210]) ).
fof(f506,plain,
( ~ strict_latt_str(boole_lattice(sK0))
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f505,f211]) ).
fof(f505,plain,
( ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0))
| ~ spl20_3 ),
inference(subsumption_resolution,[],[f465,f205]) ).
fof(f205,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746',fc1_subset_1) ).
fof(f465,plain,
( empty(powerset(sK0))
| ~ latt_str(boole_lattice(sK0))
| ~ strict_latt_str(boole_lattice(sK0))
| ~ spl20_3 ),
inference(superposition,[],[f450,f300]) ).
fof(f450,plain,
( empty(the_carrier(boole_lattice(sK0)))
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f455,plain,
( spl20_3
| spl20_4 ),
inference(avatar_split_clause,[],[f313,f452,f448]) ).
fof(f452,plain,
( spl20_4
<=> in(sK1,the_carrier(boole_lattice(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_4])]) ).
fof(f313,plain,
( in(sK1,the_carrier(boole_lattice(sK0)))
| empty(the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f200,f247]) ).
fof(f403,plain,
( ~ spl20_1
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f202,f400,f396]) ).
fof(f202,plain,
( set_intersection2(sK1,sK2) != meet(boole_lattice(sK0),sK1,sK2)
| set_union2(sK1,sK2) != join(boole_lattice(sK0),sK1,sK2) ),
inference(cnf_transformation,[],[f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 21:06:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.qIA2a5y1mw/Vampire---4.8_8746
% 0.13/0.35 % (8883)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.40 % (8884)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.19/0.40 % (8888)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.19/0.41 % (8894)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.19/0.41 % (8892)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.19/0.41 % (8897)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.19/0.41 % (8890)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.19/0.41 % (8886)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.19/0.62 % (8888)First to succeed.
% 0.19/0.63 % (8888)Refutation found. Thanks to Tanya!
% 0.19/0.63 % SZS status Theorem for Vampire---4
% 0.19/0.63 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.63 % (8888)------------------------------
% 0.19/0.63 % (8888)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.63 % (8888)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.63 % (8888)Termination reason: Refutation
% 0.19/0.63
% 0.19/0.63 % (8888)Memory used [KB]: 14328
% 0.19/0.63 % (8888)Time elapsed: 0.218 s
% 0.19/0.63 % (8888)------------------------------
% 0.19/0.63 % (8888)------------------------------
% 0.19/0.63 % (8883)Success in time 0.274 s
% 0.19/0.63 % Vampire---4.8 exiting
%------------------------------------------------------------------------------