TSTP Solution File: SEU344+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Sun May 5 09:34:24 EDT 2024
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 108
% Syntax : Number of formulae : 1300 ( 335 unt; 0 def)
% Number of atoms : 3578 ( 439 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 4195 (1917 ~;2056 |; 127 &)
% ( 33 <=>; 61 =>; 0 <=; 1 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 44 ( 42 usr; 27 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 13 con; 0-6 aty)
% Number of variables : 1820 (1773 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3667,plain,
$false,
inference(avatar_sat_refutation,[],[f289,f353,f401,f480,f486,f487,f488,f853,f861,f872,f1203,f1211,f1225,f1245,f1247,f1249,f1259,f1428,f1431,f1445,f1580,f1625,f1665,f2182,f2709,f2711,f2713,f2716,f2719,f2736,f2738,f2740,f2766,f2769,f2772,f2787,f2871,f2875,f2899,f2902,f2905,f2933,f2935,f2937,f2939,f2944,f2946,f2949,f2951,f2953,f2955,f2957,f2960,f2964,f2985,f3181,f3183,f3186,f3188,f3190,f3499,f3508,f3666]) ).
fof(f3666,plain,
( spl18_1
| ~ spl18_2
| ~ spl18_17 ),
inference(avatar_contradiction_clause,[],[f3665]) ).
fof(f3665,plain,
( $false
| spl18_1
| ~ spl18_2
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f3664,f186]) ).
fof(f186,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(f3664,plain,
( empty_carrier(boole_lattice(sK0))
| spl18_1
| ~ spl18_2
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f3663,f1422]) ).
fof(f1422,plain,
( join_semilatt_str(boole_lattice(sK0))
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1421,plain,
( spl18_17
<=> join_semilatt_str(boole_lattice(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
fof(f3663,plain,
( ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| spl18_1
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f3662,f177]) ).
fof(f177,plain,
element(sK1,the_carrier(boole_lattice(sK0))),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ( ~ subset(sK1,sK2)
| ~ below(boole_lattice(sK0),sK1,sK2) )
& ( subset(sK1,sK2)
| below(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])],[f140,f142,f141]) ).
fof(f141,plain,
( ? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ below(boole_lattice(X0),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))) )
=> ( ? [X2] :
( ( ~ subset(sK1,X2)
| ~ below(boole_lattice(sK0),sK1,X2) )
& ( subset(sK1,X2)
| below(boole_lattice(sK0),sK1,X2) )
& element(X2,the_carrier(boole_lattice(sK0))) )
& element(sK1,the_carrier(boole_lattice(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
( ? [X2] :
( ( ~ subset(sK1,X2)
| ~ below(boole_lattice(sK0),sK1,X2) )
& ( subset(sK1,X2)
| below(boole_lattice(sK0),sK1,X2) )
& element(X2,the_carrier(boole_lattice(sK0))) )
=> ( ( ~ subset(sK1,sK2)
| ~ below(boole_lattice(sK0),sK1,sK2) )
& ( subset(sK1,sK2)
| below(boole_lattice(sK0),sK1,sK2) )
& element(sK2,the_carrier(boole_lattice(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f140,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ below(boole_lattice(X0),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(flattening,[],[f139]) ).
fof(f139,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ below(boole_lattice(X0),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,[],[f86]) ).
fof(f86,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,[],[f74]) ).
fof(f74,negated_conjecture,
~ ! [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) ) ) ),
inference(negated_conjecture,[],[f73]) ).
fof(f73,conjecture,
! [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/benchmark/theBenchmark.p',t2_lattice3) ).
fof(f3662,plain,
( ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| spl18_1
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f3661,f178]) ).
fof(f178,plain,
element(sK2,the_carrier(boole_lattice(sK0))),
inference(cnf_transformation,[],[f143]) ).
fof(f3661,plain,
( ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| spl18_1
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f3660,f283]) ).
fof(f283,plain,
( ~ below(boole_lattice(sK0),sK1,sK2)
| spl18_1 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f282,plain,
( spl18_1
<=> below(boole_lattice(sK0),sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f3660,plain,
( below(boole_lattice(sK0),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_2 ),
inference(trivial_inequality_removal,[],[f3658]) ).
fof(f3658,plain,
( sK2 != sK2
| below(boole_lattice(sK0),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_2 ),
inference(superposition,[],[f207,f3657]) ).
fof(f3657,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ spl18_2 ),
inference(forward_demodulation,[],[f3129,f3194]) ).
fof(f3194,plain,
( sK2 = set_union2(sK1,sK2)
| ~ spl18_2 ),
inference(resolution,[],[f288,f228]) ).
fof(f228,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f288,plain,
( subset(sK1,sK2)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f286,plain,
( spl18_2
<=> subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f3129,plain,
join(boole_lattice(sK0),sK1,sK2) = set_union2(sK1,sK2),
inference(resolution,[],[f1142,f177]) ).
fof(f1142,plain,
! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| join(boole_lattice(sK0),X0,sK2) = set_union2(X0,sK2) ),
inference(resolution,[],[f230,f178]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(boole_lattice(X0)))
| join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( ( meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2)
& join(boole_lattice(X0),X1,X2) = set_union2(X1,X2) )
| ~ element(X2,the_carrier(boole_lattice(X0))) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2)
& join(boole_lattice(X0),X1,X2) = set_union2(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
fof(f207,plain,
! [X2,X0,X1] :
( join(X0,X1,X2) != X2
| below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below(X0,X1,X2)
| join(X0,X1,X2) != X2 )
& ( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
fof(f3508,plain,
( ~ spl18_25
| ~ spl18_26
| ~ spl18_2
| spl18_4 ),
inference(avatar_split_clause,[],[f3490,f350,f286,f3505,f3501]) ).
fof(f3501,plain,
( spl18_25
<=> in(sK2,sK3(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
fof(f3505,plain,
( spl18_26
<=> in(sK9,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
fof(f350,plain,
( spl18_4
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f3490,plain,
( ~ in(sK9,sK1)
| ~ in(sK2,sK3(sK9))
| ~ spl18_2
| spl18_4 ),
inference(superposition,[],[f3234,f441]) ).
fof(f441,plain,
sK9 = set_union2(sK9,sK3(sK9)),
inference(resolution,[],[f340,f256]) ).
fof(f256,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
~ empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f60,f159]) ).
fof(f159,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f60,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f340,plain,
! [X0] :
( empty(X0)
| set_union2(X0,sK3(X0)) = X0 ),
inference(forward_demodulation,[],[f338,f222]) ).
fof(f222,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f338,plain,
! [X0] :
( set_union2(sK3(X0),X0) = X0
| empty(X0) ),
inference(resolution,[],[f228,f324]) ).
fof(f324,plain,
! [X0] :
( subset(sK3(X0),X0)
| empty(X0) ),
inference(resolution,[],[f233,f190]) ).
fof(f190,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f87,f144]) ).
fof(f144,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f233,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f3234,plain,
( ! [X0,X1] :
( ~ in(set_union2(X0,X1),sK1)
| ~ in(sK2,X1) )
| ~ spl18_2
| spl18_4 ),
inference(resolution,[],[f3222,f1078]) ).
fof(f1078,plain,
! [X2,X0,X1] :
( ~ in(set_union2(X2,X1),X0)
| ~ in(X0,X1) ),
inference(resolution,[],[f1022,f226]) ).
fof(f226,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1022,plain,
! [X2,X0,X1] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(subsumption_resolution,[],[f998,f507]) ).
fof(f507,plain,
! [X2,X0,X1] :
( ~ empty(set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(resolution,[],[f463,f305]) ).
fof(f305,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(superposition,[],[f219,f222]) ).
fof(f219,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f463,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f253,f234]) ).
fof(f234,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f998,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| empty(set_union2(X2,X1))
| in(X0,set_union2(X2,X1)) ),
inference(resolution,[],[f809,f229]) ).
fof(f229,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f809,plain,
! [X2,X0,X1] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(resolution,[],[f703,f305]) ).
fof(f703,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) ),
inference(resolution,[],[f250,f234]) ).
fof(f250,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f3222,plain,
( ! [X0] :
( in(X0,sK2)
| ~ in(X0,sK1) )
| ~ spl18_2
| spl18_4 ),
inference(subsumption_resolution,[],[f3221,f352]) ).
fof(f352,plain,
( ~ empty(sK2)
| spl18_4 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f3221,plain,
( ! [X0] :
( ~ in(X0,sK1)
| empty(sK2)
| in(X0,sK2) )
| ~ spl18_2 ),
inference(resolution,[],[f3192,f229]) ).
fof(f3192,plain,
( ! [X0] :
( element(X0,sK2)
| ~ in(X0,sK1) )
| ~ spl18_2 ),
inference(resolution,[],[f288,f703]) ).
fof(f3499,plain,
( ~ spl18_23
| ~ spl18_24
| ~ spl18_2
| spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f3477,f350,f346,f286,f3496,f3492]) ).
fof(f3492,plain,
( spl18_23
<=> in(sK2,sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
fof(f3496,plain,
( spl18_24
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
fof(f346,plain,
( spl18_3
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f3477,plain,
( ~ in(sK1,sK1)
| ~ in(sK2,sK3(sK1))
| ~ spl18_2
| spl18_3
| spl18_4 ),
inference(superposition,[],[f3234,f2967]) ).
fof(f2967,plain,
( sK1 = set_union2(sK1,sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f347,f340]) ).
fof(f347,plain,
( ~ empty(sK1)
| spl18_3 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f3190,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_contradiction_clause,[],[f3189]) ).
fof(f3189,plain,
( $false
| ~ spl18_1
| ~ spl18_2 ),
inference(global_subsumption,[],[f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612,f180,f2966,f284,f1142,f3140,f3142,f3146,f3137,f3153,f3184,f288]) ).
fof(f3184,plain,
( ~ subset(sK1,sK2)
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f180,f284]) ).
fof(f3153,plain,
! [X2,X3,X0,X1,X4] :
( join(boole_lattice(sK0),apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK2) = set_union2(sK2,apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4))
| ~ element(X4,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ function(X2)
| empty(X1)
| empty(X0) ),
inference(forward_demodulation,[],[f3138,f222]) ).
fof(f3138,plain,
! [X2,X3,X0,X1,X4] :
( join(boole_lattice(sK0),apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK2) = set_union2(apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK2)
| ~ element(X4,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ function(X2)
| empty(X1)
| empty(X0) ),
inference(resolution,[],[f1142,f254]) ).
fof(f3137,plain,
! [X0] :
( join(boole_lattice(sK0),X0,sK2) = set_union2(X0,sK2)
| ~ in(X0,the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f1142,f807]) ).
fof(f3146,plain,
join(boole_lattice(sK0),sK5(the_carrier(boole_lattice(sK0))),sK2) = set_union2(sK2,sK5(the_carrier(boole_lattice(sK0)))),
inference(forward_demodulation,[],[f3133,f222]) ).
fof(f3133,plain,
join(boole_lattice(sK0),sK5(the_carrier(boole_lattice(sK0))),sK2) = set_union2(sK5(the_carrier(boole_lattice(sK0))),sK2),
inference(resolution,[],[f1142,f212]) ).
fof(f3142,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK2) = set_union2(sK2,meet(boole_lattice(sK0),X0,X1))
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(forward_demodulation,[],[f3141,f222]) ).
fof(f3141,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK2) = set_union2(meet(boole_lattice(sK0),X0,X1),sK2)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f3131,f186]) ).
fof(f3131,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK2) = set_union2(meet(boole_lattice(sK0),X0,X1),sK2)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f1142,f241]) ).
fof(f3140,plain,
sK2 = join(boole_lattice(sK0),sK2,sK2),
inference(forward_demodulation,[],[f3130,f218]) ).
fof(f3130,plain,
set_union2(sK2,sK2) = join(boole_lattice(sK0),sK2,sK2),
inference(resolution,[],[f1142,f178]) ).
fof(f284,plain,
( below(boole_lattice(sK0),sK1,sK2)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f2966,plain,
set_union2(sK1,sK2) = join(boole_lattice(sK0),sK2,sK1),
inference(forward_demodulation,[],[f2462,f222]) ).
fof(f2462,plain,
set_union2(sK2,sK1) = join(boole_lattice(sK0),sK2,sK1),
inference(resolution,[],[f1141,f178]) ).
fof(f180,plain,
( ~ subset(sK1,sK2)
| ~ below(boole_lattice(sK0),sK1,sK2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f2612,plain,
! [X0] :
( empty(sK5(sK3(powerset(X0))))
| element(sK5(sK3(sK3(sK3(sK5(sK3(powerset(X0))))))),X0) ),
inference(resolution,[],[f2251,f718]) ).
fof(f2611,plain,
! [X0] :
( empty(sK5(sK3(powerset(X0))))
| in(sK5(sK3(sK3(sK3(sK5(sK3(powerset(X0))))))),X0) ),
inference(resolution,[],[f2251,f1053]) ).
fof(f2610,plain,
! [X0] :
( empty(sK5(sK3(powerset(X0))))
| ~ in(X0,sK5(sK3(sK3(sK3(sK5(sK3(powerset(X0)))))))) ),
inference(resolution,[],[f2251,f1127]) ).
fof(f2608,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| element(sK5(sK3(sK3(sK3(sK5(powerset(X0)))))),X0) ),
inference(resolution,[],[f2251,f706]) ).
fof(f2607,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| in(sK5(sK3(sK3(sK3(sK5(powerset(X0)))))),X0) ),
inference(resolution,[],[f2251,f1052]) ).
fof(f2606,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| ~ in(X0,sK5(sK3(sK3(sK3(sK5(powerset(X0))))))) ),
inference(resolution,[],[f2251,f1126]) ).
fof(f2596,plain,
! [X0] :
( empty(sK3(singleton(X0)))
| element(sK5(sK3(sK3(sK3(sK3(singleton(X0)))))),singleton(X0)) ),
inference(resolution,[],[f2251,f1009]) ).
fof(f2595,plain,
! [X0] :
( empty(sK3(singleton(X0)))
| in(sK5(sK3(sK3(sK3(sK3(singleton(X0)))))),singleton(X0)) ),
inference(resolution,[],[f2251,f1090]) ).
fof(f2594,plain,
! [X0] :
( empty(sK3(singleton(X0)))
| ~ in(singleton(X0),sK5(sK3(sK3(sK3(sK3(singleton(X0))))))) ),
inference(resolution,[],[f2251,f1168]) ).
fof(f2593,plain,
! [X0] :
( empty(sK3(powerset(X0)))
| element(sK5(sK3(sK3(sK3(sK3(powerset(X0)))))),powerset(X0)) ),
inference(resolution,[],[f2251,f1008]) ).
fof(f2592,plain,
! [X0] :
( empty(sK3(powerset(X0)))
| in(sK5(sK3(sK3(sK3(sK3(powerset(X0)))))),powerset(X0)) ),
inference(resolution,[],[f2251,f1089]) ).
fof(f2591,plain,
! [X0] :
( empty(sK3(powerset(X0)))
| ~ in(powerset(X0),sK5(sK3(sK3(sK3(sK3(powerset(X0))))))) ),
inference(resolution,[],[f2251,f1167]) ).
fof(f2618,plain,
! [X0] :
( element(sK5(sK3(sK3(sK3(sK3(X0))))),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f2590,f191]) ).
fof(f2590,plain,
! [X0] :
( empty(sK3(X0))
| element(sK5(sK3(sK3(sK3(sK3(X0))))),X0)
| empty(X0) ),
inference(resolution,[],[f2251,f702]) ).
fof(f2617,plain,
! [X0,X1] : relation(sK5(sK3(sK3(sK3(powerset(cartesian_product2(X0,X1))))))),
inference(subsumption_resolution,[],[f2588,f183]) ).
fof(f2588,plain,
! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| relation(sK5(sK3(sK3(sK3(powerset(cartesian_product2(X0,X1))))))) ),
inference(resolution,[],[f2251,f843]) ).
fof(f2616,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(subsumption_resolution,[],[f2586,f183]) ).
fof(f2586,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(resolution,[],[f2251,f841]) ).
fof(f2585,plain,
! [X0] :
( empty(X0)
| ~ in(X0,sK5(sK3(sK3(sK3(X0))))) ),
inference(resolution,[],[f2251,f226]) ).
fof(f2251,plain,
! [X0] :
( in(sK5(sK3(sK3(sK3(X0)))),X0)
| empty(X0) ),
inference(duplicate_literal_removal,[],[f2245]) ).
fof(f2245,plain,
! [X0] :
( empty(X0)
| empty(X0)
| in(sK5(sK3(sK3(sK3(X0)))),X0) ),
inference(resolution,[],[f806,f229]) ).
fof(f2570,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(sK3(sK3(powerset(X0)))))))),
inference(superposition,[],[f1940,f2190]) ).
fof(f2569,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(sK3(sK3(powerset(X0))))))),
inference(superposition,[],[f1939,f2190]) ).
fof(f2568,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(sK3(powerset(X0))))),
inference(superposition,[],[f1920,f2190]) ).
fof(f2564,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(sK3(sK3(powerset(X0))))),
inference(superposition,[],[f1754,f2190]) ).
fof(f2560,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f1079,f2190]) ).
fof(f2559,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f1078,f2190]) ).
fof(f2556,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f1022,f2190]) ).
fof(f2554,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f809,f2190]) ).
fof(f2190,plain,
! [X0] : set_union2(X0,sK5(sK3(sK3(powerset(X0))))) = X0,
inference(superposition,[],[f775,f222]) ).
fof(f2536,plain,
! [X0] :
( empty_set = sK5(sK3(sK3(powerset(sK5(sK3(sK3(powerset(X0))))))))
| ~ empty(X0) ),
inference(resolution,[],[f2150,f2142]) ).
fof(f2535,plain,
! [X0] :
( empty_set = sK5(sK3(sK3(powerset(sK5(sK3(powerset(X0)))))))
| ~ empty(X0) ),
inference(resolution,[],[f2150,f732]) ).
fof(f2534,plain,
! [X0] :
( empty_set = sK5(sK3(sK3(powerset(sK5(powerset(X0))))))
| ~ empty(X0) ),
inference(resolution,[],[f2150,f361]) ).
fof(f2530,plain,
! [X0] :
( empty_set = sK5(sK3(sK3(powerset(X0))))
| set_union2(X0,sK3(X0)) = X0 ),
inference(resolution,[],[f2150,f340]) ).
fof(f2150,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(sK3(sK3(powerset(X0)))) ),
inference(resolution,[],[f2142,f203]) ).
fof(f2508,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,set_union2(X1,powerset(cartesian_product2(X2,X3))))),X2,X3),
inference(resolution,[],[f2021,f653]) ).
fof(f2021,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X0,set_union2(X1,powerset(X2)))),X2),
inference(resolution,[],[f1920,f388]) ).
fof(f2013,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(sK3(powerset(X0)))))),
inference(superposition,[],[f1841,f723]) ).
fof(f2007,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK5(powerset(sK3(singleton(X0))))),
inference(superposition,[],[f1841,f673]) ).
fof(f2006,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK5(powerset(sK3(powerset(X0))))),
inference(superposition,[],[f1841,f646]) ).
fof(f2472,plain,
sK1 = join(boole_lattice(sK0),sK1,sK1),
inference(forward_demodulation,[],[f2461,f218]) ).
fof(f2461,plain,
set_union2(sK1,sK1) = join(boole_lattice(sK0),sK1,sK1),
inference(resolution,[],[f1141,f177]) ).
fof(f2488,plain,
! [X2,X3,X0,X1,X4] :
( join(boole_lattice(sK0),apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK1) = set_union2(sK1,apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4))
| ~ element(X4,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ function(X2)
| empty(X1)
| empty(X0) ),
inference(forward_demodulation,[],[f2471,f222]) ).
fof(f2471,plain,
! [X2,X3,X0,X1,X4] :
( join(boole_lattice(sK0),apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK1) = set_union2(apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),sK1)
| ~ element(X4,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ function(X2)
| empty(X1)
| empty(X0) ),
inference(resolution,[],[f1141,f254]) ).
fof(f2470,plain,
! [X0] :
( join(boole_lattice(sK0),X0,sK1) = set_union2(X0,sK1)
| ~ in(X0,the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f1141,f807]) ).
fof(f2481,plain,
join(boole_lattice(sK0),sK5(the_carrier(boole_lattice(sK0))),sK1) = set_union2(sK1,sK5(the_carrier(boole_lattice(sK0)))),
inference(forward_demodulation,[],[f2466,f222]) ).
fof(f2466,plain,
join(boole_lattice(sK0),sK5(the_carrier(boole_lattice(sK0))),sK1) = set_union2(sK5(the_carrier(boole_lattice(sK0))),sK1),
inference(resolution,[],[f1141,f212]) ).
fof(f2477,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK1) = set_union2(sK1,meet(boole_lattice(sK0),X0,X1))
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(forward_demodulation,[],[f2476,f222]) ).
fof(f2476,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK1) = set_union2(meet(boole_lattice(sK0),X0,X1),sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2464,f186]) ).
fof(f2464,plain,
! [X0,X1] :
( join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),sK1) = set_union2(meet(boole_lattice(sK0),X0,X1),sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f1141,f241]) ).
fof(f1141,plain,
! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| join(boole_lattice(sK0),X0,sK1) = set_union2(X0,sK1) ),
inference(resolution,[],[f230,f177]) ).
fof(f2456,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X0,powerset(X1)))),X1),
inference(superposition,[],[f1951,f335]) ).
fof(f2454,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X0,powerset(X1)))),X1),
inference(superposition,[],[f1951,f222]) ).
fof(f2453,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X0,powerset(X1)))),X1),
inference(superposition,[],[f1951,f222]) ).
fof(f2442,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(set_union2(X0,powerset(cartesian_product2(X1,X2))),X3)),X1,X2),
inference(resolution,[],[f1951,f653]) ).
fof(f1951,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(set_union2(X0,powerset(X1)),X2)),X1),
inference(resolution,[],[f1754,f388]) ).
fof(f2409,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(set_union2(X0,X1),X2,X3)
| ~ in(powerset(cartesian_product2(X2,X3)),X0) ),
inference(resolution,[],[f655,f1030]) ).
fof(f2408,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(set_union2(X0,X1),X2,X3)
| ~ in(powerset(cartesian_product2(X2,X3)),X1) ),
inference(resolution,[],[f655,f1078]) ).
fof(f2407,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(set_union2(X0,powerset(cartesian_product2(X1,X2))),X3)),X1,X2),
inference(resolution,[],[f655,f1754]) ).
fof(f2406,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(set_union2(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1),
inference(resolution,[],[f655,f1727]) ).
fof(f2405,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,set_union2(X1,powerset(cartesian_product2(X2,X3))))),X2,X3),
inference(resolution,[],[f655,f1920]) ).
fof(f2404,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,set_union2(powerset(cartesian_product2(X1,X2)),X3))),X1,X2),
inference(resolution,[],[f655,f1728]) ).
fof(f2403,plain,
! [X2,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,powerset(cartesian_product2(X1,X2)))),X1,X2),
inference(resolution,[],[f655,f1757]) ).
fof(f2402,plain,
! [X2,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(powerset(cartesian_product2(X0,X1)),X2)),X0,X1),
inference(resolution,[],[f655,f1726]) ).
fof(f2401,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(powerset(X0),X1,X2)
| ~ subset(powerset(cartesian_product2(X1,X2)),X0) ),
inference(resolution,[],[f655,f406]) ).
fof(f2399,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(powerset(cartesian_product2(X1,X2)),X0) ),
inference(resolution,[],[f655,f226]) ).
fof(f2396,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ),
inference(resolution,[],[f655,f841]) ).
fof(f655,plain,
! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(subsumption_resolution,[],[f654,f183]) ).
fof(f654,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ),
inference(resolution,[],[f239,f229]) ).
fof(f2379,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK5(sK3(powerset(sK3(singleton(X0)))))),
inference(superposition,[],[f1940,f436]) ).
fof(f2378,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK5(sK3(powerset(sK3(powerset(X0)))))),
inference(superposition,[],[f1940,f432]) ).
fof(f2377,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(sK3(powerset(X0))))))),
inference(superposition,[],[f1940,f738]) ).
fof(f2376,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(powerset(X0)))))),
inference(superposition,[],[f1940,f355]) ).
fof(f2375,plain,
! [X0] :
( ~ in(powerset(X0),sK5(sK3(powerset(sK3(X0)))))
| empty_set = X0 ),
inference(superposition,[],[f1940,f428]) ).
fof(f1940,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1728,f723]) ).
fof(f1934,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,singleton(X0))),sK3(singleton(X0))),
inference(superposition,[],[f1728,f673]) ).
fof(f1933,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,powerset(X0))),sK3(powerset(X0))),
inference(superposition,[],[f1728,f646]) ).
fof(f2336,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X1,powerset(X0)))),X0),
inference(superposition,[],[f1916,f335]) ).
fof(f2334,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X1,powerset(X0)))),X0),
inference(superposition,[],[f1916,f222]) ).
fof(f2333,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(X1,powerset(X0)))),X0),
inference(superposition,[],[f1916,f222]) ).
fof(f2330,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,set_union2(powerset(cartesian_product2(X1,X2)),X3))),X1,X2),
inference(resolution,[],[f1916,f653]) ).
fof(f1916,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X0,set_union2(powerset(X1),X2))),X1),
inference(resolution,[],[f1728,f388]) ).
fof(f2323,plain,
~ in(powerset(sK9),sK5(sK3(powerset(sK3(sK9))))),
inference(superposition,[],[f1842,f494]) ).
fof(f2326,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(sK3(sK3(powerset(X0)))))))),
inference(superposition,[],[f1842,f775]) ).
fof(f2325,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(sK3(powerset(X0))))))),
inference(superposition,[],[f1842,f723]) ).
fof(f2324,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(sK5(powerset(X0)))))),
inference(superposition,[],[f1842,f339]) ).
fof(f2319,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK5(sK3(powerset(sK3(singleton(X0)))))),
inference(superposition,[],[f1842,f673]) ).
fof(f2318,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK5(sK3(powerset(sK3(powerset(X0)))))),
inference(superposition,[],[f1842,f646]) ).
fof(f2317,plain,
! [X0] :
( ~ in(powerset(X0),sK5(sK3(powerset(sK3(X0)))))
| empty_set = X0 ),
inference(superposition,[],[f1842,f632]) ).
fof(f2308,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1842,f335]) ).
fof(f2306,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1842,f222]) ).
fof(f2305,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1842,f222]) ).
fof(f1842,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1727,f723]) ).
fof(f2299,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,singleton(X0))),sK3(singleton(X0))),
inference(superposition,[],[f1836,f335]) ).
fof(f2297,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,singleton(X0))),sK3(singleton(X0))),
inference(superposition,[],[f1836,f222]) ).
fof(f2296,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,singleton(X0))),sK3(singleton(X0))),
inference(superposition,[],[f1836,f222]) ).
fof(f1836,plain,
! [X0,X1] : ~ in(powerset(set_union2(singleton(X0),X1)),sK3(singleton(X0))),
inference(superposition,[],[f1727,f673]) ).
fof(f2289,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,powerset(X0))),sK3(powerset(X0))),
inference(superposition,[],[f1835,f335]) ).
fof(f2287,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,powerset(X0))),sK3(powerset(X0))),
inference(superposition,[],[f1835,f222]) ).
fof(f2286,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,powerset(X0))),sK3(powerset(X0))),
inference(superposition,[],[f1835,f222]) ).
fof(f1835,plain,
! [X0,X1] : ~ in(powerset(set_union2(powerset(X0),X1)),sK3(powerset(X0))),
inference(superposition,[],[f1727,f646]) ).
fof(f2279,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(powerset(X0),X1))),X0),
inference(superposition,[],[f1818,f335]) ).
fof(f2277,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(powerset(X0),X1))),X0),
inference(superposition,[],[f1818,f222]) ).
fof(f2276,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(X2,set_union2(powerset(X0),X1))),X0),
inference(superposition,[],[f1818,f222]) ).
fof(f2270,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(set_union2(X1,powerset(X0)),X2)),X0),
inference(superposition,[],[f1818,f335]) ).
fof(f2268,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(set_union2(X1,powerset(X0)),X2)),X0),
inference(superposition,[],[f1818,f222]) ).
fof(f2267,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(set_union2(X1,powerset(X0)),X2)),X0),
inference(superposition,[],[f1818,f222]) ).
fof(f2264,plain,
! [X2,X3,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(set_union2(powerset(cartesian_product2(X0,X1)),X2),X3)),X0,X1),
inference(resolution,[],[f1818,f653]) ).
fof(f1818,plain,
! [X2,X0,X1] : ~ subset(powerset(set_union2(set_union2(powerset(X0),X1),X2)),X0),
inference(resolution,[],[f1727,f388]) ).
fof(f2261,plain,
! [X0,X1] : relation(sK5(sK3(sK3(sK3(powerset(cartesian_product2(X0,X1))))))),
inference(resolution,[],[f2254,f417]) ).
fof(f2260,plain,
! [X0] : set_union2(sK5(sK3(sK3(sK3(powerset(X0))))),X0) = X0,
inference(resolution,[],[f2254,f228]) ).
fof(f2259,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(sK3(sK3(powerset(X1))))))
| ~ empty(X1) ),
inference(resolution,[],[f2254,f463]) ).
fof(f2258,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(sK3(sK3(powerset(X1))))))
| element(X0,X1) ),
inference(resolution,[],[f2254,f703]) ).
fof(f2254,plain,
! [X0] : subset(sK5(sK3(sK3(sK3(powerset(X0))))),X0),
inference(subsumption_resolution,[],[f2243,f183]) ).
fof(f2243,plain,
! [X0] :
( empty(powerset(X0))
| subset(sK5(sK3(sK3(sK3(powerset(X0))))),X0) ),
inference(resolution,[],[f806,f233]) ).
fof(f2257,plain,
! [X0,X1] :
( meet(X0,X1,sK5(sK3(sK3(sK3(the_carrier(X0)))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,sK5(sK3(sK3(sK3(the_carrier(X0))))))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(global_subsumption,[],[f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f655,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1141,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1818,f1819,f1820,f1822,f1823,f1825,f1834,f1835,f1836,f1842,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1916,f1917,f1918,f1921,f1923,f1932,f1933,f1934,f1940,f1749,f1754,f1951,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2006,f2007,f2013,f2011,f524,f2020,f1920,f2021,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f2150,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2190,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2254,f2255,f2251,f2246,f2247,f2248,f2256,f2249]) ).
fof(f2249,plain,
! [X0,X1] :
( empty(the_carrier(X0))
| meet(X0,X1,sK5(sK3(sK3(sK3(the_carrier(X0)))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,sK5(sK3(sK3(sK3(the_carrier(X0))))))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f806,f204]) ).
fof(f2256,plain,
! [X0,X1] :
( join(X0,X1,sK5(sK3(sK3(sK3(the_carrier(X0)))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK5(sK3(sK3(sK3(the_carrier(X0))))))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(global_subsumption,[],[f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f655,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1141,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1818,f1819,f1820,f1822,f1823,f1825,f1834,f1835,f1836,f1842,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1916,f1917,f1918,f1921,f1923,f1932,f1933,f1934,f1940,f1749,f1754,f1951,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2006,f2007,f2013,f2011,f524,f2020,f1920,f2021,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f2150,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2190,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2254,f2255,f2251,f2246,f2247,f2248]) ).
fof(f2248,plain,
! [X0,X1] :
( empty(the_carrier(X0))
| join(X0,X1,sK5(sK3(sK3(sK3(the_carrier(X0)))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK5(sK3(sK3(sK3(the_carrier(X0))))))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f806,f205]) ).
fof(f2247,plain,
! [X0,X1] :
( empty(the_carrier(boole_lattice(X0)))
| join(boole_lattice(X0),X1,sK5(sK3(sK3(sK3(the_carrier(boole_lattice(X0))))))) = set_union2(X1,sK5(sK3(sK3(sK3(the_carrier(boole_lattice(X0)))))))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f806,f230]) ).
fof(f2246,plain,
! [X0,X1] :
( empty(the_carrier(boole_lattice(X0)))
| meet(boole_lattice(X0),X1,sK5(sK3(sK3(sK3(the_carrier(boole_lattice(X0))))))) = set_intersection2(X1,sK5(sK3(sK3(sK3(the_carrier(boole_lattice(X0)))))))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f806,f231]) ).
fof(f2255,plain,
! [X0,X1] : relation(sK5(sK3(sK3(sK3(powerset(cartesian_product2(X0,X1))))))),
inference(subsumption_resolution,[],[f2244,f183]) ).
fof(f2244,plain,
! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| relation(sK5(sK3(sK3(sK3(powerset(cartesian_product2(X0,X1))))))) ),
inference(resolution,[],[f806,f240]) ).
fof(f2253,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(subsumption_resolution,[],[f2242,f183]) ).
fof(f2242,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(resolution,[],[f806,f253]) ).
fof(f2252,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(subsumption_resolution,[],[f2241,f183]) ).
fof(f2241,plain,
! [X0,X1] :
( empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(sK3(powerset(X0)))))) ),
inference(resolution,[],[f806,f250]) ).
fof(f806,plain,
! [X0] :
( element(sK5(sK3(sK3(sK3(X0)))),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f802,f191]) ).
fof(f802,plain,
! [X0] :
( empty(sK3(X0))
| element(sK5(sK3(sK3(sK3(X0)))),X0)
| empty(X0) ),
inference(resolution,[],[f769,f702]) ).
fof(f2211,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(sK3(powerset(X0))))),
inference(superposition,[],[f1726,f775]) ).
fof(f2239,plain,
( empty(sK3(sK3(powerset(empty_set))))
| in(empty_set,sK3(sK3(powerset(empty_set)))) ),
inference(resolution,[],[f2238,f229]) ).
fof(f2238,plain,
element(empty_set,sK3(sK3(powerset(empty_set)))),
inference(superposition,[],[f212,f2192]) ).
fof(f2237,plain,
( in(empty_set,sK3(sK3(powerset(empty_set))))
| empty(sK3(sK3(powerset(empty_set)))) ),
inference(superposition,[],[f379,f2192]) ).
fof(f2192,plain,
empty_set = sK5(sK3(sK3(powerset(empty_set)))),
inference(superposition,[],[f775,f185]) ).
fof(f2222,plain,
empty_set = sK5(sK3(sK3(powerset(empty_set)))),
inference(superposition,[],[f185,f775]) ).
fof(f2216,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(sK3(sK3(powerset(X0))))))),
inference(superposition,[],[f1841,f775]) ).
fof(f2213,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(sK3(powerset(X0))))),
inference(superposition,[],[f1728,f775]) ).
fof(f2212,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(sK3(sK3(powerset(X0))))),
inference(superposition,[],[f1727,f775]) ).
fof(f2208,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f1031,f775]) ).
fof(f2207,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f1030,f775]) ).
fof(f2205,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f997,f775]) ).
fof(f2203,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(superposition,[],[f808,f775]) ).
fof(f2195,plain,
! [X0] : set_union2(X0,sK5(sK3(sK3(powerset(X0))))) = X0,
inference(superposition,[],[f222,f775]) ).
fof(f2194,plain,
! [X0] : set_union2(X0,sK5(sK3(sK3(powerset(X0))))) = X0,
inference(superposition,[],[f222,f775]) ).
fof(f2191,plain,
! [X0] : set_union2(X0,sK5(sK3(sK3(powerset(X0))))) = X0,
inference(superposition,[],[f775,f222]) ).
fof(f775,plain,
! [X0] : set_union2(sK5(sK3(sK3(powerset(X0)))),X0) = X0,
inference(resolution,[],[f772,f228]) ).
fof(f761,plain,
( in(empty_set,sK3(powerset(empty_set)))
| empty(sK3(powerset(empty_set))) ),
inference(superposition,[],[f379,f740]) ).
fof(f1750,plain,
! [X0,X1] :
( ~ in(powerset(X1),sK5(powerset(X0)))
| ~ subset(X0,X1) ),
inference(superposition,[],[f1031,f339]) ).
fof(f2172,plain,
! [X0] :
( ~ in(singleton(X0),sK5(sK3(sK3(sK3(singleton(X0))))))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1168,f769]) ).
fof(f2171,plain,
! [X0] :
( ~ in(singleton(X0),sK5(sK3(sK3(singleton(X0)))))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1168,f717]) ).
fof(f2170,plain,
! [X0] :
( ~ in(singleton(X0),sK5(sK3(singleton(X0))))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1168,f379]) ).
fof(f1168,plain,
! [X0,X1] :
( ~ in(X1,sK3(singleton(X0)))
| ~ in(singleton(X0),X1) ),
inference(superposition,[],[f1078,f436]) ).
fof(f2169,plain,
! [X0] :
( ~ in(powerset(X0),sK5(sK3(sK3(sK3(powerset(X0))))))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1167,f769]) ).
fof(f2168,plain,
! [X0] :
( ~ in(powerset(X0),sK5(sK3(sK3(powerset(X0)))))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1167,f717]) ).
fof(f1167,plain,
! [X0,X1] :
( ~ in(X1,sK3(powerset(X0)))
| ~ in(powerset(X0),X1) ),
inference(superposition,[],[f1078,f432]) ).
fof(f2165,plain,
! [X0] :
( ~ in(X0,sK5(sK3(sK3(sK5(sK3(powerset(X0)))))))
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1127,f769]) ).
fof(f2164,plain,
! [X0] :
( ~ in(X0,sK5(sK3(sK5(sK3(powerset(X0))))))
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1127,f717]) ).
fof(f2163,plain,
! [X0] :
( ~ in(X0,sK5(sK5(sK3(powerset(X0)))))
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1127,f379]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(powerset(X0))))
| ~ in(X0,X1) ),
inference(superposition,[],[f1030,f723]) ).
fof(f2161,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f223,f593]) ).
fof(f2160,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f590,f593]) ).
fof(f2159,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f593,f593]) ).
fof(f2158,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f593,f590]) ).
fof(f2157,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f593,f223]) ).
fof(f2156,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f593,f220]) ).
fof(f2155,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f593,f220]) ).
fof(f593,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f223,f220]) ).
fof(f2153,plain,
! [X0] :
( in(sK5(sK3(sK3(sK5(sK3(powerset(X0)))))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1053,f769]) ).
fof(f2152,plain,
! [X0] :
( in(sK5(sK3(sK5(sK3(powerset(X0))))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1053,f717]) ).
fof(f2151,plain,
! [X0] :
( in(sK5(sK5(sK3(powerset(X0)))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f1053,f379]) ).
fof(f1053,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(powerset(X0))))
| in(X1,X0) ),
inference(superposition,[],[f997,f723]) ).
fof(f2149,plain,
! [X0,X1] :
( ~ empty(X0)
| sK5(sK3(sK3(powerset(X0)))) = X1
| ~ empty(X1) ),
inference(resolution,[],[f2142,f235]) ).
fof(f2148,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(powerset(sK5(sK3(sK3(powerset(X0)))))) ),
inference(resolution,[],[f2142,f368]) ).
fof(f2147,plain,
! [X0,X1] :
( ~ empty(X0)
| sK5(powerset(X1)) = sK5(sK3(sK3(powerset(X0))))
| ~ empty(X1) ),
inference(resolution,[],[f2142,f367]) ).
fof(f2146,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(sK3(powerset(sK5(sK3(sK3(powerset(X0))))))) ),
inference(resolution,[],[f2142,f737]) ).
fof(f2145,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(powerset(sK5(powerset(sK5(sK3(sK3(powerset(X0)))))))) ),
inference(resolution,[],[f2142,f409]) ).
fof(f2142,plain,
! [X0] :
( empty(sK5(sK3(sK3(powerset(X0)))))
| ~ empty(X0) ),
inference(resolution,[],[f771,f379]) ).
fof(f2144,plain,
! [X0] :
( ~ empty(X0)
| empty(sK5(sK3(sK3(powerset(X0))))) ),
inference(resolution,[],[f771,f769]) ).
fof(f2143,plain,
! [X0] :
( ~ empty(X0)
| empty(sK5(sK3(sK3(powerset(X0))))) ),
inference(resolution,[],[f771,f717]) ).
fof(f771,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(sK3(powerset(X0)))))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f765,f183]) ).
fof(f765,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(resolution,[],[f731,f253]) ).
fof(f2130,plain,
! [X0] :
( empty_set = sK5(powerset(sK5(powerset(sK5(sK3(powerset(X0)))))))
| ~ empty(X0) ),
inference(resolution,[],[f409,f732]) ).
fof(f2129,plain,
! [X0] :
( empty_set = sK5(powerset(sK5(powerset(sK5(powerset(X0))))))
| ~ empty(X0) ),
inference(resolution,[],[f409,f361]) ).
fof(f2125,plain,
! [X0] :
( empty_set = sK5(powerset(sK5(powerset(X0))))
| set_union2(X0,sK3(X0)) = X0 ),
inference(resolution,[],[f409,f340]) ).
fof(f409,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(powerset(sK5(powerset(X0)))) ),
inference(resolution,[],[f368,f361]) ).
fof(f2124,plain,
! [X0] :
( in(sK5(sK3(sK3(sK3(singleton(X0))))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1090,f769]) ).
fof(f2123,plain,
! [X0] :
( in(sK5(sK3(sK3(singleton(X0)))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1090,f717]) ).
fof(f2122,plain,
! [X0] :
( in(sK5(sK3(singleton(X0))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1090,f379]) ).
fof(f1090,plain,
! [X0,X1] :
( ~ in(X1,sK3(singleton(X0)))
| in(X1,singleton(X0)) ),
inference(superposition,[],[f1022,f436]) ).
fof(f2121,plain,
! [X0] :
( in(sK5(sK3(sK3(sK3(powerset(X0))))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1089,f769]) ).
fof(f2120,plain,
! [X0] :
( in(sK5(sK3(sK3(powerset(X0)))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1089,f717]) ).
fof(f2119,plain,
! [X0] :
( in(sK5(sK3(powerset(X0))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1089,f379]) ).
fof(f1089,plain,
! [X0,X1] :
( ~ in(X1,sK3(powerset(X0)))
| in(X1,powerset(X0)) ),
inference(superposition,[],[f1022,f432]) ).
fof(f2106,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| ~ in(powerset(X1),sK3(singleton(X0))) ),
inference(superposition,[],[f1079,f436]) ).
fof(f2105,plain,
! [X0,X1] :
( ~ subset(powerset(X0),X1)
| ~ in(powerset(X1),sK3(powerset(X0))) ),
inference(superposition,[],[f1079,f432]) ).
fof(f2104,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f1079,f738]) ).
fof(f2103,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK5(powerset(X0))) ),
inference(superposition,[],[f1079,f355]) ).
fof(f2102,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1079,f428]) ).
fof(f2095,plain,
! [X2,X3,X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),X2)
| ~ relation_of2_as_subset(set_union2(X3,X2),X0,X1) ),
inference(resolution,[],[f1079,f653]) ).
fof(f1079,plain,
! [X2,X0,X1] :
( ~ subset(set_union2(X2,X1),X0)
| ~ in(powerset(X0),X1) ),
inference(resolution,[],[f1022,f406]) ).
fof(f2012,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(powerset(X0))))),
inference(superposition,[],[f1841,f339]) ).
fof(f2089,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f220,f590]) ).
fof(f2088,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f220,f590]) ).
fof(f2087,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f223,f590]) ).
fof(f2086,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f590,f220]) ).
fof(f2085,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f590,f220]) ).
fof(f2084,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
inference(superposition,[],[f590,f590]) ).
fof(f2083,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f590,f223]) ).
fof(f590,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f223,f220]) ).
fof(f2066,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK5(powerset(sK3(singleton(X0))))),
inference(superposition,[],[f1939,f436]) ).
fof(f2065,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK5(powerset(sK3(powerset(X0))))),
inference(superposition,[],[f1939,f432]) ).
fof(f2064,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(sK3(powerset(X0)))))),
inference(superposition,[],[f1939,f738]) ).
fof(f2063,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(sK5(powerset(X0))))),
inference(superposition,[],[f1939,f355]) ).
fof(f2062,plain,
! [X0] :
( ~ in(powerset(X0),sK5(powerset(sK3(X0))))
| empty_set = X0 ),
inference(superposition,[],[f1939,f428]) ).
fof(f1939,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(powerset(X0))),
inference(superposition,[],[f1728,f339]) ).
fof(f2034,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,singleton(X0))),sK3(singleton(X0))),
inference(superposition,[],[f1920,f436]) ).
fof(f2033,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,powerset(X0))),sK3(powerset(X0))),
inference(superposition,[],[f1920,f432]) ).
fof(f2032,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1920,f738]) ).
fof(f2031,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(powerset(X0))),
inference(superposition,[],[f1920,f355]) ).
fof(f2030,plain,
! [X0,X1] :
( ~ in(powerset(set_union2(X1,X0)),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1920,f428]) ).
fof(f2023,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X2),
inference(resolution,[],[f1920,f997]) ).
fof(f2022,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X3),
inference(resolution,[],[f1920,f1022]) ).
fof(f1920,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X1,X0))),X0),
inference(superposition,[],[f1728,f222]) ).
fof(f2020,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ in(powerset(the_carrier(X0)),sK4(X0)) ),
inference(resolution,[],[f524,f226]) ).
fof(f524,plain,
! [X0] :
( in(sK4(X0),powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(subsumption_resolution,[],[f523,f183]) ).
fof(f523,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| in(sK4(X0),powerset(the_carrier(X0))) ),
inference(resolution,[],[f209,f229]) ).
fof(f2011,plain,
~ in(powerset(sK9),sK5(powerset(sK3(sK9)))),
inference(superposition,[],[f1841,f494]) ).
fof(f2005,plain,
! [X0] :
( ~ in(powerset(X0),sK5(powerset(sK3(X0))))
| empty_set = X0 ),
inference(superposition,[],[f1841,f632]) ).
fof(f1996,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(powerset(X0))),
inference(superposition,[],[f1841,f335]) ).
fof(f1994,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(powerset(X0))),
inference(superposition,[],[f1841,f222]) ).
fof(f1993,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),sK5(powerset(X0))),
inference(superposition,[],[f1841,f222]) ).
fof(f1841,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(powerset(X0))),
inference(superposition,[],[f1727,f339]) ).
fof(f1769,plain,
! [X0] :
( ~ in(powerset(X0),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1726,f632]) ).
fof(f1989,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_L_meet(sK17) = X2
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f249,f971]) ).
fof(f1988,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_L_meet(sK16) = X2
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f249,f970]) ).
fof(f1987,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_L_meet(sK17) = X2
| ~ relation_of2(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_meet(sK17))
| ~ relation_of2(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_join(sK17)) ),
inference(superposition,[],[f249,f971]) ).
fof(f1986,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_L_meet(sK16) = X2
| ~ relation_of2(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_meet(sK16))
| ~ relation_of2(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_join(sK16)) ),
inference(superposition,[],[f249,f970]) ).
fof(f249,plain,
! [X2,X3,X0,X1,X4,X5] :
( latt_str_of(X0,X1,X2) != latt_str_of(X3,X4,X5)
| X2 = X5
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( X2 = X5
& X1 = X4
& X0 = X3 )
| latt_str_of(X0,X1,X2) != latt_str_of(X3,X4,X5) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( X2 = X5
& X1 = X4
& X0 = X3 )
| latt_str_of(X0,X1,X2) != latt_str_of(X3,X4,X5) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( relation_of2(X2,cartesian_product2(X0,X0),X0)
& quasi_total(X2,cartesian_product2(X0,X0),X0)
& function(X2)
& relation_of2(X1,cartesian_product2(X0,X0),X0)
& quasi_total(X1,cartesian_product2(X0,X0),X0)
& function(X1) )
=> ! [X3,X4,X5] :
( latt_str_of(X0,X1,X2) = latt_str_of(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(f1981,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X1),
inference(superposition,[],[f1754,f335]) ).
fof(f1979,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X1),
inference(superposition,[],[f1754,f222]) ).
fof(f1978,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X1),
inference(superposition,[],[f1754,f222]) ).
fof(f1964,plain,
! [X0,X1] : ~ in(powerset(set_union2(singleton(X0),X1)),sK3(singleton(X0))),
inference(superposition,[],[f1754,f436]) ).
fof(f1963,plain,
! [X0,X1] : ~ in(powerset(set_union2(powerset(X0),X1)),sK3(powerset(X0))),
inference(superposition,[],[f1754,f432]) ).
fof(f1962,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1754,f738]) ).
fof(f1961,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),sK5(powerset(X0))),
inference(superposition,[],[f1754,f355]) ).
fof(f1960,plain,
! [X0,X1] :
( ~ in(powerset(set_union2(X0,X1)),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1754,f428]) ).
fof(f1953,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X1),
inference(resolution,[],[f1754,f997]) ).
fof(f1952,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X2),
inference(resolution,[],[f1754,f1022]) ).
fof(f1754,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X1),
inference(resolution,[],[f1726,f1022]) ).
fof(f1749,plain,
! [X0] :
( ~ in(powerset(X0),sK3(sK9))
| ~ subset(sK9,X0) ),
inference(superposition,[],[f1031,f494]) ).
fof(f1932,plain,
! [X0,X1] :
( ~ in(powerset(set_union2(X1,X0)),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1728,f632]) ).
fof(f1923,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X1,X0))),X0),
inference(superposition,[],[f1728,f335]) ).
fof(f1921,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X1,X0))),X0),
inference(superposition,[],[f1728,f222]) ).
fof(f1918,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X1),
inference(resolution,[],[f1728,f997]) ).
fof(f1917,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X2),
inference(resolution,[],[f1728,f1022]) ).
fof(f1728,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X1),
inference(resolution,[],[f1031,f305]) ).
fof(f1900,plain,
! [X0] : ~ in(powerset(set_union2(X0,sK9)),sK3(sK9)),
inference(superposition,[],[f1840,f222]) ).
fof(f1903,plain,
! [X0] : ~ in(powerset(set_union2(X0,sK9)),sK3(sK9)),
inference(superposition,[],[f1840,f335]) ).
fof(f1901,plain,
! [X0] : ~ in(powerset(set_union2(X0,sK9)),sK3(sK9)),
inference(superposition,[],[f1840,f222]) ).
fof(f1840,plain,
! [X0] : ~ in(powerset(set_union2(sK9,X0)),sK3(sK9)),
inference(superposition,[],[f1727,f494]) ).
fof(f1886,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_L_join(sK17) = X1
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f248,f971]) ).
fof(f1885,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_L_join(sK16) = X1
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f248,f970]) ).
fof(f1884,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_L_join(sK17) = X1
| ~ relation_of2(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_meet(sK17))
| ~ relation_of2(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_join(sK17)) ),
inference(superposition,[],[f248,f971]) ).
fof(f1883,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_L_join(sK16) = X1
| ~ relation_of2(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_meet(sK16))
| ~ relation_of2(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_join(sK16)) ),
inference(superposition,[],[f248,f970]) ).
fof(f248,plain,
! [X2,X3,X0,X1,X4,X5] :
( latt_str_of(X0,X1,X2) != latt_str_of(X3,X4,X5)
| X1 = X4
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f1848,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X0),
inference(superposition,[],[f1727,f335]) ).
fof(f1846,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X0),
inference(superposition,[],[f1727,f222]) ).
fof(f1845,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X2,set_union2(X0,X1))),X0),
inference(superposition,[],[f1727,f222]) ).
fof(f1834,plain,
! [X0,X1] :
( ~ in(powerset(set_union2(X0,X1)),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1727,f632]) ).
fof(f1825,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X1,X0),X2)),X0),
inference(superposition,[],[f1727,f335]) ).
fof(f1823,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X1,X0),X2)),X0),
inference(superposition,[],[f1727,f222]) ).
fof(f1822,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X1,X0),X2)),X0),
inference(superposition,[],[f1727,f222]) ).
fof(f1820,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X0),
inference(resolution,[],[f1727,f997]) ).
fof(f1819,plain,
! [X2,X3,X0,X1] : ~ in(powerset(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X1),
inference(resolution,[],[f1727,f1022]) ).
fof(f1727,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X0),
inference(resolution,[],[f1031,f219]) ).
fof(f1816,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_carrier(sK17) = X0
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f247,f971]) ).
fof(f1815,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_carrier(sK16) = X0
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(superposition,[],[f247,f970]) ).
fof(f1814,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK17
| the_carrier(sK17) = X0
| ~ relation_of2(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_meet(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_meet(sK17))
| ~ relation_of2(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ quasi_total(the_L_join(sK17),cartesian_product2(the_carrier(sK17),the_carrier(sK17)),the_carrier(sK17))
| ~ function(the_L_join(sK17)) ),
inference(superposition,[],[f247,f971]) ).
fof(f1813,plain,
! [X2,X0,X1] :
( latt_str_of(X0,X1,X2) != sK16
| the_carrier(sK16) = X0
| ~ relation_of2(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_meet(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_meet(sK16))
| ~ relation_of2(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ quasi_total(the_L_join(sK16),cartesian_product2(the_carrier(sK16),the_carrier(sK16)),the_carrier(sK16))
| ~ function(the_L_join(sK16)) ),
inference(superposition,[],[f247,f970]) ).
fof(f247,plain,
! [X2,X3,X0,X1,X4,X5] :
( latt_str_of(X0,X1,X2) != latt_str_of(X3,X4,X5)
| X0 = X3
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f1777,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1726,f723]) ).
fof(f1771,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK3(singleton(X0))),
inference(superposition,[],[f1726,f673]) ).
fof(f1770,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK3(powerset(X0))),
inference(superposition,[],[f1726,f646]) ).
fof(f1776,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(X0))),
inference(superposition,[],[f1726,f339]) ).
fof(f1810,plain,
! [X2,X3,X0,X1,X4] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| apply_binary_as_element(X3,X1,X4,sK8(cartesian_product2(X3,X1),X4),X2,X0) = apply_binary(sK8(cartesian_product2(X3,X1),X4),X2,X0)
| ~ quasi_total(sK8(cartesian_product2(X3,X1),X4),cartesian_product2(X3,X1),X4)
| ~ function(sK8(cartesian_product2(X3,X1),X4))
| empty(X1)
| empty(X3) ),
inference(resolution,[],[f255,f420]) ).
fof(f1809,plain,
! [X2,X3,X0,X1,X4] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| apply_binary_as_element(X3,X1,X4,sK7(cartesian_product2(X3,X1),X4),X2,X0) = apply_binary(sK7(cartesian_product2(X3,X1),X4),X2,X0)
| ~ quasi_total(sK7(cartesian_product2(X3,X1),X4),cartesian_product2(X3,X1),X4)
| ~ function(sK7(cartesian_product2(X3,X1),X4))
| empty(X1)
| empty(X3) ),
inference(resolution,[],[f255,f237]) ).
fof(f255,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,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,[],[f137]) ).
fof(f137,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,[],[f65]) ).
fof(f65,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(f1796,plain,
! [X0] : ~ in(powerset(singleton(X0)),sK3(singleton(X0))),
inference(superposition,[],[f1757,f436]) ).
fof(f1795,plain,
! [X0] : ~ in(powerset(powerset(X0)),sK3(powerset(X0))),
inference(superposition,[],[f1757,f432]) ).
fof(f1794,plain,
! [X0] : ~ in(powerset(X0),sK5(sK3(powerset(X0)))),
inference(superposition,[],[f1757,f738]) ).
fof(f1793,plain,
! [X0] : ~ in(powerset(X0),sK5(powerset(X0))),
inference(superposition,[],[f1757,f355]) ).
fof(f1792,plain,
! [X0] :
( ~ in(powerset(X0),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1757,f428]) ).
fof(f1785,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X1),
inference(resolution,[],[f1757,f997]) ).
fof(f1784,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X2),
inference(resolution,[],[f1757,f1022]) ).
fof(f1757,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),X0),
inference(superposition,[],[f1726,f222]) ).
fof(f1775,plain,
~ in(powerset(sK9),sK3(sK9)),
inference(superposition,[],[f1726,f494]) ).
fof(f1781,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),X1),
inference(resolution,[],[f1756,f1022]) ).
fof(f1756,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(superposition,[],[f1726,f218]) ).
fof(f1778,plain,
~ in(powerset(sK9),sK9),
inference(superposition,[],[f1726,f441]) ).
fof(f1766,plain,
! [X0] : ~ in(powerset(singleton(X0)),singleton(X0)),
inference(superposition,[],[f1726,f436]) ).
fof(f1765,plain,
! [X0] : ~ in(powerset(powerset(X0)),powerset(X0)),
inference(superposition,[],[f1726,f432]) ).
fof(f1764,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(superposition,[],[f1726,f738]) ).
fof(f1763,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(superposition,[],[f1726,f355]) ).
fof(f1779,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(global_subsumption,[],[f188,f244,f249,f248,f247,f255,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f409,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f524,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f590,f591,f592,f593,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f655,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f761,f762,f763,f731,f770,f771,f772,f774,f775,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f806,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f1053,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1079,f1086,f1087,f1088,f1089,f1090,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1127,f1125,f1138,f1139,f1140,f230,f1141,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1167,f1168,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1727,f1728,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1749,f1750,f1751,f1726,f1754,f1755,f1756,f1757,f1758,f1760,f1761,f1762]) ).
fof(f1762,plain,
! [X0] :
( ~ in(powerset(X0),X0)
| empty_set = X0 ),
inference(superposition,[],[f1726,f428]) ).
fof(f1761,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(superposition,[],[f1726,f185]) ).
fof(f1760,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),X0),
inference(superposition,[],[f1726,f335]) ).
fof(f1758,plain,
! [X0,X1] : ~ in(powerset(set_union2(X1,X0)),X0),
inference(superposition,[],[f1726,f222]) ).
fof(f1755,plain,
! [X2,X0,X1] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X0),
inference(resolution,[],[f1726,f997]) ).
fof(f1726,plain,
! [X0,X1] : ~ in(powerset(set_union2(X0,X1)),X0),
inference(resolution,[],[f1031,f215]) ).
fof(f1751,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f1031,f723]) ).
fof(f1745,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| ~ in(powerset(X1),sK3(singleton(X0))) ),
inference(superposition,[],[f1031,f673]) ).
fof(f1744,plain,
! [X0,X1] :
( ~ subset(powerset(X0),X1)
| ~ in(powerset(X1),sK3(powerset(X0))) ),
inference(superposition,[],[f1031,f646]) ).
fof(f1743,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(powerset(X1),sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1031,f632]) ).
fof(f1734,plain,
! [X2,X0,X1] :
( ~ subset(set_union2(X1,X0),X2)
| ~ in(powerset(X2),X0) ),
inference(superposition,[],[f1031,f335]) ).
fof(f1732,plain,
! [X2,X0,X1] :
( ~ subset(set_union2(X1,X0),X2)
| ~ in(powerset(X2),X0) ),
inference(superposition,[],[f1031,f222]) ).
fof(f1731,plain,
! [X2,X0,X1] :
( ~ subset(set_union2(X1,X0),X2)
| ~ in(powerset(X2),X0) ),
inference(superposition,[],[f1031,f222]) ).
fof(f1729,plain,
! [X2,X3,X0,X1] :
( ~ in(powerset(cartesian_product2(X0,X1)),X2)
| ~ relation_of2_as_subset(set_union2(X2,X3),X0,X1) ),
inference(resolution,[],[f1031,f653]) ).
fof(f1031,plain,
! [X2,X0,X1] :
( ~ subset(set_union2(X1,X2),X0)
| ~ in(powerset(X0),X1) ),
inference(resolution,[],[f997,f406]) ).
fof(f1725,plain,
! [X0] :
( element(sK5(sK3(sK3(sK3(singleton(X0))))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1009,f769]) ).
fof(f1724,plain,
! [X0] :
( element(sK5(sK3(sK3(singleton(X0)))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1009,f717]) ).
fof(f1723,plain,
! [X0] :
( element(sK5(sK3(singleton(X0))),singleton(X0))
| empty(sK3(singleton(X0))) ),
inference(resolution,[],[f1009,f379]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ in(X1,sK3(singleton(X0)))
| element(X1,singleton(X0)) ),
inference(superposition,[],[f809,f436]) ).
fof(f1722,plain,
! [X0] :
( element(sK5(sK3(sK3(sK3(powerset(X0))))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1008,f769]) ).
fof(f1721,plain,
! [X0] :
( element(sK5(sK3(sK3(powerset(X0)))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1008,f717]) ).
fof(f1720,plain,
! [X0] :
( element(sK5(sK3(powerset(X0))),powerset(X0))
| empty(sK3(powerset(X0))) ),
inference(resolution,[],[f1008,f379]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ in(X1,sK3(powerset(X0)))
| element(X1,powerset(X0)) ),
inference(superposition,[],[f809,f432]) ).
fof(f1718,plain,
! [X0,X1] :
( ~ in(singleton(X0),X1)
| ~ in(X1,sK3(singleton(X0))) ),
inference(superposition,[],[f1030,f673]) ).
fof(f1716,plain,
! [X0,X1] :
( in(X1,singleton(X0))
| ~ in(X1,sK3(singleton(X0))) ),
inference(superposition,[],[f997,f673]) ).
fof(f1714,plain,
! [X0,X1] :
( element(X1,singleton(X0))
| ~ in(X1,sK3(singleton(X0))) ),
inference(superposition,[],[f808,f673]) ).
fof(f673,plain,
! [X0] : singleton(X0) = set_union2(sK3(singleton(X0)),singleton(X0)),
inference(superposition,[],[f335,f436]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ in(X1,sK3(powerset(X0))) ),
inference(superposition,[],[f1030,f646]) ).
fof(f1698,plain,
! [X0,X1] :
( in(X1,powerset(X0))
| ~ in(X1,sK3(powerset(X0))) ),
inference(superposition,[],[f997,f646]) ).
fof(f1696,plain,
! [X0,X1] :
( element(X1,powerset(X0))
| ~ in(X1,sK3(powerset(X0))) ),
inference(superposition,[],[f808,f646]) ).
fof(f646,plain,
! [X0] : powerset(X0) = set_union2(sK3(powerset(X0)),powerset(X0)),
inference(superposition,[],[f335,f432]) ).
fof(f1682,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(subsumption_resolution,[],[f1681,f183]) ).
fof(f1681,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0)))))
| empty(powerset(X0)) ),
inference(resolution,[],[f841,f769]) ).
fof(f841,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,X0) ),
inference(resolution,[],[f807,f253]) ).
fof(f1674,plain,
! [X0] :
( element(sK5(sK3(sK3(sK5(sK3(powerset(X0)))))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f718,f769]) ).
fof(f1673,plain,
! [X0] :
( element(sK5(sK3(sK5(sK3(powerset(X0))))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f718,f717]) ).
fof(f1672,plain,
! [X0] :
( element(sK5(sK5(sK3(powerset(X0)))),X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f718,f379]) ).
fof(f718,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(powerset(X0))))
| element(X1,X0) ),
inference(subsumption_resolution,[],[f712,f183]) ).
fof(f712,plain,
! [X0,X1] :
( empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f711,f250]) ).
fof(f971,plain,
sK17 = latt_str_of(the_carrier(sK17),the_L_join(sK17),the_L_meet(sK17)),
inference(subsumption_resolution,[],[f968,f267]) ).
fof(f968,plain,
( sK17 = latt_str_of(the_carrier(sK17),the_L_join(sK17),the_L_meet(sK17))
| ~ latt_str(sK17) ),
inference(resolution,[],[f202,f268]) ).
fof(f1671,plain,
! [X0,X1] :
( ~ empty_carrier(latt_str_of(X0,X1,sK8(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK8(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK8(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(resolution,[],[f243,f420]) ).
fof(f1670,plain,
! [X0,X1] :
( ~ empty_carrier(latt_str_of(X0,X1,sK7(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK7(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK7(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(resolution,[],[f243,f237]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ empty_carrier(latt_str_of(X0,X1,X2))
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( strict_latt_str(latt_str_of(X0,X1,X2))
& ~ empty_carrier(latt_str_of(X0,X1,X2)) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( strict_latt_str(latt_str_of(X0,X1,X2))
& ~ empty_carrier(latt_str_of(X0,X1,X2)) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1,X2] :
( ( relation_of2(X2,cartesian_product2(X0,X0),X0)
& quasi_total(X2,cartesian_product2(X0,X0),X0)
& function(X2)
& relation_of2(X1,cartesian_product2(X0,X0),X0)
& quasi_total(X1,cartesian_product2(X0,X0),X0)
& function(X1)
& ~ empty(X0) )
=> ( strict_latt_str(latt_str_of(X0,X1,X2))
& ~ empty_carrier(latt_str_of(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
fof(f970,plain,
sK16 = latt_str_of(the_carrier(sK16),the_L_join(sK16),the_L_meet(sK16)),
inference(subsumption_resolution,[],[f967,f264]) ).
fof(f967,plain,
( sK16 = latt_str_of(the_carrier(sK16),the_L_join(sK16),the_L_meet(sK16))
| ~ latt_str(sK16) ),
inference(resolution,[],[f202,f266]) ).
fof(f1652,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| meet(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = apply_binary_as_element(the_carrier(X5),the_carrier(X5),the_carrier(X5),the_L_meet(X5),X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ meet_semilatt_str(X5)
| empty_carrier(X5) ),
inference(resolution,[],[f254,f204]) ).
fof(f1651,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = apply_binary_as_element(the_carrier(X5),the_carrier(X5),the_carrier(X5),the_L_join(X5),X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| empty_carrier(X5) ),
inference(resolution,[],[f254,f205]) ).
fof(f1650,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(boole_lattice(X5)))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(boole_lattice(X5)))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(boole_lattice(X5),X6,apply_binary_as_element(X3,X1,the_carrier(boole_lattice(X5)),X4,X2,X0)) = set_union2(X6,apply_binary_as_element(X3,X1,the_carrier(boole_lattice(X5)),X4,X2,X0))
| ~ element(X6,the_carrier(boole_lattice(X5))) ),
inference(resolution,[],[f254,f230]) ).
fof(f1649,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(boole_lattice(X5)))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(boole_lattice(X5)))
| ~ function(X4)
| empty(X1)
| empty(X3)
| meet(boole_lattice(X5),X6,apply_binary_as_element(X3,X1,the_carrier(boole_lattice(X5)),X4,X2,X0)) = set_intersection2(X6,apply_binary_as_element(X3,X1,the_carrier(boole_lattice(X5)),X4,X2,X0))
| ~ element(X6,the_carrier(boole_lattice(X5))) ),
inference(resolution,[],[f254,f231]) ).
fof(f1648,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),X5)
| ~ quasi_total(X4,cartesian_product2(X3,X1),X5)
| ~ function(X4)
| empty(X1)
| empty(X3)
| empty(X5)
| in(apply_binary_as_element(X3,X1,X5,X4,X2,X0),X5) ),
inference(resolution,[],[f254,f229]) ).
fof(f1647,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(cartesian_product2(X5,X6)))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(cartesian_product2(X5,X6)))
| ~ function(X4)
| empty(X1)
| empty(X3)
| relation(apply_binary_as_element(X3,X1,powerset(cartesian_product2(X5,X6)),X4,X2,X0)) ),
inference(resolution,[],[f254,f240]) ).
fof(f1646,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| subset(apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0),X5) ),
inference(resolution,[],[f254,f233]) ).
fof(f1645,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| ~ empty(X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) ),
inference(resolution,[],[f254,f253]) ).
fof(f1644,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| element(X6,X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) ),
inference(resolution,[],[f254,f250]) ).
fof(f254,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,[],[f136]) ).
fof(f136,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,[],[f135]) ).
fof(f135,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,[],[f20]) ).
fof(f20,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/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
fof(f1571,plain,
! [X0,X1] :
( latt_str(latt_str_of(X0,X1,sK8(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK8(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK8(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(resolution,[],[f246,f420]) ).
fof(f1570,plain,
! [X0,X1] :
( latt_str(latt_str_of(X0,X1,sK7(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK7(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK7(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(resolution,[],[f246,f237]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| latt_str(latt_str_of(X0,X1,X2))
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( latt_str(latt_str_of(X0,X1,X2))
& strict_latt_str(latt_str_of(X0,X1,X2)) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ( latt_str(latt_str_of(X0,X1,X2))
& strict_latt_str(latt_str_of(X0,X1,X2)) )
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( relation_of2(X2,cartesian_product2(X0,X0),X0)
& quasi_total(X2,cartesian_product2(X0,X0),X0)
& function(X2)
& relation_of2(X1,cartesian_product2(X0,X0),X0)
& quasi_total(X1,cartesian_product2(X0,X0),X0)
& function(X1) )
=> ( latt_str(latt_str_of(X0,X1,X2))
& strict_latt_str(latt_str_of(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
fof(f1521,plain,
! [X0,X1] :
( strict_latt_str(latt_str_of(X0,X1,sK8(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK8(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK8(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(resolution,[],[f245,f420]) ).
fof(f1520,plain,
! [X0,X1] :
( strict_latt_str(latt_str_of(X0,X1,sK7(cartesian_product2(X0,X0),X0)))
| ~ quasi_total(sK7(cartesian_product2(X0,X0),X0),cartesian_product2(X0,X0),X0)
| ~ function(sK7(cartesian_product2(X0,X0),X0))
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(resolution,[],[f245,f237]) ).
fof(f245,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| strict_latt_str(latt_str_of(X0,X1,X2))
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f1498,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(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ in(X2,the_carrier(X0)) ),
inference(resolution,[],[f205,f807]) ).
fof(f1497,plain,
! [X0,X1] :
( join(X0,X1,sK5(sK3(sK3(the_carrier(X0))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK5(sK3(sK3(the_carrier(X0)))))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f205,f731]) ).
fof(f1496,plain,
! [X0,X1] :
( join(X0,X1,sK5(sK3(the_carrier(X0)))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK5(sK3(the_carrier(X0))))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f205,f711]) ).
fof(f1495,plain,
! [X0,X1] :
( join(X0,X1,sK5(the_carrier(X0))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK5(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f205,f212]) ).
fof(f1499,plain,
! [X2,X3,X0,X1] :
( join(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(duplicate_literal_removal,[],[f1494]) ).
fof(f1494,plain,
! [X2,X3,X0,X1] :
( join(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f205,f242]) ).
fof(f1500,plain,
! [X2,X3,X0,X1] :
( join(X0,X1,meet(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,meet(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(duplicate_literal_removal,[],[f1493]) ).
fof(f1493,plain,
! [X2,X3,X0,X1] :
( join(X0,X1,meet(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,meet(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f205,f241]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ 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)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,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,[],[f98]) ).
fof(f98,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,[],[f8]) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
fof(f1436,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ join_semilatt_str(boole_lattice(sK0))
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f1435,f186]) ).
fof(f1435,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f1434,f177]) ).
fof(f1434,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f1433,f178]) ).
fof(f1433,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(resolution,[],[f284,f206]) ).
fof(f1186,plain,
! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| meet(boole_lattice(sK0),X0,sK2) = set_intersection2(X0,sK2) ),
inference(resolution,[],[f231,f178]) ).
fof(f1407,plain,
! [X0] :
( meet(boole_lattice(sK0),X0,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)),X0,sK2)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f1396,f186]) ).
fof(f1396,plain,
! [X0] :
( meet(boole_lattice(sK0),X0,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)),X0,sK2)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f204,f178]) ).
fof(f1403,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(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ~ in(X2,the_carrier(X0)) ),
inference(resolution,[],[f204,f807]) ).
fof(f1402,plain,
! [X0,X1] :
( meet(X0,X1,sK5(sK3(sK3(the_carrier(X0))))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,sK5(sK3(sK3(the_carrier(X0)))))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f204,f731]) ).
fof(f1401,plain,
! [X0,X1] :
( meet(X0,X1,sK5(sK3(the_carrier(X0)))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,sK5(sK3(the_carrier(X0))))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f204,f711]) ).
fof(f1400,plain,
! [X0,X1] :
( meet(X0,X1,sK5(the_carrier(X0))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,sK5(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f204,f212]) ).
fof(f1404,plain,
! [X2,X3,X0,X1] :
( meet(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(duplicate_literal_removal,[],[f1399]) ).
fof(f1399,plain,
! [X2,X3,X0,X1] :
( meet(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f204,f242]) ).
fof(f1405,plain,
! [X2,X3,X0,X1] :
( meet(X0,X1,meet(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,meet(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(duplicate_literal_removal,[],[f1398]) ).
fof(f1398,plain,
! [X2,X3,X0,X1] :
( meet(X0,X1,meet(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_meet(X0),X1,meet(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f204,f241]) ).
fof(f1406,plain,
! [X0] :
( meet(boole_lattice(sK0),X0,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)),X0,sK1)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f1395,f186]) ).
fof(f1395,plain,
! [X0] :
( meet(boole_lattice(sK0),X0,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)),X0,sK1)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f204,f177]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ 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)
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,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,[],[f96]) ).
fof(f96,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,[],[f9]) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ below(X0,X1,X2)
| join(X0,X1,X2) = X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f1304,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(join(X1,X2,X0),the_carrier(X1)) ),
inference(resolution,[],[f242,f229]) ).
fof(f1306,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ join_semilatt_str(boole_lattice(X1))
| join(boole_lattice(X1),X3,join(boole_lattice(X1),X2,X0)) = set_union2(X3,join(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(subsumption_resolution,[],[f1303,f186]) ).
fof(f1303,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ join_semilatt_str(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| join(boole_lattice(X1),X3,join(boole_lattice(X1),X2,X0)) = set_union2(X3,join(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(resolution,[],[f242,f230]) ).
fof(f1305,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ join_semilatt_str(boole_lattice(X1))
| meet(boole_lattice(X1),X3,join(boole_lattice(X1),X2,X0)) = set_intersection2(X3,join(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(subsumption_resolution,[],[f1302,f186]) ).
fof(f1302,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ join_semilatt_str(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X3,join(boole_lattice(X1),X2,X0)) = set_intersection2(X3,join(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(resolution,[],[f242,f231]) ).
fof(f242,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,[],[f125]) ).
fof(f125,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,[],[f124]) ).
fof(f124,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,[],[f16]) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(f1233,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(meet(X1,X2,X0),the_carrier(X1)) ),
inference(resolution,[],[f241,f229]) ).
fof(f1235,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| join(boole_lattice(X1),X3,meet(boole_lattice(X1),X2,X0)) = set_union2(X3,meet(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(subsumption_resolution,[],[f1232,f186]) ).
fof(f1232,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| join(boole_lattice(X1),X3,meet(boole_lattice(X1),X2,X0)) = set_union2(X3,meet(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(resolution,[],[f241,f230]) ).
fof(f1234,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| meet(boole_lattice(X1),X3,meet(boole_lattice(X1),X2,X0)) = set_intersection2(X3,meet(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(subsumption_resolution,[],[f1231,f186]) ).
fof(f1231,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X3,meet(boole_lattice(X1),X2,X0)) = set_intersection2(X3,meet(boole_lattice(X1),X2,X0))
| ~ element(X3,the_carrier(boole_lattice(X1))) ),
inference(resolution,[],[f241,f231]) ).
fof(f241,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,[],[f123]) ).
fof(f123,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,[],[f122]) ).
fof(f122,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,[],[f21]) ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(f959,plain,
( element(sK5(sK3(sK9)),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f819,f379]) ).
fof(f1191,plain,
! [X2,X0,X1] :
( meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ in(X2,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f231,f807]) ).
fof(f1190,plain,
! [X0,X1] :
( meet(boole_lattice(X0),X1,sK5(sK3(sK3(the_carrier(boole_lattice(X0)))))) = set_intersection2(X1,sK5(sK3(sK3(the_carrier(boole_lattice(X0))))))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| empty(the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f231,f731]) ).
fof(f1189,plain,
! [X0,X1] :
( meet(boole_lattice(X0),X1,sK5(sK3(the_carrier(boole_lattice(X0))))) = set_intersection2(X1,sK5(sK3(the_carrier(boole_lattice(X0)))))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| empty(the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f231,f711]) ).
fof(f1188,plain,
! [X0,X1] :
( meet(boole_lattice(X0),X1,sK5(the_carrier(boole_lattice(X0)))) = set_intersection2(X1,sK5(the_carrier(boole_lattice(X0))))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f231,f212]) ).
fof(f1185,plain,
! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| meet(boole_lattice(sK0),X0,sK1) = set_intersection2(X0,sK1) ),
inference(resolution,[],[f231,f177]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(boole_lattice(X0)))
| meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f1183,plain,
! [X0] :
( ~ in(X0,sK5(sK3(sK3(sK5(powerset(X0))))))
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1126,f769]) ).
fof(f1182,plain,
! [X0] :
( ~ in(X0,sK5(sK3(sK5(powerset(X0)))))
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1126,f717]) ).
fof(f1181,plain,
! [X0] :
( ~ in(X0,sK5(sK5(powerset(X0))))
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1126,f379]) ).
fof(f1126,plain,
! [X0,X1] :
( ~ in(X1,sK5(powerset(X0)))
| ~ in(X0,X1) ),
inference(superposition,[],[f1030,f339]) ).
fof(f1166,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f1078,f738]) ).
fof(f1165,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK5(powerset(X0))) ),
inference(superposition,[],[f1078,f355]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1078,f428]) ).
fof(f1157,plain,
! [X2,X3,X0,X1] :
( ~ in(set_union2(X0,X1),X2)
| ~ in(set_union2(X3,X2),X0) ),
inference(resolution,[],[f1078,f997]) ).
fof(f1156,plain,
! [X2,X3,X0,X1] :
( ~ in(set_union2(X0,X1),X2)
| ~ in(set_union2(X3,X2),X1) ),
inference(resolution,[],[f1078,f1022]) ).
fof(f1155,plain,
! [X2,X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(set_union2(X2,X1),X0) ),
inference(resolution,[],[f1078,f388]) ).
fof(f1153,plain,
! [X0] :
( in(sK5(sK3(sK3(sK5(powerset(X0))))),X0)
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1052,f769]) ).
fof(f1152,plain,
! [X0] :
( in(sK5(sK3(sK5(powerset(X0)))),X0)
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1052,f717]) ).
fof(f1151,plain,
! [X0] :
( in(sK5(sK5(powerset(X0))),X0)
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f1052,f379]) ).
fof(f1052,plain,
! [X0,X1] :
( ~ in(X1,sK5(powerset(X0)))
| in(X1,X0) ),
inference(superposition,[],[f997,f339]) ).
fof(f1147,plain,
! [X2,X0,X1] :
( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ in(X2,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f230,f807]) ).
fof(f1146,plain,
! [X0,X1] :
( join(boole_lattice(X0),X1,sK5(sK3(sK3(the_carrier(boole_lattice(X0)))))) = set_union2(X1,sK5(sK3(sK3(the_carrier(boole_lattice(X0))))))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| empty(the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f230,f731]) ).
fof(f1145,plain,
! [X0,X1] :
( join(boole_lattice(X0),X1,sK5(sK3(the_carrier(boole_lattice(X0))))) = set_union2(X1,sK5(sK3(the_carrier(boole_lattice(X0)))))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| empty(the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f230,f711]) ).
fof(f1144,plain,
! [X0,X1] :
( join(boole_lattice(X0),X1,sK5(the_carrier(boole_lattice(X0)))) = set_union2(X1,sK5(the_carrier(boole_lattice(X0))))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(resolution,[],[f230,f212]) ).
fof(f1140,plain,
( ~ in(sK9,sK5(sK3(sK3(sK3(sK9)))))
| empty(sK3(sK9)) ),
inference(resolution,[],[f1125,f769]) ).
fof(f1139,plain,
( ~ in(sK9,sK5(sK3(sK3(sK9))))
| empty(sK3(sK9)) ),
inference(resolution,[],[f1125,f717]) ).
fof(f1138,plain,
( ~ in(sK9,sK5(sK3(sK9)))
| empty(sK3(sK9)) ),
inference(resolution,[],[f1125,f379]) ).
fof(f1125,plain,
! [X0] :
( ~ in(X0,sK3(sK9))
| ~ in(sK9,X0) ),
inference(superposition,[],[f1030,f494]) ).
fof(f1119,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1030,f632]) ).
fof(f1110,plain,
! [X2,X0,X1] :
( ~ in(set_union2(X1,X0),X2)
| ~ in(X2,X0) ),
inference(superposition,[],[f1030,f335]) ).
fof(f1108,plain,
! [X2,X0,X1] :
( ~ in(set_union2(X1,X0),X2)
| ~ in(X2,X0) ),
inference(superposition,[],[f1030,f222]) ).
fof(f1107,plain,
! [X2,X0,X1] :
( ~ in(set_union2(X1,X0),X2)
| ~ in(X2,X0) ),
inference(superposition,[],[f1030,f222]) ).
fof(f1105,plain,
! [X2,X3,X0,X1] :
( ~ in(set_union2(X0,X1),X2)
| ~ in(set_union2(X2,X3),X0) ),
inference(resolution,[],[f1030,f997]) ).
fof(f1104,plain,
! [X2,X3,X0,X1] :
( ~ in(set_union2(X0,X1),X2)
| ~ in(set_union2(X2,X3),X1) ),
inference(resolution,[],[f1030,f1022]) ).
fof(f1103,plain,
! [X2,X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(set_union2(X1,X2),X0) ),
inference(resolution,[],[f1030,f388]) ).
fof(f1030,plain,
! [X2,X0,X1] :
( ~ in(set_union2(X1,X2),X0)
| ~ in(X0,X1) ),
inference(resolution,[],[f997,f226]) ).
fof(f1088,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f1022,f738]) ).
fof(f1087,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK5(powerset(X0))) ),
inference(superposition,[],[f1022,f355]) ).
fof(f1086,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f1022,f428]) ).
fof(f1076,plain,
( in(sK5(sK3(sK3(sK3(sK9)))),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f1051,f769]) ).
fof(f1075,plain,
( in(sK5(sK3(sK3(sK9))),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f1051,f717]) ).
fof(f1074,plain,
( in(sK5(sK3(sK9)),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f1051,f379]) ).
fof(f1051,plain,
! [X0] :
( ~ in(X0,sK3(sK9))
| in(X0,sK9) ),
inference(superposition,[],[f997,f494]) ).
fof(f1065,plain,
! [X2,X0,X1] :
( ~ join_semilatt_str(X0)
| apply_binary(the_L_join(X0),X1,X2) = apply(the_L_join(X0),ordered_pair(X1,X2)) ),
inference(subsumption_resolution,[],[f1063,f933]) ).
fof(f1063,plain,
! [X2,X0,X1] :
( apply_binary(the_L_join(X0),X1,X2) = apply(the_L_join(X0),ordered_pair(X1,X2))
| ~ relation(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(resolution,[],[f211,f197]) ).
fof(f1064,plain,
! [X2,X0,X1] :
( ~ meet_semilatt_str(X0)
| apply_binary(the_L_meet(X0),X1,X2) = apply(the_L_meet(X0),ordered_pair(X1,X2)) ),
inference(subsumption_resolution,[],[f1062,f797]) ).
fof(f1062,plain,
! [X2,X0,X1] :
( apply_binary(the_L_meet(X0),X1,X2) = apply(the_L_meet(X0),ordered_pair(X1,X2))
| ~ relation(the_L_meet(X0))
| ~ meet_semilatt_str(X0) ),
inference(resolution,[],[f211,f193]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ function(X0)
| apply_binary(X0,X1,X2) = apply(X0,ordered_pair(X1,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1,X2] : apply_binary(X0,X1,X2) = apply(X0,ordered_pair(X1,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1,X2] : apply_binary(X0,X1,X2) = apply(X0,ordered_pair(X1,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] : apply_binary(X0,X1,X2) = apply(X0,ordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
fof(f1045,plain,
! [X0,X1] :
( in(X1,X0)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f997,f632]) ).
fof(f1036,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f997,f335]) ).
fof(f1034,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f997,f222]) ).
fof(f1033,plain,
! [X2,X0,X1] :
( in(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f997,f222]) ).
fof(f997,plain,
! [X2,X0,X1] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(subsumption_resolution,[],[f973,f506]) ).
fof(f973,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| empty(set_union2(X1,X2))
| in(X0,set_union2(X1,X2)) ),
inference(resolution,[],[f808,f229]) ).
fof(f843,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(resolution,[],[f807,f240]) ).
fof(f1007,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f809,f738]) ).
fof(f1005,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f809,f428]) ).
fof(f995,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(superposition,[],[f808,f723]) ).
fof(f987,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK3(X0))
| empty_set = X0 ),
inference(superposition,[],[f808,f632]) ).
fof(f978,plain,
! [X2,X0,X1] :
( element(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f808,f335]) ).
fof(f976,plain,
! [X2,X0,X1] :
( element(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f808,f222]) ).
fof(f975,plain,
! [X2,X0,X1] :
( element(X2,set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f808,f222]) ).
fof(f808,plain,
! [X2,X0,X1] :
( element(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(resolution,[],[f703,f219]) ).
fof(f972,plain,
! [X0] : boole_lattice(X0) = latt_str_of(the_carrier(boole_lattice(X0)),the_L_join(boole_lattice(X0)),the_L_meet(boole_lattice(X0))),
inference(subsumption_resolution,[],[f969,f189]) ).
fof(f969,plain,
! [X0] :
( boole_lattice(X0) = latt_str_of(the_carrier(boole_lattice(X0)),the_L_join(boole_lattice(X0)),the_L_meet(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0)) ),
inference(resolution,[],[f202,f187]) ).
fof(f202,plain,
! [X0] :
( ~ strict_latt_str(X0)
| latt_str_of(the_carrier(X0),the_L_join(X0),the_L_meet(X0)) = X0
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( latt_str_of(the_carrier(X0),the_L_join(X0),the_L_meet(X0)) = X0
| ~ strict_latt_str(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0] :
( latt_str_of(the_carrier(X0),the_L_join(X0),the_L_meet(X0)) = X0
| ~ strict_latt_str(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( latt_str(X0)
=> ( strict_latt_str(X0)
=> latt_str_of(the_carrier(X0),the_L_join(X0),the_L_meet(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(f961,plain,
( element(sK5(sK3(sK3(sK3(sK9)))),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f819,f769]) ).
fof(f960,plain,
( element(sK5(sK3(sK3(sK9))),sK9)
| empty(sK3(sK9)) ),
inference(resolution,[],[f819,f717]) ).
fof(f819,plain,
! [X0] :
( ~ in(X0,sK3(sK9))
| element(X0,sK9) ),
inference(resolution,[],[f703,f490]) ).
fof(f842,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(resolution,[],[f807,f233]) ).
fof(f933,plain,
! [X0] :
( relation(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(resolution,[],[f199,f651]) ).
fof(f934,plain,
! [X0] :
( relation_of2(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(resolution,[],[f199,f251]) ).
fof(f199,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,[],[f91]) ).
fof(f91,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,[],[f36]) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(f840,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,X0) ),
inference(resolution,[],[f807,f250]) ).
fof(f807,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(resolution,[],[f703,f215]) ).
fof(f198,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,[],[f91]) ).
fof(f812,plain,
( ! [X0] :
( element(X0,sK2)
| ~ in(X0,sK1) )
| ~ spl18_2 ),
inference(resolution,[],[f703,f288]) ).
fof(f823,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(sK3(powerset(X1)))))
| element(X0,X1) ),
inference(resolution,[],[f703,f772]) ).
fof(f822,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(powerset(X1))))
| element(X0,X1) ),
inference(resolution,[],[f703,f720]) ).
fof(f820,plain,
! [X0,X1] :
( ~ in(X0,sK4(X1))
| element(X0,the_carrier(X1))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(resolution,[],[f703,f522]) ).
fof(f816,plain,
! [X0,X1] :
( ~ in(X0,sK3(singleton(X1)))
| element(X0,singleton(X1)) ),
inference(resolution,[],[f703,f671]) ).
fof(f815,plain,
! [X0,X1] :
( ~ in(X0,sK3(powerset(X1)))
| element(X0,powerset(X1)) ),
inference(resolution,[],[f703,f644]) ).
fof(f813,plain,
! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty_set = X1 ),
inference(resolution,[],[f703,f630]) ).
fof(f810,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| element(X0,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(resolution,[],[f703,f653]) ).
fof(f800,plain,
! [X0] :
( ~ in(X0,sK5(sK3(sK3(X0))))
| empty(X0) ),
inference(resolution,[],[f769,f226]) ).
fof(f773,plain,
! [X0,X1] : relation(sK5(sK3(sK3(powerset(cartesian_product2(X0,X1)))))),
inference(subsumption_resolution,[],[f767,f183]) ).
fof(f767,plain,
! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| relation(sK5(sK3(sK3(powerset(cartesian_product2(X0,X1)))))) ),
inference(resolution,[],[f731,f240]) ).
fof(f803,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| element(sK5(sK3(sK3(sK5(powerset(X0))))),X0) ),
inference(resolution,[],[f769,f706]) ).
fof(f769,plain,
! [X0] :
( in(sK5(sK3(sK3(X0))),X0)
| empty(X0) ),
inference(duplicate_literal_removal,[],[f768]) ).
fof(f768,plain,
! [X0] :
( empty(X0)
| empty(X0)
| in(sK5(sK3(sK3(X0))),X0) ),
inference(resolution,[],[f731,f229]) ).
fof(f797,plain,
! [X0] :
( relation(the_L_meet(X0))
| ~ meet_semilatt_str(X0) ),
inference(resolution,[],[f195,f651]) ).
fof(f798,plain,
! [X0] :
( relation_of2(the_L_meet(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ meet_semilatt_str(X0) ),
inference(resolution,[],[f195,f251]) ).
fof(f195,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,[],[f89]) ).
fof(f89,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,[],[f34]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(f738,plain,
! [X0] : set_union2(X0,sK5(sK3(powerset(X0)))) = X0,
inference(superposition,[],[f723,f222]) ).
fof(f780,plain,
! [X0] :
( empty_set = sK5(sK3(powerset(sK5(sK3(powerset(X0))))))
| ~ empty(X0) ),
inference(resolution,[],[f737,f732]) ).
fof(f779,plain,
! [X0] :
( empty_set = sK5(sK3(powerset(sK5(powerset(X0)))))
| ~ empty(X0) ),
inference(resolution,[],[f737,f361]) ).
fof(f777,plain,
! [X0] :
( empty_set = sK5(sK3(powerset(X0)))
| set_union2(X0,sK3(X0)) = X0 ),
inference(resolution,[],[f737,f340]) ).
fof(f737,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(sK3(powerset(X0))) ),
inference(resolution,[],[f732,f203]) ).
fof(f776,plain,
! [X0,X1] : relation(sK5(sK3(sK3(powerset(cartesian_product2(X0,X1)))))),
inference(resolution,[],[f772,f417]) ).
fof(f774,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(sK3(powerset(X1)))))
| ~ empty(X1) ),
inference(resolution,[],[f772,f463]) ).
fof(f772,plain,
! [X0] : subset(sK5(sK3(sK3(powerset(X0)))),X0),
inference(subsumption_resolution,[],[f766,f183]) ).
fof(f766,plain,
! [X0] :
( empty(powerset(X0))
| subset(sK5(sK3(sK3(powerset(X0)))),X0) ),
inference(resolution,[],[f731,f233]) ).
fof(f770,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(subsumption_resolution,[],[f764,f183]) ).
fof(f764,plain,
! [X0,X1] :
( empty(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK5(sK3(sK3(powerset(X0))))) ),
inference(resolution,[],[f731,f250]) ).
fof(f731,plain,
! [X0] :
( element(sK5(sK3(sK3(X0))),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f728,f191]) ).
fof(f728,plain,
! [X0] :
( empty(sK3(X0))
| element(sK5(sK3(sK3(X0))),X0)
| empty(X0) ),
inference(resolution,[],[f717,f702]) ).
fof(f763,plain,
( empty(sK3(powerset(empty_set)))
| in(empty_set,sK3(powerset(empty_set))) ),
inference(resolution,[],[f762,f229]) ).
fof(f762,plain,
element(empty_set,sK3(powerset(empty_set))),
inference(superposition,[],[f212,f740]) ).
fof(f740,plain,
empty_set = sK5(sK3(powerset(empty_set))),
inference(superposition,[],[f723,f185]) ).
fof(f752,plain,
empty_set = sK5(sK3(powerset(empty_set))),
inference(superposition,[],[f185,f723]) ).
fof(f743,plain,
! [X0] : set_union2(X0,sK5(sK3(powerset(X0)))) = X0,
inference(superposition,[],[f222,f723]) ).
fof(f742,plain,
! [X0] : set_union2(X0,sK5(sK3(powerset(X0)))) = X0,
inference(superposition,[],[f222,f723]) ).
fof(f739,plain,
! [X0] : set_union2(X0,sK5(sK3(powerset(X0)))) = X0,
inference(superposition,[],[f723,f222]) ).
fof(f723,plain,
! [X0] : set_union2(sK5(sK3(powerset(X0))),X0) = X0,
inference(resolution,[],[f720,f228]) ).
fof(f194,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,[],[f89]) ).
fof(f736,plain,
! [X0,X1] :
( ~ empty(X0)
| sK5(sK3(powerset(X0))) = X1
| ~ empty(X1) ),
inference(resolution,[],[f732,f235]) ).
fof(f735,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(powerset(sK5(sK3(powerset(X0))))) ),
inference(resolution,[],[f732,f368]) ).
fof(f734,plain,
! [X0,X1] :
( ~ empty(X0)
| sK5(powerset(X1)) = sK5(sK3(powerset(X0)))
| ~ empty(X1) ),
inference(resolution,[],[f732,f367]) ).
fof(f732,plain,
! [X0] :
( empty(sK5(sK3(powerset(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f719,f379]) ).
fof(f733,plain,
! [X0] :
( ~ empty(X0)
| empty(sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f719,f717]) ).
fof(f719,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(powerset(X0))))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f713,f183]) ).
fof(f713,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f711,f253]) ).
fof(f726,plain,
! [X0] :
( ~ in(X0,sK5(sK3(X0)))
| empty(X0) ),
inference(resolution,[],[f717,f226]) ).
fof(f721,plain,
! [X0,X1] : relation(sK5(sK3(powerset(cartesian_product2(X0,X1))))),
inference(subsumption_resolution,[],[f715,f183]) ).
fof(f715,plain,
! [X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| relation(sK5(sK3(powerset(cartesian_product2(X0,X1))))) ),
inference(resolution,[],[f711,f240]) ).
fof(f729,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| element(sK5(sK3(sK5(powerset(X0)))),X0) ),
inference(resolution,[],[f717,f706]) ).
fof(f717,plain,
! [X0] :
( in(sK5(sK3(X0)),X0)
| empty(X0) ),
inference(duplicate_literal_removal,[],[f716]) ).
fof(f716,plain,
! [X0] :
( empty(X0)
| empty(X0)
| in(sK5(sK3(X0)),X0) ),
inference(resolution,[],[f711,f229]) ).
fof(f724,plain,
! [X0,X1] : relation(sK5(sK3(powerset(cartesian_product2(X0,X1))))),
inference(resolution,[],[f720,f417]) ).
fof(f722,plain,
! [X0,X1] :
( ~ in(X0,sK5(sK3(powerset(X1))))
| ~ empty(X1) ),
inference(resolution,[],[f720,f463]) ).
fof(f720,plain,
! [X0] : subset(sK5(sK3(powerset(X0))),X0),
inference(subsumption_resolution,[],[f714,f183]) ).
fof(f714,plain,
! [X0] :
( empty(powerset(X0))
| subset(sK5(sK3(powerset(X0))),X0) ),
inference(resolution,[],[f711,f233]) ).
fof(f711,plain,
! [X0] :
( element(sK5(sK3(X0)),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f710,f191]) ).
fof(f710,plain,
! [X0] :
( element(sK5(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) ),
inference(resolution,[],[f702,f379]) ).
fof(f702,plain,
! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty(X1) ),
inference(resolution,[],[f250,f190]) ).
fof(f708,plain,
! [X0] :
( element(sK5(sK5(powerset(X0))),X0)
| empty(sK5(powerset(X0))) ),
inference(resolution,[],[f706,f379]) ).
fof(f706,plain,
! [X0,X1] :
( ~ in(X0,sK5(powerset(X1)))
| element(X0,X1) ),
inference(resolution,[],[f250,f212]) ).
fof(f705,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f250,f239]) ).
fof(f704,plain,
! [X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,sK4(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(resolution,[],[f250,f209]) ).
fof(f632,plain,
! [X0] :
( set_union2(sK3(X0),X0) = X0
| empty_set = X0 ),
inference(superposition,[],[f335,f428]) ).
fof(f680,plain,
! [X0,X1] :
( sK5(powerset(X0)) = sK5(powerset(X1))
| ~ empty(X0)
| ~ empty(X1) ),
inference(resolution,[],[f367,f361]) ).
fof(f678,plain,
! [X0,X1] :
( sK5(powerset(X0)) = X1
| ~ empty(X0)
| set_union2(X1,sK3(X1)) = X1 ),
inference(resolution,[],[f367,f340]) ).
fof(f367,plain,
! [X0,X1] :
( ~ empty(X1)
| sK5(powerset(X0)) = X1
| ~ empty(X0) ),
inference(resolution,[],[f361,f235]) ).
fof(f677,plain,
! [X0] : singleton(X0) = set_union2(sK3(singleton(X0)),singleton(X0)),
inference(resolution,[],[f671,f228]) ).
fof(f671,plain,
! [X0] : subset(sK3(singleton(X0)),singleton(X0)),
inference(superposition,[],[f305,f436]) ).
fof(f436,plain,
! [X0] : singleton(X0) = set_union2(singleton(X0),sK3(singleton(X0))),
inference(resolution,[],[f340,f182]) ).
fof(f667,plain,
! [X0,X1] : ~ relation_of2(powerset(powerset(cartesian_product2(X0,X1))),X0,X1),
inference(resolution,[],[f665,f252]) ).
fof(f665,plain,
! [X0,X1] : ~ relation_of2_as_subset(powerset(powerset(cartesian_product2(X0,X1))),X0,X1),
inference(resolution,[],[f653,f555]) ).
fof(f666,plain,
! [X2,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(powerset(cartesian_product2(X0,X1)),X2)),X0,X1),
inference(resolution,[],[f653,f556]) ).
fof(f664,plain,
! [X2,X0,X1] : ~ relation_of2_as_subset(powerset(set_union2(X0,powerset(cartesian_product2(X1,X2)))),X1,X2),
inference(resolution,[],[f653,f557]) ).
fof(f663,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(powerset(X0),X1,X2)
| ~ subset(powerset(cartesian_product2(X1,X2)),X0) ),
inference(resolution,[],[f653,f407]) ).
fof(f662,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| cartesian_product2(X1,X2) = set_union2(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f653,f228]) ).
fof(f661,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(X3,X0)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(resolution,[],[f653,f463]) ).
fof(f653,plain,
! [X2,X0,X1] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[],[f239,f233]) ).
fof(f658,plain,
! [X0,X1] : relation(sK7(X0,X1)),
inference(resolution,[],[f657,f237]) ).
fof(f657,plain,
! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f651,f252]) ).
fof(f656,plain,
! [X0,X1] : relation(sK8(X0,X1)),
inference(resolution,[],[f651,f238]) ).
fof(f651,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f239,f240]) ).
fof(f652,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ),
inference(resolution,[],[f239,f253]) ).
fof(f239,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f650,plain,
! [X0] : powerset(X0) = set_union2(sK3(powerset(X0)),powerset(X0)),
inference(resolution,[],[f644,f228]) ).
fof(f644,plain,
! [X0] : subset(sK3(powerset(X0)),powerset(X0)),
inference(superposition,[],[f305,f432]) ).
fof(f432,plain,
! [X0] : powerset(X0) = set_union2(powerset(X0),sK3(powerset(X0))),
inference(resolution,[],[f340,f183]) ).
fof(f639,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
| relation(sK3(cartesian_product2(X0,X1))) ),
inference(resolution,[],[f630,f417]) ).
fof(f638,plain,
! [X0] :
( empty_set = X0
| set_union2(sK3(X0),X0) = X0 ),
inference(resolution,[],[f630,f228]) ).
fof(f630,plain,
! [X0] :
( subset(sK3(X0),X0)
| empty_set = X0 ),
inference(superposition,[],[f305,f428]) ).
fof(f428,plain,
! [X0] :
( set_union2(X0,sK3(X0)) = X0
| empty_set = X0 ),
inference(resolution,[],[f340,f203]) ).
fof(f335,plain,
! [X0,X1] : set_union2(X1,X0) = set_union2(X0,set_union2(X1,X0)),
inference(resolution,[],[f228,f305]) ).
fof(f601,plain,
! [X0] :
( the_carrier(X0) = set_union2(the_carrier(X0),sK4(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(forward_demodulation,[],[f600,f222]) ).
fof(f600,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| the_carrier(X0) = set_union2(sK4(X0),the_carrier(X0)) ),
inference(resolution,[],[f522,f228]) ).
fof(f522,plain,
! [X0] :
( subset(sK4(X0),the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f209,f233]) ).
fof(f416,plain,
! [X0,X1] :
( relation(sK3(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ),
inference(resolution,[],[f240,f190]) ).
fof(f598,plain,
! [X0,X1] : ordered_pair(X0,X1) = set_union2(ordered_pair(X0,X1),sK3(ordered_pair(X0,X1))),
inference(resolution,[],[f597,f340]) ).
fof(f597,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(superposition,[],[f216,f223]) ).
fof(f596,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f220,f223]) ).
fof(f595,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f220,f223]) ).
fof(f594,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f223,f220]) ).
fof(f592,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f223,f223]) ).
fof(f591,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f223,f220]) ).
fof(f223,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f570,plain,
! [X0,X1] : set_union2(X1,X0) = set_union2(X0,set_union2(X1,X0)),
inference(superposition,[],[f334,f222]) ).
fof(f569,plain,
! [X0,X1] : set_union2(X1,X0) = set_union2(X0,set_union2(X1,X0)),
inference(superposition,[],[f334,f222]) ).
fof(f334,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_union2(X0,X1)),
inference(resolution,[],[f228,f219]) ).
fof(f557,plain,
! [X0,X1] : ~ subset(powerset(set_union2(X0,powerset(X1))),X1),
inference(resolution,[],[f407,f305]) ).
fof(f560,plain,
! [X0,X1] : ~ subset(powerset(set_union2(X1,powerset(X0))),X0),
inference(superposition,[],[f556,f222]) ).
fof(f559,plain,
! [X0,X1] : ~ subset(powerset(set_union2(X1,powerset(X0))),X0),
inference(superposition,[],[f556,f222]) ).
fof(f556,plain,
! [X0,X1] : ~ subset(powerset(set_union2(powerset(X0),X1)),X0),
inference(resolution,[],[f407,f219]) ).
fof(f555,plain,
! [X0] : ~ subset(powerset(powerset(X0)),X0),
inference(resolution,[],[f407,f215]) ).
fof(f407,plain,
! [X0,X1] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(resolution,[],[f406,f388]) ).
fof(f540,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| set_union2(X2,X1) = set_union2(set_union2(X2,X1),sK3(set_union2(X2,X1))) ),
inference(resolution,[],[f507,f340]) ).
fof(f528,plain,
! [X2,X0,X1] :
( ~ empty(set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f506,f222]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ empty(set_union2(X1,X0))
| ~ in(X2,X0) ),
inference(superposition,[],[f506,f222]) ).
fof(f525,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| set_union2(X1,X2) = set_union2(set_union2(X1,X2),sK3(set_union2(X1,X2))) ),
inference(resolution,[],[f506,f340]) ).
fof(f506,plain,
! [X2,X0,X1] :
( ~ empty(set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(resolution,[],[f463,f219]) ).
fof(f209,plain,
! [X0] :
( element(sK4(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( ~ empty(sK4(X0))
& element(sK4(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f105,f147]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK4(X0))
& element(sK4(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f505,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(resolution,[],[f463,f215]) ).
fof(f464,plain,
! [X0,X1] :
( ~ in(X1,sK5(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f253,f212]) ).
fof(f494,plain,
sK9 = set_union2(sK3(sK9),sK9),
inference(resolution,[],[f490,f228]) ).
fof(f490,plain,
subset(sK3(sK9),sK9),
inference(superposition,[],[f305,f441]) ).
fof(f465,plain,
! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) ),
inference(forward_demodulation,[],[f460,f271]) ).
fof(f460,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(X0)) ),
inference(resolution,[],[f253,f213]) ).
fof(f461,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,empty_set) ),
inference(resolution,[],[f253,f273]) ).
fof(f440,plain,
! [X0] :
( sK4(X0) = set_union2(sK4(X0),sK3(sK4(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f340,f210]) ).
fof(f439,plain,
! [X0] :
( sK3(X0) = set_union2(sK3(X0),sK3(sK3(X0)))
| empty(X0) ),
inference(resolution,[],[f340,f191]) ).
fof(f435,plain,
! [X0,X1] :
( set_union2(X0,X1) = set_union2(set_union2(X0,X1),sK3(set_union2(X0,X1)))
| empty(X1) ),
inference(resolution,[],[f340,f224]) ).
fof(f434,plain,
! [X0,X1] :
( set_union2(X0,X1) = set_union2(set_union2(X0,X1),sK3(set_union2(X0,X1)))
| empty(X0) ),
inference(resolution,[],[f340,f225]) ).
fof(f433,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(unordered_pair(X0,X1),sK3(unordered_pair(X0,X1))),
inference(resolution,[],[f340,f216]) ).
fof(f431,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) = set_union2(cartesian_product2(X0,X1),sK3(cartesian_product2(X0,X1)))
| empty(X1)
| empty(X0) ),
inference(resolution,[],[f340,f232]) ).
fof(f429,plain,
! [X0] :
( the_carrier(X0) = set_union2(the_carrier(X0),sK3(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[],[f340,f208]) ).
fof(f427,plain,
! [X0,X1] :
( set_union2(X0,sK3(X0)) = X0
| X0 = X1
| ~ empty(X1) ),
inference(resolution,[],[f340,f235]) ).
fof(f426,plain,
! [X0] :
( set_union2(X0,sK3(X0)) = X0
| empty_set = sK5(powerset(X0)) ),
inference(resolution,[],[f340,f368]) ).
fof(f252,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,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,[],[f66]) ).
fof(f66,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f421,plain,
! [X0,X1] : relation(cartesian_product2(X0,X1)),
inference(resolution,[],[f417,f215]) ).
fof(f423,plain,
! [X0,X1] :
( relation(sK3(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ),
inference(resolution,[],[f417,f324]) ).
fof(f417,plain,
! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) ),
inference(resolution,[],[f240,f234]) ).
fof(f420,plain,
! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1),
inference(resolution,[],[f251,f238]) ).
fof(f418,plain,
! [X0,X1] : relation(sK5(powerset(cartesian_product2(X0,X1)))),
inference(resolution,[],[f240,f212]) ).
fof(f251,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f419,plain,
relation(empty_set),
inference(forward_demodulation,[],[f414,f271]) ).
fof(f414,plain,
! [X0,X1] : relation(sK6(cartesian_product2(X0,X1))),
inference(resolution,[],[f240,f213]) ).
fof(f415,plain,
relation(empty_set),
inference(resolution,[],[f240,f273]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f368,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(powerset(X0)) ),
inference(resolution,[],[f361,f203]) ).
fof(f406,plain,
! [X0,X1] :
( ~ in(powerset(X1),X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f388,f226]) ).
fof(f405,plain,
! [X0] :
( ~ in(powerset(X0),sK3(X0))
| empty(X0) ),
inference(resolution,[],[f387,f226]) ).
fof(f388,plain,
! [X0,X1] :
( in(X1,powerset(X0))
| ~ subset(X1,X0) ),
inference(subsumption_resolution,[],[f383,f183]) ).
fof(f383,plain,
! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ),
inference(resolution,[],[f229,f234]) ).
fof(f387,plain,
! [X0] :
( in(sK3(X0),powerset(X0))
| empty(X0) ),
inference(subsumption_resolution,[],[f382,f183]) ).
fof(f382,plain,
! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ),
inference(resolution,[],[f229,f190]) ).
fof(f232,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f377,plain,
( empty(the_carrier(boole_lattice(sK0)))
| in(sK1,the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f229,f177]) ).
fof(f390,plain,
! [X0] :
( ~ in(X0,sK5(X0))
| empty(X0) ),
inference(resolution,[],[f379,f226]) ).
fof(f379,plain,
! [X0] :
( in(sK5(X0),X0)
| empty(X0) ),
inference(resolution,[],[f229,f212]) ).
fof(f389,plain,
! [X0] : ~ in(powerset(X0),empty_set),
inference(resolution,[],[f385,f226]) ).
fof(f385,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f384,f271]) ).
fof(f384,plain,
! [X0] : in(sK6(X0),powerset(X0)),
inference(subsumption_resolution,[],[f380,f183]) ).
fof(f380,plain,
! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0)) ),
inference(resolution,[],[f229,f213]) ).
fof(f386,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(subsumption_resolution,[],[f381,f183]) ).
fof(f381,plain,
! [X0] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(resolution,[],[f229,f273]) ).
fof(f378,plain,
( empty(the_carrier(boole_lattice(sK0)))
| in(sK2,the_carrier(boole_lattice(sK0))) ),
inference(resolution,[],[f229,f178]) ).
fof(f355,plain,
! [X0] : set_union2(X0,sK5(powerset(X0))) = X0,
inference(superposition,[],[f339,f222]) ).
fof(f361,plain,
! [X0] :
( empty(sK5(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[],[f225,f339]) ).
fof(f354,plain,
empty_set = sK5(powerset(empty_set)),
inference(superposition,[],[f339,f185]) ).
fof(f360,plain,
! [X0] : set_union2(X0,sK5(powerset(X0))) = X0,
inference(superposition,[],[f222,f339]) ).
fof(f359,plain,
! [X0] : set_union2(X0,sK5(powerset(X0))) = X0,
inference(superposition,[],[f222,f339]) ).
fof(f357,plain,
empty_set = sK5(powerset(empty_set)),
inference(superposition,[],[f185,f339]) ).
fof(f356,plain,
! [X0] : set_union2(X0,sK5(powerset(X0))) = X0,
inference(superposition,[],[f339,f222]) ).
fof(f339,plain,
! [X0] : set_union2(sK5(powerset(X0)),X0) = X0,
inference(resolution,[],[f228,f325]) ).
fof(f342,plain,
( ~ empty(sK2)
| empty(sK1)
| ~ spl18_2 ),
inference(superposition,[],[f225,f337]) ).
fof(f337,plain,
( sK2 = set_union2(sK1,sK2)
| ~ spl18_2 ),
inference(resolution,[],[f228,f288]) ).
fof(f235,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f325,plain,
! [X0] : subset(sK5(powerset(X0)),X0),
inference(resolution,[],[f233,f212]) ).
fof(f316,plain,
! [X0] : subset(empty_set,X0),
inference(superposition,[],[f219,f300]) ).
fof(f300,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f222,f185]) ).
fof(f309,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(superposition,[],[f219,f222]) ).
fof(f306,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f185,f222]) ).
fof(f302,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f185,f222]) ).
fof(f301,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f222,f185]) ).
fof(f292,plain,
! [X0] : empty_set = set_intersection2(empty_set,X0),
inference(superposition,[],[f221,f184]) ).
fof(f295,plain,
! [X0] : empty_set = set_intersection2(empty_set,X0),
inference(superposition,[],[f184,f221]) ).
fof(f294,plain,
! [X0] : empty_set = set_intersection2(empty_set,X0),
inference(superposition,[],[f184,f221]) ).
fof(f293,plain,
! [X0] : empty_set = set_intersection2(empty_set,X0),
inference(superposition,[],[f221,f184]) ).
fof(f221,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f220,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f210,plain,
! [X0] :
( ~ empty(sK4(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f208,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f179,plain,
( subset(sK1,sK2)
| below(boole_lattice(sK0),sK1,sK2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f238,plain,
! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f43,f156]) ).
fof(f156,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK8(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f43,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f237,plain,
! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1] : relation_of2(sK7(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f41,f154]) ).
fof(f154,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK7(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f41,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f225,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f224,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f218,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f217,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f273,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(superposition,[],[f213,f271]) ).
fof(f271,plain,
! [X0] : empty_set = sK6(X0),
inference(resolution,[],[f203,f214]) ).
fof(f213,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f59,f151]) ).
fof(f151,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f270,plain,
empty_set = sK14,
inference(resolution,[],[f203,f261]) ).
fof(f203,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f197,plain,
! [X0] :
( function(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f193,plain,
! [X0] :
( function(the_L_meet(X0))
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f191,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f185,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f184,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f216,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f212,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f42,f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f201,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( join_semilatt_str(X0)
& meet_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f200,plain,
! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f196,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f192,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f215,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f214,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f152]) ).
fof(f189,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( latt_str(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f187,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f183,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f182,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f268,plain,
strict_latt_str(sK17),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( strict_latt_str(sK17)
& latt_str(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f61,f175]) ).
fof(f175,plain,
( ? [X0] :
( strict_latt_str(X0)
& latt_str(X0) )
=> ( strict_latt_str(sK17)
& latt_str(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f61,axiom,
? [X0] :
( strict_latt_str(X0)
& latt_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
fof(f267,plain,
latt_str(sK17),
inference(cnf_transformation,[],[f176]) ).
fof(f266,plain,
strict_latt_str(sK16),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( strict_latt_str(sK16)
& ~ empty_carrier(sK16)
& latt_str(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f64,f173]) ).
fof(f173,plain,
( ? [X0] :
( strict_latt_str(X0)
& ~ empty_carrier(X0)
& latt_str(X0) )
=> ( strict_latt_str(sK16)
& ~ empty_carrier(sK16)
& latt_str(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f64,axiom,
? [X0] :
( strict_latt_str(X0)
& ~ empty_carrier(X0)
& latt_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
fof(f265,plain,
~ empty_carrier(sK16),
inference(cnf_transformation,[],[f174]) ).
fof(f264,plain,
latt_str(sK16),
inference(cnf_transformation,[],[f174]) ).
fof(f263,plain,
~ empty_carrier(sK15),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( ~ empty_carrier(sK15)
& one_sorted_str(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f62,f171]) ).
fof(f171,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK15)
& one_sorted_str(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f62,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f262,plain,
one_sorted_str(sK15),
inference(cnf_transformation,[],[f172]) ).
fof(f261,plain,
empty(sK14),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f58,f169]) ).
fof(f169,plain,
( ? [X0] : empty(X0)
=> empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f58,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f260,plain,
latt_str(sK13),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
latt_str(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f40,f167]) ).
fof(f167,plain,
( ? [X0] : latt_str(X0)
=> latt_str(sK13) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(f259,plain,
one_sorted_str(sK12),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
one_sorted_str(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f38,f165]) ).
fof(f165,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK12) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f258,plain,
join_semilatt_str(sK11),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
join_semilatt_str(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f39,f163]) ).
fof(f163,plain,
( ? [X0] : join_semilatt_str(X0)
=> join_semilatt_str(sK11) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f257,plain,
meet_semilatt_str(sK10),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
meet_semilatt_str(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f37,f161]) ).
fof(f161,plain,
( ? [X0] : meet_semilatt_str(X0)
=> meet_semilatt_str(sK10) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
? [X0] : meet_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(f181,plain,
empty(empty_set),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f244,plain,
! [X2,X0,X1] :
( strict_latt_str(latt_str_of(X0,X1,X2))
| ~ relation_of2(X2,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X2,cartesian_product2(X0,X0),X0)
| ~ function(X2)
| ~ relation_of2(X1,cartesian_product2(X0,X0),X0)
| ~ quasi_total(X1,cartesian_product2(X0,X0),X0)
| ~ function(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f188,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f3188,plain,
( ~ spl18_1
| ~ spl18_2
| spl18_4 ),
inference(avatar_contradiction_clause,[],[f3187]) ).
fof(f3187,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| spl18_4 ),
inference(global_subsumption,[],[f833,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612,f180,f2966,f284,f1142,f3140,f3142,f3146,f3137,f3153,f3184]) ).
fof(f833,plain,
( ~ in(sK2,sK1)
| ~ spl18_2
| spl18_4 ),
inference(duplicate_literal_removal,[],[f832]) ).
fof(f832,plain,
( ~ in(sK2,sK1)
| ~ in(sK2,sK1)
| ~ spl18_2
| spl18_4 ),
inference(resolution,[],[f827,f825]) ).
fof(f825,plain,
( ! [X0] :
( in(X0,sK2)
| ~ in(X0,sK1) )
| ~ spl18_2
| spl18_4 ),
inference(subsumption_resolution,[],[f824,f352]) ).
fof(f824,plain,
( ! [X0] :
( ~ in(X0,sK1)
| empty(sK2)
| in(X0,sK2) )
| ~ spl18_2 ),
inference(resolution,[],[f812,f229]) ).
fof(f827,plain,
( ! [X0] :
( ~ in(sK2,X0)
| ~ in(X0,sK1) )
| ~ spl18_2
| spl18_4 ),
inference(resolution,[],[f825,f226]) ).
fof(f3186,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_contradiction_clause,[],[f3185]) ).
fof(f3185,plain,
( $false
| ~ spl18_1
| ~ spl18_2 ),
inference(global_subsumption,[],[f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612,f180,f2966,f284,f1142,f3140,f3142,f3146,f3137,f3153,f3184]) ).
fof(f3183,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_17 ),
inference(avatar_contradiction_clause,[],[f3182]) ).
fof(f3182,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_17 ),
inference(global_subsumption,[],[f3154,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612,f180,f2966,f284,f1142,f3140,f3142,f3146,f3137,f3153]) ).
fof(f3154,plain,
( subset(sK1,sK2)
| ~ spl18_1
| ~ spl18_17 ),
inference(superposition,[],[f219,f3139]) ).
fof(f3139,plain,
( sK2 = set_union2(sK1,sK2)
| ~ spl18_1
| ~ spl18_17 ),
inference(forward_demodulation,[],[f3129,f2973]) ).
fof(f2973,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ spl18_1
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2972,f186]) ).
fof(f2972,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2971,f1422]) ).
fof(f2971,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f2970,f177]) ).
fof(f2970,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(subsumption_resolution,[],[f2969,f178]) ).
fof(f2969,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ element(sK2,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1 ),
inference(resolution,[],[f284,f206]) ).
fof(f3181,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_17 ),
inference(avatar_contradiction_clause,[],[f3180]) ).
fof(f3180,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f3154,f287]) ).
fof(f287,plain,
( ~ subset(sK1,sK2)
| spl18_2 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f2985,plain,
( spl18_11
| ~ spl18_19 ),
inference(avatar_contradiction_clause,[],[f2984]) ).
fof(f2984,plain,
( $false
| spl18_11
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f2976,f866]) ).
fof(f866,plain,
( ~ empty(sK3(sK2))
| spl18_11 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f865,plain,
( spl18_11
<=> empty(sK3(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f2976,plain,
( empty(sK3(sK2))
| ~ spl18_19 ),
inference(resolution,[],[f1575,f191]) ).
fof(f1575,plain,
( empty(sK3(sK3(sK2)))
| ~ spl18_19 ),
inference(avatar_component_clause,[],[f1573]) ).
fof(f1573,plain,
( spl18_19
<=> empty(sK3(sK3(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
fof(f2964,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f2963]) ).
fof(f2963,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(global_subsumption,[],[f2962,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2962,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2961,f2821]) ).
fof(f2821,plain,
( empty_set = sK1
| ~ spl18_3 ),
inference(resolution,[],[f348,f203]) ).
fof(f348,plain,
( empty(sK1)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f2961,plain,
( below(boole_lattice(sK0),sK1,empty_set)
| ~ spl18_1
| ~ spl18_4 ),
inference(forward_demodulation,[],[f284,f1585]) ).
fof(f1585,plain,
( empty_set = sK2
| ~ spl18_4 ),
inference(resolution,[],[f351,f203]) ).
fof(f351,plain,
( empty(sK2)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f2960,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f2959]) ).
fof(f2959,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(global_subsumption,[],[f2958,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2958,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f885,f2821]) ).
fof(f885,plain,
( below(boole_lattice(sK0),sK1,empty_set)
| ~ spl18_1
| ~ spl18_4 ),
inference(forward_demodulation,[],[f284,f877]) ).
fof(f877,plain,
( empty_set = sK2
| ~ spl18_4 ),
inference(resolution,[],[f351,f203]) ).
fof(f2957,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f2956]) ).
fof(f2956,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(global_subsumption,[],[f1243,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f1243,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_3
| ~ spl18_4 ),
inference(superposition,[],[f885,f1230]) ).
fof(f1230,plain,
( empty_set = sK1
| ~ spl18_3 ),
inference(resolution,[],[f348,f203]) ).
fof(f2955,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2954]) ).
fof(f2954,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(global_subsumption,[],[f2792,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2792,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2688,f1585]) ).
fof(f2688,plain,
( sK2 = join(boole_lattice(sK0),empty_set,sK2)
| ~ spl18_1
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(superposition,[],[f1437,f2636]) ).
fof(f2636,plain,
( empty_set = sK1
| ~ spl18_4
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2625,f1427]) ).
fof(f1427,plain,
( empty_set = join(boole_lattice(sK0),sK1,empty_set)
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f1425,plain,
( spl18_18
<=> empty_set = join(boole_lattice(sK0),sK1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
fof(f2625,plain,
( sK1 = join(boole_lattice(sK0),sK1,empty_set)
| ~ spl18_4 ),
inference(resolution,[],[f2529,f177]) ).
fof(f2529,plain,
( ! [X0] :
( ~ element(X0,the_carrier(boole_lattice(sK0)))
| join(boole_lattice(sK0),X0,empty_set) = X0 )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2528,f185]) ).
fof(f2528,plain,
( ! [X0] :
( set_union2(X0,empty_set) = join(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1142,f1585]) ).
fof(f1437,plain,
( sK2 = join(boole_lattice(sK0),sK1,sK2)
| ~ spl18_1
| ~ spl18_17 ),
inference(global_subsumption,[],[f188,f205,f244,f243,f246,f245,f249,f248,f247,f254,f255,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f409,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f524,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f590,f591,f592,f593,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f646,f644,f650,f239,f652,f655,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f673,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f718,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f761,f762,f763,f731,f770,f771,f772,f774,f775,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f806,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f198,f807,f840,f841,f180,f199,f934,f933,f842,f819,f960,f961,f202,f970,f971,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f1008,f1009,f843,f997,f1031,f1033,f1034,f1036,f1045,f1053,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1079,f1086,f1087,f1088,f1089,f1090,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1127,f1125,f1138,f1139,f1140,f230,f1141,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1167,f1168,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f1422,f284,f1436]) ).
fof(f2953,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2952]) ).
fof(f2952,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(global_subsumption,[],[f2707,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2707,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_4
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2645,f1585]) ).
fof(f2645,plain,
( below(boole_lattice(sK0),empty_set,sK2)
| ~ spl18_1
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f284,f2636]) ).
fof(f2951,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2950]) ).
fof(f2950,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(global_subsumption,[],[f2653,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2653,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_1
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f885,f2636]) ).
fof(f2949,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2948]) ).
fof(f2948,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_18 ),
inference(global_subsumption,[],[f2947,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2947,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_3
| ~ spl18_18 ),
inference(forward_demodulation,[],[f1427,f2821]) ).
fof(f2946,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2945]) ).
fof(f2945,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(global_subsumption,[],[f2705,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2705,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(superposition,[],[f2496,f2636]) ).
fof(f2496,plain,
( below(boole_lattice(sK0),sK1,sK1)
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2495,f186]) ).
fof(f2495,plain,
( below(boole_lattice(sK0),sK1,sK1)
| empty_carrier(boole_lattice(sK0))
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2494,f1422]) ).
fof(f2494,plain,
( below(boole_lattice(sK0),sK1,sK1)
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2493,f177]) ).
fof(f2493,plain,
( below(boole_lattice(sK0),sK1,sK1)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(trivial_inequality_removal,[],[f2492]) ).
fof(f2492,plain,
( sK1 != sK1
| below(boole_lattice(sK0),sK1,sK1)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(duplicate_literal_removal,[],[f2489]) ).
fof(f2489,plain,
( sK1 != sK1
| below(boole_lattice(sK0),sK1,sK1)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(superposition,[],[f207,f2472]) ).
fof(f2944,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2943]) ).
fof(f2943,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(global_subsumption,[],[f2706,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2706,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4
| ~ spl18_17
| ~ spl18_18 ),
inference(superposition,[],[f2505,f2636]) ).
fof(f2505,plain,
( below(boole_lattice(sK0),empty_set,sK1)
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2504,f186]) ).
fof(f2504,plain,
( below(boole_lattice(sK0),empty_set,sK1)
| empty_carrier(boole_lattice(sK0))
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2503,f1422]) ).
fof(f2503,plain,
( below(boole_lattice(sK0),empty_set,sK1)
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f2502,f1586]) ).
fof(f1586,plain,
( element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ spl18_4 ),
inference(superposition,[],[f178,f1585]) ).
fof(f2502,plain,
( below(boole_lattice(sK0),empty_set,sK1)
| ~ element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f2501,f177]) ).
fof(f2501,plain,
( below(boole_lattice(sK0),empty_set,sK1)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_4 ),
inference(trivial_inequality_removal,[],[f2499]) ).
fof(f2499,plain,
( sK1 != sK1
| below(boole_lattice(sK0),empty_set,sK1)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_4 ),
inference(superposition,[],[f207,f2474]) ).
fof(f2474,plain,
( sK1 = join(boole_lattice(sK0),empty_set,sK1)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2473,f300]) ).
fof(f2473,plain,
( set_union2(empty_set,sK1) = join(boole_lattice(sK0),empty_set,sK1)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2462,f1585]) ).
fof(f2939,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2938]) ).
fof(f2938,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(global_subsumption,[],[f2687,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2687,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f1427,f2636]) ).
fof(f2937,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2936]) ).
fof(f2936,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(global_subsumption,[],[f2703,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2703,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f2472,f2636]) ).
fof(f2935,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2934]) ).
fof(f2934,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(global_subsumption,[],[f2704,f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f288,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f337,f342,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f812,f198,f807,f840,f180,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1188,f1189,f1190,f1191,f959,f241,f1234,f1235,f1233,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f284,f1436,f205,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2477,f2481,f2470,f2488,f2472,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612]) ).
fof(f2704,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f2474,f2636]) ).
fof(f2933,plain,
( spl18_1
| ~ spl18_3
| ~ spl18_4
| ~ spl18_17 ),
inference(avatar_contradiction_clause,[],[f2932]) ).
fof(f2932,plain,
( $false
| spl18_1
| ~ spl18_3
| ~ spl18_4
| ~ spl18_17 ),
inference(global_subsumption,[],[f188,f244,f181,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f267,f268,f182,f183,f186,f187,f189,f214,f215,f177,f178,f192,f196,f200,f201,f212,f216,f184,f185,f191,f193,f197,f203,f270,f213,f271,f273,f217,f218,f219,f224,f225,f226,f237,f238,f179,f283,f190,f208,f210,f220,f221,f293,f294,f295,f292,f222,f301,f302,f306,f309,f300,f316,f305,f233,f325,f324,f234,f235,f228,f339,f356,f357,f359,f360,f354,f361,f355,f229,f378,f386,f385,f389,f379,f390,f377,f232,f387,f388,f405,f406,f368,f240,f415,f419,f251,f418,f420,f417,f423,f421,f252,f340,f426,f427,f429,f431,f433,f434,f435,f439,f440,f253,f461,f465,f441,f490,f494,f464,f463,f505,f209,f506,f525,f527,f528,f507,f540,f407,f555,f556,f559,f560,f557,f334,f569,f570,f223,f591,f592,f594,f595,f596,f597,f598,f416,f522,f601,f335,f428,f630,f638,f639,f432,f644,f650,f239,f652,f651,f656,f657,f658,f653,f661,f662,f663,f664,f666,f665,f667,f436,f671,f677,f367,f678,f680,f632,f250,f704,f705,f706,f708,f702,f711,f720,f722,f724,f717,f729,f721,f726,f719,f733,f732,f734,f735,f736,f194,f723,f739,f742,f743,f752,f740,f762,f763,f731,f770,f772,f774,f776,f737,f777,f779,f780,f738,f195,f798,f797,f769,f803,f773,f800,f703,f810,f813,f815,f816,f820,f822,f823,f198,f807,f840,f180,f873,f874,f875,f876,f877,f878,f199,f934,f933,f842,f819,f960,f961,f202,f972,f808,f975,f976,f978,f987,f995,f809,f1005,f1007,f843,f997,f1033,f1034,f1036,f1045,f211,f1064,f1065,f1051,f1074,f1075,f1076,f1022,f1086,f1087,f1088,f1030,f1103,f1104,f1105,f1107,f1108,f1110,f1119,f1125,f1138,f1139,f1140,f230,f1149,f1150,f1144,f1145,f1146,f1147,f1052,f1151,f1152,f1153,f1078,f1155,f1156,f1157,f1164,f1165,f1166,f1126,f1181,f1182,f1183,f231,f1185,f1193,f1194,f1188,f1189,f1190,f1191,f959,f1226,f1227,f1228,f1229,f241,f1234,f1235,f1233,f1230,f242,f1305,f1306,f1304,f206,f207,f204,f1406,f1408,f1409,f1405,f1404,f1400,f1401,f1402,f1403,f1407,f1186,f1142,f1422,f205,f1502,f1504,f1500,f1499,f1495,f1496,f1497,f1498,f245,f1520,f1521,f246,f1570,f1571,f351,f1581,f1582,f1583,f1584,f1585,f1586,f1634,f1635,f1637,f1638,f254,f1644,f1645,f1646,f1647,f1648,f1649,f1650,f1651,f1652,f970,f243,f1670,f1671,f971,f718,f1672,f1673,f1674,f841,f1682,f646,f1696,f1698,f1700,f673,f1714,f1716,f1718,f1008,f1720,f1721,f1722,f1009,f1723,f1724,f1725,f1031,f1729,f1731,f1732,f1734,f1743,f1744,f1745,f1751,f1726,f1755,f1758,f1760,f1761,f1762,f1779,f1763,f1764,f1765,f1766,f1778,f1756,f1781,f1775,f1757,f1784,f1785,f1792,f1793,f1794,f1795,f1796,f255,f1809,f1810,f1776,f1770,f1771,f1777,f247,f1813,f1814,f1815,f1816,f1727,f1819,f1820,f1822,f1823,f1825,f1834,f1845,f1846,f1848,f248,f1883,f1884,f1885,f1886,f1840,f1901,f1903,f1900,f1728,f1917,f1918,f1921,f1923,f1932,f1749,f1754,f1952,f1953,f1960,f1961,f1962,f1963,f1964,f1978,f1979,f1981,f249,f1986,f1987,f1988,f1989,f1769,f1841,f1993,f1994,f1996,f2005,f2011,f524,f2020,f1920,f2022,f2023,f2030,f2031,f2032,f2033,f2034,f1939,f2062,f2063,f2064,f2065,f2066,f590,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2012,f1079,f2095,f2102,f2103,f2104,f2105,f2106,f1089,f2119,f2120,f2121,f1090,f2122,f2123,f2124,f409,f2125,f2129,f2130,f771,f2143,f2144,f2142,f2145,f2146,f2147,f2148,f2149,f1053,f2151,f2152,f2153,f593,f2155,f2156,f2157,f2158,f2159,f2160,f2161,f1127,f2163,f2164,f2165,f1167,f2168,f2169,f1168,f2170,f2171,f2172,f1750,f761,f775,f2191,f2194,f2195,f2203,f2205,f2207,f2208,f2212,f2213,f2216,f2222,f2192,f2237,f2238,f2239,f2211,f806,f2252,f2253,f2255,f2246,f2247,f2248,f2256,f2249,f2257,f2254,f2258,f2259,f2260,f2261,f1818,f2264,f2267,f2268,f2270,f2276,f2277,f2279,f1835,f2286,f2287,f2289,f1836,f2296,f2297,f2299,f1842,f2305,f2306,f2308,f2317,f2318,f2319,f2324,f2325,f2326,f2323,f1916,f2330,f2333,f2334,f2336,f1933,f1934,f1940,f2375,f2376,f2377,f2378,f2379,f655,f2396,f2399,f2401,f2402,f2403,f2404,f2405,f2406,f2407,f2408,f2409,f1951,f2442,f2453,f2454,f2456,f1141,f2475,f2477,f2480,f2481,f2470,f2488,f2472,f2496,f2474,f2505,f2006,f2007,f2013,f2021,f2508,f2150,f2530,f2534,f2535,f2536,f2190,f2554,f2556,f2559,f2560,f2564,f2568,f2569,f2570,f2251,f2585,f2616,f2617,f2618,f2591,f2592,f2593,f2594,f2595,f2596,f2606,f2607,f2608,f2610,f2611,f2612,f2529,f2637,f2627,f2638,f2640,f2630,f2634,f2635,f2814,f2625,f2820,f348,f2822,f2823,f2824,f2825,f2826,f2827,f2821,f2864,f2865,f2866,f2867,f2931]) ).
fof(f2931,plain,
( ~ below(boole_lattice(sK0),empty_set,empty_set)
| spl18_1
| ~ spl18_3
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2820,f2821]) ).
fof(f2867,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_3
| ~ spl18_4
| ~ spl18_17 ),
inference(superposition,[],[f2505,f2821]) ).
fof(f2866,plain,
( below(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_3
| ~ spl18_17 ),
inference(superposition,[],[f2496,f2821]) ).
fof(f2865,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_3
| ~ spl18_4 ),
inference(superposition,[],[f2474,f2821]) ).
fof(f2864,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_3 ),
inference(superposition,[],[f2472,f2821]) ).
fof(f2827,plain,
( empty_set = sK5(sK3(sK3(powerset(sK1))))
| ~ spl18_3 ),
inference(resolution,[],[f348,f2150]) ).
fof(f2826,plain,
( empty_set = sK5(sK3(powerset(sK1)))
| ~ spl18_3 ),
inference(resolution,[],[f348,f737]) ).
fof(f2825,plain,
( empty_set = sK5(powerset(sK5(powerset(sK1))))
| ~ spl18_3 ),
inference(resolution,[],[f348,f409]) ).
fof(f2824,plain,
( empty_set = sK5(powerset(sK1))
| ~ spl18_3 ),
inference(resolution,[],[f348,f368]) ).
fof(f2823,plain,
( ! [X0] :
( sK1 = sK5(powerset(X0))
| ~ empty(X0) )
| ~ spl18_3 ),
inference(resolution,[],[f348,f367]) ).
fof(f2822,plain,
( ! [X0] :
( sK1 = X0
| ~ empty(X0) )
| ~ spl18_3 ),
inference(resolution,[],[f348,f235]) ).
fof(f2820,plain,
( ~ below(boole_lattice(sK0),sK1,empty_set)
| spl18_1
| ~ spl18_4 ),
inference(forward_demodulation,[],[f283,f1585]) ).
fof(f2814,plain,
( ~ below(boole_lattice(sK0),sK1,empty_set)
| ~ subset(sK1,empty_set)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2813,f1585]) ).
fof(f2813,plain,
( ~ subset(sK1,empty_set)
| ~ below(boole_lattice(sK0),sK1,sK2)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f180,f1585]) ).
fof(f2635,plain,
( ! [X2,X3,X0,X1,X4] :
( apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4) = join(boole_lattice(sK0),apply_binary_as_element(X0,X1,the_carrier(boole_lattice(sK0)),X2,X3,X4),empty_set)
| ~ element(X4,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ quasi_total(X2,cartesian_product2(X0,X1),the_carrier(boole_lattice(sK0)))
| ~ function(X2)
| empty(X1)
| empty(X0) )
| ~ spl18_4 ),
inference(resolution,[],[f2529,f254]) ).
fof(f2634,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = X0
| ~ in(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(resolution,[],[f2529,f807]) ).
fof(f2630,plain,
( sK5(the_carrier(boole_lattice(sK0))) = join(boole_lattice(sK0),sK5(the_carrier(boole_lattice(sK0))),empty_set)
| ~ spl18_4 ),
inference(resolution,[],[f2529,f212]) ).
fof(f2640,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),X0,X1) = join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),empty_set)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2639,f186]) ).
fof(f2639,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),X0,X1) = join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),empty_set)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2629,f1422]) ).
fof(f2629,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),X0,X1) = join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),empty_set)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(resolution,[],[f2529,f242]) ).
fof(f2638,plain,
( ! [X0,X1] :
( meet(boole_lattice(sK0),X0,X1) = join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),empty_set)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f2628,f186]) ).
fof(f2628,plain,
( ! [X0,X1] :
( meet(boole_lattice(sK0),X0,X1) = join(boole_lattice(sK0),meet(boole_lattice(sK0),X0,X1),empty_set)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(resolution,[],[f2529,f241]) ).
fof(f2627,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4 ),
inference(resolution,[],[f2529,f1586]) ).
fof(f2637,plain,
( empty_set = join(boole_lattice(sK0),empty_set,empty_set)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2626,f1585]) ).
fof(f2626,plain,
( sK2 = join(boole_lattice(sK0),sK2,empty_set)
| ~ spl18_4 ),
inference(resolution,[],[f2529,f178]) ).
fof(f2480,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),sK1) = set_union2(sK1,join(boole_lattice(sK0),X0,X1))
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_17 ),
inference(forward_demodulation,[],[f2479,f222]) ).
fof(f2479,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),sK1) = set_union2(join(boole_lattice(sK0),X0,X1),sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2478,f186]) ).
fof(f2478,plain,
( ! [X0,X1] :
( join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),sK1) = set_union2(join(boole_lattice(sK0),X0,X1),sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f2465,f1422]) ).
fof(f2465,plain,
! [X0,X1] :
( join(boole_lattice(sK0),join(boole_lattice(sK0),X0,X1),sK1) = set_union2(join(boole_lattice(sK0),X0,X1),sK1)
| ~ element(X1,the_carrier(boole_lattice(sK0)))
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f1141,f242]) ).
fof(f2475,plain,
( sK1 = join(boole_lattice(sK0),empty_set,sK1)
| ~ spl18_4 ),
inference(forward_demodulation,[],[f2463,f300]) ).
fof(f2463,plain,
( set_union2(empty_set,sK1) = join(boole_lattice(sK0),empty_set,sK1)
| ~ spl18_4 ),
inference(resolution,[],[f1141,f1586]) ).
fof(f1638,plain,
( ! [X0] :
( meet(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1632,f186]) ).
fof(f1632,plain,
( ! [X0] :
( meet(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(resolution,[],[f1586,f204]) ).
fof(f1637,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1636,f186]) ).
fof(f1636,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1631,f1422]) ).
fof(f1631,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(resolution,[],[f1586,f205]) ).
fof(f1635,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = X0
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1630,f185]) ).
fof(f1630,plain,
( ! [X0] :
( set_union2(X0,empty_set) = join(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(resolution,[],[f1586,f230]) ).
fof(f1634,plain,
( ! [X0] :
( empty_set = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1629,f184]) ).
fof(f1629,plain,
( ! [X0] :
( set_intersection2(X0,empty_set) = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(resolution,[],[f1586,f231]) ).
fof(f1584,plain,
( ! [X0] :
( sK2 = X0
| ~ empty(X0) )
| ~ spl18_4 ),
inference(resolution,[],[f351,f235]) ).
fof(f1583,plain,
( empty_set = sK5(powerset(sK2))
| ~ spl18_4 ),
inference(resolution,[],[f351,f368]) ).
fof(f1582,plain,
( ! [X0] :
( sK2 = sK5(powerset(X0))
| ~ empty(X0) )
| ~ spl18_4 ),
inference(resolution,[],[f351,f367]) ).
fof(f1581,plain,
( empty_set = sK5(sK3(powerset(sK2)))
| ~ spl18_4 ),
inference(resolution,[],[f351,f737]) ).
fof(f1504,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK2)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1503,f186]) ).
fof(f1503,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK2)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1492,f1422]) ).
fof(f1492,plain,
! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK2)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f205,f178]) ).
fof(f1502,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK1)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1501,f186]) ).
fof(f1501,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK1)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_17 ),
inference(subsumption_resolution,[],[f1491,f1422]) ).
fof(f1491,plain,
! [X0] :
( join(boole_lattice(sK0),X0,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)),X0,sK1)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) ),
inference(resolution,[],[f205,f177]) ).
fof(f1409,plain,
( ! [X0] :
( meet(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1397,f186]) ).
fof(f1397,plain,
( ! [X0] :
( meet(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(resolution,[],[f204,f878]) ).
fof(f1408,plain,
( ! [X0] :
( meet(boole_lattice(sK0),X0,empty_set) = 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)),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0)))
| ~ meet_semilatt_str(boole_lattice(sK0)) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1407,f877]) ).
fof(f1229,plain,
( ! [X0] :
( sK1 = X0
| ~ empty(X0) )
| ~ spl18_3 ),
inference(resolution,[],[f348,f235]) ).
fof(f1228,plain,
( empty_set = sK5(powerset(sK1))
| ~ spl18_3 ),
inference(resolution,[],[f348,f368]) ).
fof(f1227,plain,
( ! [X0] :
( sK1 = sK5(powerset(X0))
| ~ empty(X0) )
| ~ spl18_3 ),
inference(resolution,[],[f348,f367]) ).
fof(f1226,plain,
( empty_set = sK5(sK3(powerset(sK1)))
| ~ spl18_3 ),
inference(resolution,[],[f348,f737]) ).
fof(f1194,plain,
( ! [X0] :
( empty_set = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1187,f184]) ).
fof(f1187,plain,
( ! [X0] :
( set_intersection2(X0,empty_set) = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(resolution,[],[f231,f878]) ).
fof(f1193,plain,
( ! [X0] :
( empty_set = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1192,f184]) ).
fof(f1192,plain,
( ! [X0] :
( set_intersection2(X0,empty_set) = meet(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1186,f877]) ).
fof(f1150,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = X0
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1143,f185]) ).
fof(f1143,plain,
( ! [X0] :
( set_union2(X0,empty_set) = join(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(resolution,[],[f230,f878]) ).
fof(f1149,plain,
( ! [X0] :
( join(boole_lattice(sK0),X0,empty_set) = X0
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1148,f185]) ).
fof(f1148,plain,
( ! [X0] :
( set_union2(X0,empty_set) = join(boole_lattice(sK0),X0,empty_set)
| ~ element(X0,the_carrier(boole_lattice(sK0))) )
| ~ spl18_4 ),
inference(forward_demodulation,[],[f1142,f877]) ).
fof(f878,plain,
( element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ spl18_4 ),
inference(superposition,[],[f178,f877]) ).
fof(f876,plain,
( ! [X0] :
( sK2 = X0
| ~ empty(X0) )
| ~ spl18_4 ),
inference(resolution,[],[f351,f235]) ).
fof(f875,plain,
( empty_set = sK5(powerset(sK2))
| ~ spl18_4 ),
inference(resolution,[],[f351,f368]) ).
fof(f874,plain,
( ! [X0] :
( sK2 = sK5(powerset(X0))
| ~ empty(X0) )
| ~ spl18_4 ),
inference(resolution,[],[f351,f367]) ).
fof(f873,plain,
( empty_set = sK5(sK3(powerset(sK2)))
| ~ spl18_4 ),
inference(resolution,[],[f351,f737]) ).
fof(f2905,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(avatar_contradiction_clause,[],[f2904]) ).
fof(f2904,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(subsumption_resolution,[],[f2903,f479]) ).
fof(f479,plain,
( ! [X1] : ~ in(X1,empty_set)
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f478,plain,
( spl18_8
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
fof(f2903,plain,
( in(sK5(sK3(sK3(sK3(empty_set)))),empty_set)
| ~ spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(forward_demodulation,[],[f2854,f1605]) ).
fof(f1605,plain,
( empty_set = sK3(empty_set)
| ~ spl18_4
| ~ spl18_11 ),
inference(resolution,[],[f1599,f203]) ).
fof(f1599,plain,
( empty(sK3(empty_set))
| ~ spl18_4
| ~ spl18_11 ),
inference(forward_demodulation,[],[f867,f1585]) ).
fof(f867,plain,
( empty(sK3(sK2))
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f2854,plain,
( in(sK5(sK3(sK3(sK3(sK3(empty_set))))),sK3(empty_set))
| ~ spl18_3
| spl18_9
| spl18_15 ),
inference(superposition,[],[f1376,f2821]) ).
fof(f1376,plain,
( in(sK5(sK3(sK3(sK3(sK3(sK1))))),sK3(sK1))
| spl18_9
| spl18_15 ),
inference(subsumption_resolution,[],[f1373,f1219]) ).
fof(f1219,plain,
( ~ empty(sK3(sK3(sK1)))
| spl18_15 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1218,plain,
( spl18_15
<=> empty(sK3(sK3(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f1373,plain,
( in(sK5(sK3(sK3(sK3(sK3(sK1))))),sK3(sK1))
| empty(sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f1341,f769]) ).
fof(f1341,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK1)))
| in(X0,sK3(sK1)) )
| spl18_9 ),
inference(superposition,[],[f1022,f1251]) ).
fof(f1251,plain,
( sK3(sK1) = set_union2(sK3(sK1),sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f847,f340]) ).
fof(f847,plain,
( ~ empty(sK3(sK1))
| spl18_9 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f846,plain,
( spl18_9
<=> empty(sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
fof(f2902,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(avatar_contradiction_clause,[],[f2901]) ).
fof(f2901,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(subsumption_resolution,[],[f2900,f479]) ).
fof(f2900,plain,
( in(sK5(sK3(sK3(empty_set))),empty_set)
| ~ spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(forward_demodulation,[],[f2853,f1605]) ).
fof(f2853,plain,
( in(sK5(sK3(sK3(sK3(empty_set)))),sK3(empty_set))
| ~ spl18_3
| spl18_9
| spl18_15 ),
inference(superposition,[],[f1375,f2821]) ).
fof(f1375,plain,
( in(sK5(sK3(sK3(sK3(sK1)))),sK3(sK1))
| spl18_9
| spl18_15 ),
inference(subsumption_resolution,[],[f1372,f1219]) ).
fof(f1372,plain,
( in(sK5(sK3(sK3(sK3(sK1)))),sK3(sK1))
| empty(sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f1341,f717]) ).
fof(f2899,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(avatar_contradiction_clause,[],[f2898]) ).
fof(f2898,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(subsumption_resolution,[],[f2897,f479]) ).
fof(f2897,plain,
( in(sK5(sK3(empty_set)),empty_set)
| ~ spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15 ),
inference(forward_demodulation,[],[f2852,f1605]) ).
fof(f2852,plain,
( in(sK5(sK3(sK3(empty_set))),sK3(empty_set))
| ~ spl18_3
| spl18_9
| spl18_15 ),
inference(superposition,[],[f1374,f2821]) ).
fof(f1374,plain,
( in(sK5(sK3(sK3(sK1))),sK3(sK1))
| spl18_9
| spl18_15 ),
inference(subsumption_resolution,[],[f1371,f1219]) ).
fof(f1371,plain,
( in(sK5(sK3(sK3(sK1))),sK3(sK1))
| empty(sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f1341,f379]) ).
fof(f2875,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_11
| spl18_15 ),
inference(avatar_contradiction_clause,[],[f2874]) ).
fof(f2874,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_11
| spl18_15 ),
inference(subsumption_resolution,[],[f2873,f1599]) ).
fof(f2873,plain,
( ~ empty(sK3(empty_set))
| ~ spl18_3
| ~ spl18_4
| ~ spl18_11
| spl18_15 ),
inference(forward_demodulation,[],[f2842,f1605]) ).
fof(f2842,plain,
( ~ empty(sK3(sK3(empty_set)))
| ~ spl18_3
| spl18_15 ),
inference(superposition,[],[f1219,f2821]) ).
fof(f2871,plain,
( ~ spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_11 ),
inference(avatar_contradiction_clause,[],[f2870]) ).
fof(f2870,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_11 ),
inference(subsumption_resolution,[],[f2840,f1599]) ).
fof(f2840,plain,
( ~ empty(sK3(empty_set))
| ~ spl18_3
| spl18_9 ),
inference(superposition,[],[f847,f2821]) ).
fof(f2787,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2786]) ).
fof(f2786,plain,
( $false
| spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2685,f479]) ).
fof(f2685,plain,
( in(sK5(sK3(sK3(sK3(sK3(empty_set))))),empty_set)
| spl18_3
| ~ spl18_4
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(superposition,[],[f1411,f2636]) ).
fof(f1411,plain,
( in(sK5(sK3(sK3(sK3(sK3(sK1))))),sK1)
| spl18_3
| spl18_9
| spl18_15 ),
inference(resolution,[],[f1376,f1272]) ).
fof(f1272,plain,
( ! [X0] :
( ~ in(X0,sK3(sK1))
| in(X0,sK1) )
| spl18_3 ),
inference(superposition,[],[f1022,f1250]) ).
fof(f1250,plain,
( sK1 = set_union2(sK1,sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f347,f340]) ).
fof(f2772,plain,
( ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2771]) ).
fof(f2771,plain,
( $false
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2770,f479]) ).
fof(f2770,plain,
( in(sK5(sK3(sK3(sK3(empty_set)))),empty_set)
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2680,f1605]) ).
fof(f2680,plain,
( in(sK5(sK3(sK3(sK3(sK3(empty_set))))),sK3(empty_set))
| ~ spl18_4
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(superposition,[],[f1376,f2636]) ).
fof(f2769,plain,
( ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2768]) ).
fof(f2768,plain,
( $false
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2767,f479]) ).
fof(f2767,plain,
( in(sK5(sK3(sK3(empty_set))),empty_set)
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2679,f1605]) ).
fof(f2679,plain,
( in(sK5(sK3(sK3(sK3(empty_set)))),sK3(empty_set))
| ~ spl18_4
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(superposition,[],[f1375,f2636]) ).
fof(f2766,plain,
( ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2765]) ).
fof(f2765,plain,
( $false
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2764,f479]) ).
fof(f2764,plain,
( in(sK5(sK3(empty_set)),empty_set)
| ~ spl18_4
| spl18_9
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2678,f1605]) ).
fof(f2678,plain,
( in(sK5(sK3(sK3(empty_set))),sK3(empty_set))
| ~ spl18_4
| spl18_9
| spl18_15
| ~ spl18_18 ),
inference(superposition,[],[f1374,f2636]) ).
fof(f2740,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2739]) ).
fof(f2739,plain,
( $false
| spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2667,f479]) ).
fof(f2667,plain,
( in(sK5(sK3(sK3(sK3(empty_set)))),empty_set)
| spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_18 ),
inference(superposition,[],[f1312,f2636]) ).
fof(f1312,plain,
( in(sK5(sK3(sK3(sK3(sK1)))),sK1)
| spl18_3
| spl18_9 ),
inference(subsumption_resolution,[],[f1309,f847]) ).
fof(f1309,plain,
( in(sK5(sK3(sK3(sK3(sK1)))),sK1)
| empty(sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f1272,f769]) ).
fof(f2738,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2737]) ).
fof(f2737,plain,
( $false
| spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2666,f479]) ).
fof(f2666,plain,
( in(sK5(sK3(sK3(empty_set))),empty_set)
| spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_18 ),
inference(superposition,[],[f1311,f2636]) ).
fof(f1311,plain,
( in(sK5(sK3(sK3(sK1))),sK1)
| spl18_3
| spl18_9 ),
inference(subsumption_resolution,[],[f1308,f847]) ).
fof(f1308,plain,
( in(sK5(sK3(sK3(sK1))),sK1)
| empty(sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f1272,f717]) ).
fof(f2736,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2735]) ).
fof(f2735,plain,
( $false
| spl18_3
| ~ spl18_4
| ~ spl18_8
| spl18_9
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2665,f479]) ).
fof(f2665,plain,
( in(sK5(sK3(empty_set)),empty_set)
| spl18_3
| ~ spl18_4
| spl18_9
| ~ spl18_18 ),
inference(superposition,[],[f1310,f2636]) ).
fof(f1310,plain,
( in(sK5(sK3(sK1)),sK1)
| spl18_3
| spl18_9 ),
inference(subsumption_resolution,[],[f1307,f847]) ).
fof(f1307,plain,
( in(sK5(sK3(sK1)),sK1)
| empty(sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f1272,f379]) ).
fof(f2719,plain,
( ~ spl18_4
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2718]) ).
fof(f2718,plain,
( $false
| ~ spl18_4
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2717,f1599]) ).
fof(f2717,plain,
( ~ empty(sK3(empty_set))
| ~ spl18_4
| ~ spl18_11
| spl18_15
| ~ spl18_18 ),
inference(forward_demodulation,[],[f2654,f1605]) ).
fof(f2654,plain,
( ~ empty(sK3(sK3(empty_set)))
| ~ spl18_4
| spl18_15
| ~ spl18_18 ),
inference(superposition,[],[f1219,f2636]) ).
fof(f2716,plain,
( spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2715]) ).
fof(f2715,plain,
( $false
| spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2652,f316]) ).
fof(f2652,plain,
( ~ subset(empty_set,empty_set)
| spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f879,f2636]) ).
fof(f879,plain,
( ~ subset(sK1,empty_set)
| spl18_2
| ~ spl18_4 ),
inference(superposition,[],[f287,f877]) ).
fof(f2713,plain,
( ~ spl18_4
| spl18_9
| ~ spl18_11
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2712]) ).
fof(f2712,plain,
( $false
| ~ spl18_4
| spl18_9
| ~ spl18_11
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2650,f1599]) ).
fof(f2650,plain,
( ~ empty(sK3(empty_set))
| ~ spl18_4
| spl18_9
| ~ spl18_18 ),
inference(superposition,[],[f847,f2636]) ).
fof(f2711,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2710]) ).
fof(f2710,plain,
( $false
| spl18_3
| ~ spl18_4
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2647,f181]) ).
fof(f2647,plain,
( ~ empty(empty_set)
| spl18_3
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f347,f2636]) ).
fof(f2709,plain,
( spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f2708]) ).
fof(f2708,plain,
( $false
| spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f2646,f316]) ).
fof(f2646,plain,
( ~ subset(empty_set,sK2)
| spl18_2
| ~ spl18_4
| ~ spl18_18 ),
inference(superposition,[],[f287,f2636]) ).
fof(f2182,plain,
( spl18_21
| spl18_22 ),
inference(avatar_split_clause,[],[f761,f2179,f2175]) ).
fof(f2175,plain,
( spl18_21
<=> empty(sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
fof(f2179,plain,
( spl18_22
<=> in(empty_set,sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
fof(f1665,plain,
( ~ spl18_4
| ~ spl18_11
| spl18_20 ),
inference(avatar_contradiction_clause,[],[f1664]) ).
fof(f1664,plain,
( $false
| ~ spl18_4
| ~ spl18_11
| spl18_20 ),
inference(subsumption_resolution,[],[f1663,f212]) ).
fof(f1663,plain,
( ~ element(sK5(empty_set),empty_set)
| ~ spl18_4
| ~ spl18_11
| spl18_20 ),
inference(forward_demodulation,[],[f1662,f1605]) ).
fof(f1662,plain,
( ~ element(sK5(sK3(empty_set)),empty_set)
| ~ spl18_4
| ~ spl18_11
| spl18_20 ),
inference(forward_demodulation,[],[f1661,f1605]) ).
fof(f1661,plain,
( ~ element(sK5(sK3(sK3(empty_set))),sK3(empty_set))
| ~ spl18_4
| spl18_20 ),
inference(forward_demodulation,[],[f1578,f1585]) ).
fof(f1578,plain,
( ~ element(sK5(sK3(sK3(sK2))),sK3(sK2))
| spl18_20 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f1577,plain,
( spl18_20
<=> element(sK5(sK3(sK3(sK2))),sK3(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
fof(f1625,plain,
( ~ spl18_4
| ~ spl18_11
| spl18_19 ),
inference(avatar_contradiction_clause,[],[f1624]) ).
fof(f1624,plain,
( $false
| ~ spl18_4
| ~ spl18_11
| spl18_19 ),
inference(subsumption_resolution,[],[f1623,f1599]) ).
fof(f1623,plain,
( ~ empty(sK3(empty_set))
| ~ spl18_4
| ~ spl18_11
| spl18_19 ),
inference(forward_demodulation,[],[f1622,f1605]) ).
fof(f1622,plain,
( ~ empty(sK3(sK3(empty_set)))
| ~ spl18_4
| spl18_19 ),
inference(forward_demodulation,[],[f1574,f1585]) ).
fof(f1574,plain,
( ~ empty(sK3(sK3(sK2)))
| spl18_19 ),
inference(avatar_component_clause,[],[f1573]) ).
fof(f1580,plain,
( spl18_19
| spl18_20
| spl18_11 ),
inference(avatar_split_clause,[],[f1561,f865,f1577,f1573]) ).
fof(f1561,plain,
( element(sK5(sK3(sK3(sK2))),sK3(sK2))
| empty(sK3(sK3(sK2)))
| spl18_11 ),
inference(resolution,[],[f1535,f379]) ).
fof(f1535,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK2)))
| element(X0,sK3(sK2)) )
| spl18_11 ),
inference(superposition,[],[f809,f1446]) ).
fof(f1446,plain,
( sK3(sK2) = set_union2(sK3(sK2),sK3(sK3(sK2)))
| spl18_11 ),
inference(resolution,[],[f866,f340]) ).
fof(f1445,plain,
( spl18_4
| ~ spl18_11 ),
inference(avatar_contradiction_clause,[],[f1444]) ).
fof(f1444,plain,
( $false
| spl18_4
| ~ spl18_11 ),
inference(subsumption_resolution,[],[f1438,f352]) ).
fof(f1438,plain,
( empty(sK2)
| ~ spl18_11 ),
inference(resolution,[],[f867,f191]) ).
fof(f1431,plain,
spl18_17,
inference(avatar_contradiction_clause,[],[f1430]) ).
fof(f1430,plain,
( $false
| spl18_17 ),
inference(subsumption_resolution,[],[f1429,f189]) ).
fof(f1429,plain,
( ~ latt_str(boole_lattice(sK0))
| spl18_17 ),
inference(resolution,[],[f1423,f201]) ).
fof(f1423,plain,
( ~ join_semilatt_str(boole_lattice(sK0))
| spl18_17 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1428,plain,
( ~ spl18_17
| spl18_18
| ~ spl18_1
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f1326,f350,f282,f1425,f1421]) ).
fof(f1326,plain,
( empty_set = join(boole_lattice(sK0),sK1,empty_set)
| ~ join_semilatt_str(boole_lattice(sK0))
| ~ spl18_1
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1325,f186]) ).
fof(f1325,plain,
( empty_set = join(boole_lattice(sK0),sK1,empty_set)
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1324,f177]) ).
fof(f1324,plain,
( empty_set = join(boole_lattice(sK0),sK1,empty_set)
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1323,f878]) ).
fof(f1323,plain,
( empty_set = join(boole_lattice(sK0),sK1,empty_set)
| ~ element(empty_set,the_carrier(boole_lattice(sK0)))
| ~ element(sK1,the_carrier(boole_lattice(sK0)))
| ~ join_semilatt_str(boole_lattice(sK0))
| empty_carrier(boole_lattice(sK0))
| ~ spl18_1
| ~ spl18_4 ),
inference(resolution,[],[f206,f885]) ).
fof(f1259,plain,
( spl18_9
| ~ spl18_15 ),
inference(avatar_contradiction_clause,[],[f1258]) ).
fof(f1258,plain,
( $false
| spl18_9
| ~ spl18_15 ),
inference(subsumption_resolution,[],[f1252,f847]) ).
fof(f1252,plain,
( empty(sK3(sK1))
| ~ spl18_15 ),
inference(resolution,[],[f1220,f191]) ).
fof(f1220,plain,
( empty(sK3(sK3(sK1)))
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1249,plain,
( spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f1248]) ).
fof(f1248,plain,
( $false
| spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f1242,f316]) ).
fof(f1242,plain,
( ~ subset(empty_set,empty_set)
| spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(superposition,[],[f879,f1230]) ).
fof(f1247,plain,
( ~ spl18_3
| ~ spl18_4
| ~ spl18_10
| spl18_12 ),
inference(avatar_contradiction_clause,[],[f1246]) ).
fof(f1246,plain,
( $false
| ~ spl18_3
| ~ spl18_4
| ~ spl18_10
| spl18_12 ),
inference(subsumption_resolution,[],[f1241,f892]) ).
fof(f892,plain,
( ~ element(sK5(sK3(empty_set)),empty_set)
| ~ spl18_4
| spl18_12 ),
inference(forward_demodulation,[],[f870,f877]) ).
fof(f870,plain,
( ~ element(sK5(sK3(sK2)),sK2)
| spl18_12 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f869,plain,
( spl18_12
<=> element(sK5(sK3(sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f1241,plain,
( element(sK5(sK3(empty_set)),empty_set)
| ~ spl18_3
| ~ spl18_10 ),
inference(superposition,[],[f852,f1230]) ).
fof(f852,plain,
( element(sK5(sK3(sK1)),sK1)
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f850,plain,
( spl18_10
<=> element(sK5(sK3(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
fof(f1245,plain,
( spl18_2
| ~ spl18_3 ),
inference(avatar_contradiction_clause,[],[f1244]) ).
fof(f1244,plain,
( $false
| spl18_2
| ~ spl18_3 ),
inference(subsumption_resolution,[],[f1237,f316]) ).
fof(f1237,plain,
( ~ subset(empty_set,sK2)
| spl18_2
| ~ spl18_3 ),
inference(superposition,[],[f287,f1230]) ).
fof(f1225,plain,
( spl18_15
| spl18_16
| spl18_9 ),
inference(avatar_split_clause,[],[f947,f846,f1222,f1218]) ).
fof(f1222,plain,
( spl18_16
<=> element(sK5(sK3(sK3(sK1))),sK3(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f947,plain,
( element(sK5(sK3(sK3(sK1))),sK3(sK1))
| empty(sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f907,f379]) ).
fof(f907,plain,
( ! [X0] :
( ~ in(X0,sK3(sK3(sK1)))
| element(X0,sK3(sK1)) )
| spl18_9 ),
inference(resolution,[],[f902,f703]) ).
fof(f902,plain,
( subset(sK3(sK3(sK1)),sK3(sK1))
| spl18_9 ),
inference(superposition,[],[f305,f862]) ).
fof(f862,plain,
( sK3(sK1) = set_union2(sK3(sK1),sK3(sK3(sK1)))
| spl18_9 ),
inference(resolution,[],[f847,f340]) ).
fof(f1211,plain,
~ spl18_13,
inference(avatar_contradiction_clause,[],[f1210]) ).
fof(f1210,plain,
( $false
| ~ spl18_13 ),
inference(subsumption_resolution,[],[f1204,f256]) ).
fof(f1204,plain,
( empty(sK9)
| ~ spl18_13 ),
inference(resolution,[],[f1198,f191]) ).
fof(f1198,plain,
( empty(sK3(sK9))
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f1196]) ).
fof(f1196,plain,
( spl18_13
<=> empty(sK3(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f1203,plain,
( spl18_13
| spl18_14 ),
inference(avatar_split_clause,[],[f959,f1200,f1196]) ).
fof(f1200,plain,
( spl18_14
<=> element(sK5(sK3(sK9)),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f872,plain,
( spl18_11
| spl18_12
| spl18_4 ),
inference(avatar_split_clause,[],[f837,f350,f869,f865]) ).
fof(f837,plain,
( element(sK5(sK3(sK2)),sK2)
| empty(sK3(sK2))
| spl18_4 ),
inference(resolution,[],[f818,f379]) ).
fof(f818,plain,
( ! [X0] :
( ~ in(X0,sK3(sK2))
| element(X0,sK2) )
| spl18_4 ),
inference(resolution,[],[f703,f447]) ).
fof(f447,plain,
( subset(sK3(sK2),sK2)
| spl18_4 ),
inference(superposition,[],[f305,f438]) ).
fof(f438,plain,
( sK2 = set_union2(sK2,sK3(sK2))
| spl18_4 ),
inference(resolution,[],[f340,f352]) ).
fof(f861,plain,
( spl18_3
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f860]) ).
fof(f860,plain,
( $false
| spl18_3
| ~ spl18_9 ),
inference(subsumption_resolution,[],[f854,f347]) ).
fof(f854,plain,
( empty(sK1)
| ~ spl18_9 ),
inference(resolution,[],[f848,f191]) ).
fof(f848,plain,
( empty(sK3(sK1))
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f853,plain,
( spl18_9
| spl18_10
| spl18_3 ),
inference(avatar_split_clause,[],[f834,f346,f850,f846]) ).
fof(f834,plain,
( element(sK5(sK3(sK1)),sK1)
| empty(sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f817,f379]) ).
fof(f817,plain,
( ! [X0] :
( ~ in(X0,sK3(sK1))
| element(X0,sK1) )
| spl18_3 ),
inference(resolution,[],[f703,f442]) ).
fof(f442,plain,
( subset(sK3(sK1),sK1)
| spl18_3 ),
inference(superposition,[],[f305,f437]) ).
fof(f437,plain,
( sK1 = set_union2(sK1,sK3(sK1))
| spl18_3 ),
inference(resolution,[],[f340,f347]) ).
fof(f488,plain,
~ spl18_7,
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f482,plain,
( $false
| ~ spl18_7 ),
inference(resolution,[],[f476,f181]) ).
fof(f476,plain,
( ! [X0] : ~ empty(X0)
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f475,plain,
( spl18_7
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f487,plain,
~ spl18_7,
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f484,plain,
( $false
| ~ spl18_7 ),
inference(resolution,[],[f476,f214]) ).
fof(f486,plain,
~ spl18_7,
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f485,plain,
( $false
| ~ spl18_7 ),
inference(resolution,[],[f476,f261]) ).
fof(f480,plain,
( spl18_7
| spl18_8 ),
inference(avatar_split_clause,[],[f465,f478,f475]) ).
fof(f401,plain,
( spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f377,f398,f394]) ).
fof(f394,plain,
( spl18_5
<=> in(sK1,the_carrier(boole_lattice(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
fof(f398,plain,
( spl18_6
<=> empty(the_carrier(boole_lattice(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f353,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f342,f286,f350,f346]) ).
fof(f289,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f179,f286,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 11:40:34 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (16517)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (16520)WARNING: value z3 for option sas not known
% 0.14/0.36 % (16519)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 % (16518)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (16521)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (16523)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.36 % (16520)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.36 % (16522)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.36 % (16524)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.41 TRYING [2]
% 0.14/0.41 TRYING [3]
% 0.20/0.48 % (16520)First to succeed.
% 0.20/0.48 TRYING [4]
% 0.20/0.49 TRYING [4]
% 0.20/0.49 TRYING [3]
% 0.20/0.49 % (16520)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16517"
% 0.20/0.50 % (16520)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (16520)------------------------------
% 0.20/0.50 % (16520)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.50 % (16520)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (16520)Memory used [KB]: 2259
% 0.20/0.50 % (16520)Time elapsed: 0.132 s
% 0.20/0.50 % (16520)Instructions burned: 257 (million)
% 0.20/0.50 % (16517)Success in time 0.144 s
%------------------------------------------------------------------------------