TSTP Solution File: SEU319+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU319+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 : n023.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 09:33:40 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 234 ( 40 unt; 0 def)
% Number of atoms : 604 ( 76 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 675 ( 305 ~; 306 |; 24 &)
% ( 19 <=>; 20 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 150 ( 134 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f322,plain,
$false,
inference(avatar_sat_refutation,[],[f73,f101,f106,f111,f131,f135,f150,f206,f209,f239,f242,f267,f280,f300,f306,f312,f314,f317,f319,f321]) ).
fof(f321,plain,
( spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f320,plain,
( $false
| spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f71,f47,f63,f64,f57,f48,f51,f56,f49,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f50,f309,f303]) ).
fof(f303,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0)
| ~ spl5_4
| ~ spl5_8 ),
inference(forward_demodulation,[],[f302,f205]) ).
fof(f302,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| closed_subset(sK1,sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f301,f47]) ).
fof(f301,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| closed_subset(sK1,sK0)
| ~ top_str(sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f291,f48]) ).
fof(f291,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ spl5_4 ),
inference(superposition,[],[f55,f157]) ).
fof(f309,plain,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0)
| ~ spl5_4
| ~ spl5_8 ),
inference(forward_demodulation,[],[f308,f205]) ).
fof(f308,plain,
( open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f307,f47]) ).
fof(f307,plain,
( open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0)
| ~ top_str(sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f243,f48]) ).
fof(f243,plain,
( open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ spl5_4 ),
inference(superposition,[],[f54,f157]) ).
fof(f50,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) )
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f36,f38,f37]) ).
fof(f37,plain,
( ? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(sK0),X1),sK0)
| ~ closed_subset(X1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),X1),sK0)
| closed_subset(X1,sK0) )
& element(X1,powerset(the_carrier(sK0))) )
& top_str(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(sK0),X1),sK0)
| ~ closed_subset(X1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),X1),sK0)
| closed_subset(X1,sK0) )
& element(X1,powerset(the_carrier(sK0))) )
=> ( ( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) )
& element(sK1,powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ( closed_subset(X1,X0)
<~> open_subset(subset_complement(the_carrier(X0),X1),X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f55,plain,
! [X0,X1] :
( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(f288,plain,
set_difference(sK2(powerset(the_carrier(sK0))),sK1) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(sK2(powerset(the_carrier(sK0))),sK1))),
inference(resolution,[],[f283,f59]) ).
fof(f287,plain,
subset_complement(the_carrier(sK0),set_difference(sK2(powerset(the_carrier(sK0))),sK1)) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(sK2(powerset(the_carrier(sK0))),sK1)))),
inference(resolution,[],[f283,f76]) ).
fof(f286,plain,
! [X0] :
( subset_difference(the_carrier(sK0),X0,set_difference(sK2(powerset(the_carrier(sK0))),sK1)) = set_difference(X0,set_difference(sK2(powerset(the_carrier(sK0))),sK1))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f283,f62]) ).
fof(f284,plain,
subset_difference(the_carrier(sK0),set_difference(sK2(powerset(the_carrier(sK0))),sK1),sK1) = set_difference(set_difference(sK2(powerset(the_carrier(sK0))),sK1),sK1),
inference(resolution,[],[f283,f142]) ).
fof(f283,plain,
element(set_difference(sK2(powerset(the_carrier(sK0))),sK1),powerset(the_carrier(sK0))),
inference(subsumption_resolution,[],[f282,f56]) ).
fof(f282,plain,
( element(set_difference(sK2(powerset(the_carrier(sK0))),sK1),powerset(the_carrier(sK0)))
| ~ element(sK2(powerset(the_carrier(sK0))),powerset(the_carrier(sK0))) ),
inference(subsumption_resolution,[],[f281,f48]) ).
fof(f281,plain,
( element(set_difference(sK2(powerset(the_carrier(sK0))),sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(sK2(powerset(the_carrier(sK0))),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f61,f162]) ).
fof(f162,plain,
subset_difference(the_carrier(sK0),sK2(powerset(the_carrier(sK0))),sK1) = set_difference(sK2(powerset(the_carrier(sK0))),sK1),
inference(resolution,[],[f142,f56]) ).
fof(f54,plain,
! [X0,X1] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f179,plain,
( element(set_difference(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ element(the_carrier(sK0),powerset(the_carrier(sK0))) ),
inference(subsumption_resolution,[],[f178,f48]) ).
fof(f178,plain,
( element(set_difference(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(the_carrier(sK0),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f61,f177]) ).
fof(f169,plain,
set_difference(sK1,sK1) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(sK1,sK1))),
inference(resolution,[],[f165,f59]) ).
fof(f228,plain,
set_difference(set_difference(sK1,sK1),sK1) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(set_difference(sK1,sK1),sK1))),
inference(resolution,[],[f223,f59]) ).
fof(f227,plain,
subset_complement(the_carrier(sK0),set_difference(set_difference(sK1,sK1),sK1)) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(set_difference(sK1,sK1),sK1)))),
inference(resolution,[],[f223,f76]) ).
fof(f226,plain,
! [X0] :
( subset_difference(the_carrier(sK0),X0,set_difference(set_difference(sK1,sK1),sK1)) = set_difference(X0,set_difference(set_difference(sK1,sK1),sK1))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f223,f62]) ).
fof(f224,plain,
subset_difference(the_carrier(sK0),set_difference(set_difference(sK1,sK1),sK1),sK1) = set_difference(set_difference(set_difference(sK1,sK1),sK1),sK1),
inference(resolution,[],[f223,f142]) ).
fof(f223,plain,
element(set_difference(set_difference(sK1,sK1),sK1),powerset(the_carrier(sK0))),
inference(subsumption_resolution,[],[f222,f165]) ).
fof(f222,plain,
( element(set_difference(set_difference(sK1,sK1),sK1),powerset(the_carrier(sK0)))
| ~ element(set_difference(sK1,sK1),powerset(the_carrier(sK0))) ),
inference(subsumption_resolution,[],[f221,f48]) ).
fof(f221,plain,
( element(set_difference(set_difference(sK1,sK1),sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(set_difference(sK1,sK1),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f61,f166]) ).
fof(f166,plain,
subset_difference(the_carrier(sK0),set_difference(sK1,sK1),sK1) = set_difference(set_difference(sK1,sK1),sK1),
inference(resolution,[],[f165,f142]) ).
fof(f214,plain,
( ! [X0] :
( subset_difference(the_carrier(sK0),X0,subset_complement(the_carrier(sK0),sK1)) = set_difference(X0,subset_complement(the_carrier(sK0),sK1))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl5_4
| ~ spl5_8 ),
inference(resolution,[],[f211,f62]) ).
fof(f212,plain,
( subset_difference(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1),sK1) = set_difference(subset_complement(the_carrier(sK0),sK1),sK1)
| ~ spl5_4
| ~ spl5_8 ),
inference(resolution,[],[f211,f142]) ).
fof(f211,plain,
( element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ spl5_4
| ~ spl5_8 ),
inference(superposition,[],[f172,f205]) ).
fof(f205,plain,
( subset_complement(the_carrier(sK0),sK1) = set_difference(cast_as_carrier_subset(sK0),sK1)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f203,plain,
( spl5_8
<=> subset_complement(the_carrier(sK0),sK1) = set_difference(cast_as_carrier_subset(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f197,plain,
( subset_complement(the_carrier(sK0),sK1) = set_difference(cast_as_carrier_subset(sK0),sK1)
| ~ one_sorted_str(sK0)
| ~ spl5_4 ),
inference(forward_demodulation,[],[f190,f157]) ).
fof(f190,plain,
( subset_complement(the_carrier(sK0),sK1) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1)
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f53,f48]) ).
fof(f191,plain,
! [X0] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),sK2(powerset(the_carrier(X0)))) = subset_complement(the_carrier(X0),sK2(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f53,f56]) ).
fof(f189,plain,
( subset_complement(the_carrier(sK0),set_difference(cast_as_carrier_subset(sK0),sK1)) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),set_difference(cast_as_carrier_subset(sK0),sK1))
| ~ one_sorted_str(sK0)
| ~ spl5_4 ),
inference(resolution,[],[f53,f172]) ).
fof(f188,plain,
( subset_complement(the_carrier(sK0),set_difference(sK1,sK1)) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),set_difference(sK1,sK1))
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f53,f165]) ).
fof(f185,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_complement(the_carrier(X0),X1)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),X1))
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(resolution,[],[f53,f58]) ).
fof(f184,plain,
! [X2,X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),X1,X2)) = subset_complement(the_carrier(X0),subset_difference(the_carrier(X0),X1,X2))
| ~ one_sorted_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(resolution,[],[f53,f61]) ).
fof(f182,plain,
( subset_complement(the_carrier(sK0),cast_as_carrier_subset(sK0)) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),cast_as_carrier_subset(sK0))
| ~ one_sorted_str(sK0)
| ~ spl5_4 ),
inference(resolution,[],[f53,f100]) ).
fof(f192,plain,
! [X0] :
( subset_complement(the_carrier(X0),cast_as_carrier_subset(X0)) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0) ),
inference(duplicate_literal_removal,[],[f181]) ).
fof(f181,plain,
! [X0] :
( subset_complement(the_carrier(X0),cast_as_carrier_subset(X0)) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f53,f52]) ).
fof(f180,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ one_sorted_str(X0)
| ~ subset(X1,the_carrier(X0)) ),
inference(resolution,[],[f53,f60]) ).
fof(f53,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ! [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f177,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) = set_difference(the_carrier(sK0),sK1),
inference(resolution,[],[f155,f57]) ).
fof(f155,plain,
! [X0] :
( ~ subset(X0,the_carrier(sK0))
| subset_difference(the_carrier(sK0),X0,sK1) = set_difference(X0,sK1) ),
inference(resolution,[],[f142,f60]) ).
fof(f176,plain,
( set_difference(cast_as_carrier_subset(sK0),sK1) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(cast_as_carrier_subset(sK0),sK1)))
| ~ spl5_4 ),
inference(resolution,[],[f172,f59]) ).
fof(f175,plain,
( subset_complement(the_carrier(sK0),set_difference(cast_as_carrier_subset(sK0),sK1)) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(cast_as_carrier_subset(sK0),sK1))))
| ~ spl5_4 ),
inference(resolution,[],[f172,f76]) ).
fof(f174,plain,
( ! [X0] :
( subset_difference(the_carrier(sK0),X0,set_difference(cast_as_carrier_subset(sK0),sK1)) = set_difference(X0,set_difference(cast_as_carrier_subset(sK0),sK1))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl5_4 ),
inference(resolution,[],[f172,f62]) ).
fof(f173,plain,
( subset_difference(the_carrier(sK0),set_difference(cast_as_carrier_subset(sK0),sK1),sK1) = set_difference(set_difference(cast_as_carrier_subset(sK0),sK1),sK1)
| ~ spl5_4 ),
inference(resolution,[],[f172,f142]) ).
fof(f172,plain,
( element(set_difference(cast_as_carrier_subset(sK0),sK1),powerset(the_carrier(sK0)))
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f171,f100]) ).
fof(f171,plain,
( element(set_difference(cast_as_carrier_subset(sK0),sK1),powerset(the_carrier(sK0)))
| ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f170,f48]) ).
fof(f170,plain,
( element(set_difference(cast_as_carrier_subset(sK0),sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| ~ spl5_4 ),
inference(superposition,[],[f61,f157]) ).
fof(f157,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) = set_difference(cast_as_carrier_subset(sK0),sK1)
| ~ spl5_4 ),
inference(resolution,[],[f142,f100]) ).
fof(f168,plain,
subset_complement(the_carrier(sK0),set_difference(sK1,sK1)) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),set_difference(sK1,sK1)))),
inference(resolution,[],[f165,f76]) ).
fof(f167,plain,
! [X0] :
( subset_difference(the_carrier(sK0),X0,set_difference(sK1,sK1)) = set_difference(X0,set_difference(sK1,sK1))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f165,f62]) ).
fof(f165,plain,
element(set_difference(sK1,sK1),powerset(the_carrier(sK0))),
inference(subsumption_resolution,[],[f164,f48]) ).
fof(f164,plain,
( element(set_difference(sK1,sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(duplicate_literal_removal,[],[f163]) ).
fof(f163,plain,
( element(set_difference(sK1,sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(superposition,[],[f61,f161]) ).
fof(f161,plain,
subset_difference(the_carrier(sK0),sK1,sK1) = set_difference(sK1,sK1),
inference(resolution,[],[f142,f48]) ).
fof(f159,plain,
! [X0] :
( subset_difference(the_carrier(sK0),subset_complement(the_carrier(sK0),X0),sK1) = set_difference(subset_complement(the_carrier(sK0),X0),sK1)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f142,f58]) ).
fof(f158,plain,
! [X0,X1] :
( subset_difference(the_carrier(sK0),subset_difference(the_carrier(sK0),X0,X1),sK1) = set_difference(subset_difference(the_carrier(sK0),X0,X1),sK1)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f142,f61]) ).
fof(f156,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) = set_difference(cast_as_carrier_subset(sK0),sK1)
| ~ one_sorted_str(sK0) ),
inference(resolution,[],[f142,f52]) ).
fof(f142,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK0)))
| subset_difference(the_carrier(sK0),X0,sK1) = set_difference(X0,sK1) ),
inference(resolution,[],[f62,f48]) ).
fof(f143,plain,
! [X0,X1] :
( subset_difference(X0,X1,sK2(powerset(X0))) = set_difference(X1,sK2(powerset(X0)))
| ~ element(X1,powerset(X0)) ),
inference(resolution,[],[f62,f56]) ).
fof(f140,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,subset_complement(X0,X2)) = set_difference(X1,subset_complement(X0,X2))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(resolution,[],[f62,f58]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( subset_difference(X0,X1,subset_difference(X0,X2,X3)) = set_difference(X1,subset_difference(X0,X2,X3))
| ~ element(X1,powerset(X0))
| ~ element(X3,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(resolution,[],[f62,f61]) ).
fof(f138,plain,
( ! [X0] :
( subset_difference(the_carrier(sK0),X0,cast_as_carrier_subset(sK0)) = set_difference(X0,cast_as_carrier_subset(sK0))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl5_4 ),
inference(resolution,[],[f62,f100]) ).
fof(f137,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = set_difference(X1,cast_as_carrier_subset(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f62,f52]) ).
fof(f136,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ subset(X2,X0) ),
inference(resolution,[],[f62,f60]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f87,plain,
( element(cast_as_carrier_subset(sK3),powerset(the_carrier(sK3)))
| ~ element(subset_complement(the_carrier(sK3),cast_as_carrier_subset(sK3)),powerset(the_carrier(sK3))) ),
inference(superposition,[],[f58,f85]) ).
fof(f113,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| subset_complement(X0,X1) = subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))) ),
inference(resolution,[],[f76,f60]) ).
fof(f117,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = subset_complement(X0,subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))))
| ~ element(X1,powerset(X0)) ),
inference(resolution,[],[f76,f58]) ).
fof(f116,plain,
! [X2,X0,X1] :
( subset_complement(X0,subset_difference(X0,X1,X2)) = subset_complement(X0,subset_complement(X0,subset_complement(X0,subset_difference(X0,X1,X2))))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(resolution,[],[f76,f61]) ).
fof(f114,plain,
! [X0] :
( subset_complement(the_carrier(X0),cast_as_carrier_subset(X0)) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),cast_as_carrier_subset(X0))))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f76,f52]) ).
fof(f76,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = subset_complement(X0,subset_complement(X0,subset_complement(X0,X1))) ),
inference(resolution,[],[f59,f58]) ).
fof(f100,plain,
( element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f98,plain,
( spl5_4
<=> element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f90,plain,
( element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| ~ element(subset_complement(the_carrier(sK0),cast_as_carrier_subset(sK0)),powerset(the_carrier(sK0))) ),
inference(superposition,[],[f58,f88]) ).
fof(f92,plain,
( element(cast_as_carrier_subset(sK4),powerset(the_carrier(sK4)))
| ~ element(subset_complement(the_carrier(sK4),cast_as_carrier_subset(sK4)),powerset(the_carrier(sK4))) ),
inference(superposition,[],[f58,f89]) ).
fof(f89,plain,
cast_as_carrier_subset(sK4) = subset_complement(the_carrier(sK4),subset_complement(the_carrier(sK4),cast_as_carrier_subset(sK4))),
inference(resolution,[],[f86,f64]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| subset_difference(X1,X2,X0) = subset_complement(X1,subset_complement(X1,subset_difference(X1,X2,X0))) ),
inference(resolution,[],[f61,f59]) ).
fof(f61,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f88,plain,
cast_as_carrier_subset(sK0) = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),cast_as_carrier_subset(sK0))),
inference(resolution,[],[f86,f47]) ).
fof(f86,plain,
! [X0] :
( ~ top_str(X0)
| cast_as_carrier_subset(X0) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),cast_as_carrier_subset(X0))) ),
inference(resolution,[],[f75,f51]) ).
fof(f85,plain,
cast_as_carrier_subset(sK3) = subset_complement(the_carrier(sK3),subset_complement(the_carrier(sK3),cast_as_carrier_subset(sK3))),
inference(resolution,[],[f75,f63]) ).
fof(f75,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = subset_complement(the_carrier(X0),subset_complement(the_carrier(X0),cast_as_carrier_subset(X0))) ),
inference(resolution,[],[f59,f52]) ).
fof(f78,plain,
! [X0] : sK2(powerset(X0)) = subset_complement(X0,subset_complement(X0,sK2(powerset(X0)))),
inference(resolution,[],[f59,f56]) ).
fof(f83,plain,
! [X0] :
( ~ subset(subset_complement(X0,X0),X0)
| element(X0,powerset(X0)) ),
inference(resolution,[],[f81,f60]) ).
fof(f81,plain,
! [X0] :
( ~ element(subset_complement(X0,X0),powerset(X0))
| element(X0,powerset(X0)) ),
inference(superposition,[],[f58,f80]) ).
fof(f80,plain,
! [X0] : subset_complement(X0,subset_complement(X0,X0)) = X0,
inference(resolution,[],[f74,f57]) ).
fof(f74,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(resolution,[],[f59,f60]) ).
fof(f77,plain,
sK1 = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)),
inference(resolution,[],[f59,f48]) ).
fof(f59,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f58,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f52,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f60,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f49,plain,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f56,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f13,f41]) ).
fof(f41,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f51,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f48,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f64,plain,
top_str(sK4),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
top_str(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f11,f45]) ).
fof(f45,plain,
( ? [X0] : top_str(X0)
=> top_str(sK4) ),
introduced(choice_axiom,[]) ).
fof(f11,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f63,plain,
one_sorted_str(sK3),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
one_sorted_str(sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f12,f43]) ).
fof(f43,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK3) ),
introduced(choice_axiom,[]) ).
fof(f12,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f47,plain,
top_str(sK0),
inference(cnf_transformation,[],[f39]) ).
fof(f71,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| spl5_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f70,plain,
( spl5_2
<=> open_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f319,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f318,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f47,f63,f64,f57,f48,f51,f56,f49,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f68,f50,f315,f309,f303]) ).
fof(f315,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ spl5_1 ),
inference(global_subsumption,[],[f47,f63,f64,f57,f48,f51,f56,f49,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f76,f114,f116,f117,f113,f87,f62,f136,f137,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f155,f177,f53,f180,f192,f184,f185,f188,f191,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f68,f50]) ).
fof(f68,plain,
( closed_subset(sK1,sK0)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f66,plain,
( spl5_1
<=> closed_subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f317,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f316,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f47,f63,f64,f57,f48,f51,f56,f49,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f68,f50,f315,f309]) ).
fof(f314,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f313,plain,
( $false
| ~ spl5_1
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f68,f50,f47,f63,f64,f57,f48,f51,f56,f49,f72,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f304,f310]) ).
fof(f310,plain,
( ~ closed_subset(sK1,sK0)
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f50,f72]) ).
fof(f304,plain,
( closed_subset(sK1,sK0)
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f303,f72]) ).
fof(f72,plain,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f312,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f311,plain,
( $false
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f50,f47,f63,f64,f57,f48,f51,f56,f49,f72,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f304,f310]) ).
fof(f306,plain,
( ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f305,plain,
( $false
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(global_subsumption,[],[f50,f47,f63,f64,f57,f48,f51,f56,f49,f72,f60,f52,f58,f59,f77,f74,f80,f81,f83,f78,f75,f85,f86,f88,f61,f91,f89,f92,f90,f100,f76,f114,f116,f117,f113,f87,f62,f136,f137,f138,f139,f140,f143,f142,f156,f158,f159,f161,f165,f167,f168,f157,f172,f173,f174,f175,f176,f155,f177,f53,f180,f192,f182,f184,f185,f188,f189,f191,f197,f205,f211,f212,f214,f166,f223,f224,f226,f227,f228,f169,f179,f54,f162,f283,f284,f286,f287,f288,f55,f304]) ).
fof(f300,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f299,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_4
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f298,f72]) ).
fof(f298,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| spl5_1
| ~ spl5_4
| ~ spl5_8 ),
inference(forward_demodulation,[],[f297,f205]) ).
fof(f297,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| spl5_1
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f296,f47]) ).
fof(f296,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| ~ top_str(sK0)
| spl5_1
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f295,f48]) ).
fof(f295,plain,
( ~ open_subset(set_difference(cast_as_carrier_subset(sK0),sK1),sK0)
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| spl5_1
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f291,f67]) ).
fof(f67,plain,
( ~ closed_subset(sK1,sK0)
| spl5_1 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f280,plain,
( ~ spl5_13
| spl5_14
| ~ spl5_7
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f271,f232,f199,f277,f273]) ).
fof(f273,plain,
( spl5_13
<=> closed_subset(the_carrier(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f277,plain,
( spl5_14
<=> open_subset(subset_complement(the_carrier(sK0),the_carrier(sK0)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f199,plain,
( spl5_7
<=> one_sorted_str(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f232,plain,
( spl5_9
<=> element(the_carrier(sK0),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f271,plain,
( open_subset(subset_complement(the_carrier(sK0),the_carrier(sK0)),sK0)
| ~ closed_subset(the_carrier(sK0),sK0)
| ~ spl5_7
| ~ spl5_9 ),
inference(subsumption_resolution,[],[f270,f47]) ).
fof(f270,plain,
( open_subset(subset_complement(the_carrier(sK0),the_carrier(sK0)),sK0)
| ~ closed_subset(the_carrier(sK0),sK0)
| ~ top_str(sK0)
| ~ spl5_7
| ~ spl5_9 ),
inference(subsumption_resolution,[],[f268,f233]) ).
fof(f233,plain,
( element(the_carrier(sK0),powerset(the_carrier(sK0)))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f268,plain,
( open_subset(subset_complement(the_carrier(sK0),the_carrier(sK0)),sK0)
| ~ closed_subset(the_carrier(sK0),sK0)
| ~ element(the_carrier(sK0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ spl5_7
| ~ spl5_9 ),
inference(superposition,[],[f54,f252]) ).
fof(f252,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),the_carrier(sK0)) = subset_complement(the_carrier(sK0),the_carrier(sK0))
| ~ spl5_7
| ~ spl5_9 ),
inference(subsumption_resolution,[],[f248,f200]) ).
fof(f200,plain,
( one_sorted_str(sK0)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f248,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),the_carrier(sK0)) = subset_complement(the_carrier(sK0),the_carrier(sK0))
| ~ one_sorted_str(sK0)
| ~ spl5_9 ),
inference(resolution,[],[f233,f53]) ).
fof(f267,plain,
( ~ spl5_11
| spl5_12
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f246,f203,f199,f98,f264,f260]) ).
fof(f260,plain,
( spl5_11
<=> closed_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f264,plain,
( spl5_12
<=> open_subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f246,plain,
( open_subset(sK1,sK0)
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f245,f47]) ).
fof(f245,plain,
( open_subset(sK1,sK0)
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ top_str(sK0)
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f244,f211]) ).
fof(f244,plain,
( open_subset(sK1,sK0)
| ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(superposition,[],[f54,f218]) ).
fof(f218,plain,
( sK1 = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_complement(the_carrier(sK0),sK1))
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(forward_demodulation,[],[f217,f77]) ).
fof(f217,plain,
( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_complement(the_carrier(sK0),sK1))
| ~ spl5_4
| ~ spl5_7
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f213,f200]) ).
fof(f213,plain,
( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_complement(the_carrier(sK0),sK1))
| ~ one_sorted_str(sK0)
| ~ spl5_4
| ~ spl5_8 ),
inference(resolution,[],[f211,f53]) ).
fof(f242,plain,
spl5_9,
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f241,plain,
( $false
| spl5_9 ),
inference(subsumption_resolution,[],[f240,f57]) ).
fof(f240,plain,
( ~ subset(the_carrier(sK0),the_carrier(sK0))
| spl5_9 ),
inference(resolution,[],[f234,f60]) ).
fof(f234,plain,
( ~ element(the_carrier(sK0),powerset(the_carrier(sK0)))
| spl5_9 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f239,plain,
( ~ spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f179,f236,f232]) ).
fof(f236,plain,
( spl5_10
<=> element(set_difference(the_carrier(sK0),sK1),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f209,plain,
spl5_7,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f208,plain,
( $false
| spl5_7 ),
inference(subsumption_resolution,[],[f207,f47]) ).
fof(f207,plain,
( ~ top_str(sK0)
| spl5_7 ),
inference(resolution,[],[f201,f51]) ).
fof(f201,plain,
( ~ one_sorted_str(sK0)
| spl5_7 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f206,plain,
( ~ spl5_7
| spl5_8
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f197,f98,f203,f199]) ).
fof(f150,plain,
( spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f149]) ).
fof(f149,plain,
( $false
| spl5_5
| ~ spl5_6 ),
inference(subsumption_resolution,[],[f147,f130]) ).
fof(f130,plain,
( element(cast_as_carrier_subset(sK3),powerset(the_carrier(sK3)))
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f128,plain,
( spl5_6
<=> element(cast_as_carrier_subset(sK3),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f147,plain,
( ~ element(cast_as_carrier_subset(sK3),powerset(the_carrier(sK3)))
| spl5_5 ),
inference(resolution,[],[f126,f58]) ).
fof(f126,plain,
( ~ element(subset_complement(the_carrier(sK3),cast_as_carrier_subset(sK3)),powerset(the_carrier(sK3)))
| spl5_5 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl5_5
<=> element(subset_complement(the_carrier(sK3),cast_as_carrier_subset(sK3)),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f135,plain,
spl5_6,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f134,plain,
( $false
| spl5_6 ),
inference(subsumption_resolution,[],[f132,f63]) ).
fof(f132,plain,
( ~ one_sorted_str(sK3)
| spl5_6 ),
inference(resolution,[],[f129,f52]) ).
fof(f129,plain,
( ~ element(cast_as_carrier_subset(sK3),powerset(the_carrier(sK3)))
| spl5_6 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f87,f128,f124]) ).
fof(f111,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f110,plain,
( $false
| spl5_3
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f108,f100]) ).
fof(f108,plain,
( ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| spl5_3 ),
inference(resolution,[],[f96,f58]) ).
fof(f96,plain,
( ~ element(subset_complement(the_carrier(sK0),cast_as_carrier_subset(sK0)),powerset(the_carrier(sK0)))
| spl5_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f94,plain,
( spl5_3
<=> element(subset_complement(the_carrier(sK0),cast_as_carrier_subset(sK0)),powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f106,plain,
spl5_4,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f105,plain,
( $false
| spl5_4 ),
inference(subsumption_resolution,[],[f104,f47]) ).
fof(f104,plain,
( ~ top_str(sK0)
| spl5_4 ),
inference(resolution,[],[f102,f51]) ).
fof(f102,plain,
( ~ one_sorted_str(sK0)
| spl5_4 ),
inference(resolution,[],[f99,f52]) ).
fof(f99,plain,
( ~ element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0)))
| spl5_4 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( ~ spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f90,f98,f94]) ).
fof(f73,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f49,f70,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU319+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 12:00:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (15483)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (15486)WARNING: value z3 for option sas not known
% 0.15/0.38 % (15484)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (15485)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (15486)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)
% 0.15/0.38 % (15487)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (15488)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)
% 0.15/0.38 % (15489)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)
% 0.15/0.38 % (15490)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 % (15486)First to succeed.
% 0.15/0.39 % (15488)Also succeeded, but the first one will report.
% 0.15/0.40 TRYING [4]
% 0.15/0.40 % (15486)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15483"
% 0.15/0.40 % (15486)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (15486)------------------------------
% 0.15/0.40 % (15486)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (15486)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (15486)Memory used [KB]: 918
% 0.15/0.40 % (15486)Time elapsed: 0.017 s
% 0.15/0.40 % (15486)Instructions burned: 22 (million)
% 0.15/0.40 % (15483)Success in time 0.032 s
%------------------------------------------------------------------------------