TSTP Solution File: SET637+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 : Tue Apr 30 15:08:59 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 181 ( 17 unt; 0 def)
% Number of atoms : 459 ( 92 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 437 ( 159 ~; 234 |; 30 &)
% ( 9 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 390 ( 377 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f400,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f325,f331,f399]) ).
fof(f399,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f398,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f397,f335]) ).
fof(f335,plain,
( intersect(sK1,sK0)
| ~ spl4_1 ),
inference(resolution,[],[f51,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f51,plain,
( intersect(sK0,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f49,plain,
( spl4_1
<=> intersect(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f397,plain,
( ~ intersect(sK1,sK0)
| spl4_2 ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f394,plain,
( ~ intersect(sK1,sK0)
| ~ intersect(sK1,sK0)
| spl4_2 ),
inference(resolution,[],[f386,f39]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f386,plain,
( ! [X0] :
( ~ member(sK3(sK1,X0),sK0)
| ~ intersect(sK1,X0) )
| spl4_2 ),
inference(resolution,[],[f360,f38]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f360,plain,
( ! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0) )
| spl4_2 ),
inference(subsumption_resolution,[],[f349,f29]) ).
fof(f29,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f349,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK1)
| ~ member(X0,sK0) )
| spl4_2 ),
inference(superposition,[],[f43,f342]) ).
fof(f342,plain,
( empty_set = intersection(sK0,sK1)
| spl4_2 ),
inference(resolution,[],[f54,f37]) ).
fof(f37,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f54,plain,
( ~ not_equal(intersection(sK0,sK1),empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl4_2
<=> not_equal(intersection(sK0,sK1),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f331,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f330,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(global_subsumption,[],[f28,f29,f46,f31,f37,f27,f55,f30,f38,f57,f39,f58,f41,f61,f62,f42,f63,f64,f40,f43,f71,f67,f76,f78,f68,f81,f82,f59,f87,f88,f89,f90,f91,f86,f95,f34,f97,f98,f99,f101,f102,f103,f94,f96,f108,f109,f100,f112,f113,f114,f93,f116,f115,f92,f120,f119,f110,f132,f127,f35,f137,f131,f150,f151,f146,f153,f154,f156,f157,f147,f148,f181,f183,f186,f187,f188,f189,f191,f192,f182,f203,f204,f205,f206,f149,f212,f215,f216,f217,f218,f220,f221,f60,f237,f229,f230,f231,f232,f233,f236,f242,f244,f247,f246,f251,f252,f253,f211,f262,f263,f266,f267,f268,f269,f250,f275,f277,f278,f281,f282,f283,f284,f329,f51]) ).
fof(f329,plain,
( ~ intersect(sK0,sK1)
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f28,f55]) ).
fof(f284,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,X0) ),
inference(resolution,[],[f250,f93]) ).
fof(f283,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,X0) ),
inference(resolution,[],[f250,f115]) ).
fof(f282,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2)) ),
inference(resolution,[],[f250,f92]) ).
fof(f281,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,intersection(X2,X1)) ),
inference(resolution,[],[f250,f119]) ).
fof(f278,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,X2) ),
inference(resolution,[],[f250,f236]) ).
fof(f277,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,X2) ),
inference(resolution,[],[f250,f246]) ).
fof(f275,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(X0,X1) ),
inference(resolution,[],[f250,f31]) ).
fof(f250,plain,
! [X0,X1] :
( intersect(X0,X1)
| empty_set = intersection(X1,X0) ),
inference(resolution,[],[f246,f149]) ).
fof(f269,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(resolution,[],[f211,f93]) ).
fof(f268,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,intersection(X0,X1)) ),
inference(resolution,[],[f211,f115]) ).
fof(f267,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(resolution,[],[f211,f92]) ).
fof(f266,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,intersection(X1,X0)) ),
inference(resolution,[],[f211,f119]) ).
fof(f263,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(resolution,[],[f211,f236]) ).
fof(f262,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,intersection(X0,X1)) ),
inference(resolution,[],[f211,f246]) ).
fof(f211,plain,
! [X0,X1] :
( intersect(X0,X0)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f149,f78]) ).
fof(f253,plain,
! [X0,X1] :
( intersect(X0,intersection(X1,X0))
| empty_set = intersection(X1,X0) ),
inference(resolution,[],[f246,f131]) ).
fof(f252,plain,
! [X2,X0,X1] :
( intersect(X0,intersection(X1,X0))
| empty_set = intersection(X2,intersection(X1,X0)) ),
inference(resolution,[],[f246,f182]) ).
fof(f251,plain,
! [X0,X1] :
( intersect(X0,X1)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f246,f148]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ intersect(X2,intersection(X1,X0))
| intersect(X0,X2) ),
inference(superposition,[],[f236,f30]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ intersect(X2,intersection(X1,X0))
| intersect(X0,X2) ),
inference(superposition,[],[f236,f30]) ).
fof(f244,plain,
! [X2,X0,X1] :
( intersect(X0,intersection(X0,X1))
| empty_set = intersection(X2,intersection(X0,X1)) ),
inference(resolution,[],[f236,f182]) ).
fof(f242,plain,
! [X0,X1] :
( intersect(X0,X0)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f236,f149]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X1,X0) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X1,X0)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f60,f67]) ).
fof(f233,plain,
! [X2,X0,X1] :
( member(sK3(X2,intersection(X1,X0)),X0)
| ~ intersect(X2,intersection(X0,X1)) ),
inference(superposition,[],[f60,f30]) ).
fof(f232,plain,
! [X2,X0,X1] :
( member(sK3(X2,intersection(X1,X0)),X0)
| ~ intersect(X2,intersection(X0,X1)) ),
inference(superposition,[],[f60,f30]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X3,X1)
| ~ member(sK3(X0,intersection(X1,X2)),X3) ),
inference(resolution,[],[f60,f40]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( ~ intersect(X0,intersection(intersection(X1,X2),X3))
| member(sK3(X0,intersection(intersection(X1,X2),X3)),X1) ),
inference(resolution,[],[f60,f41]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( ~ intersect(X0,intersection(intersection(X1,X2),X3))
| member(sK3(X0,intersection(intersection(X1,X2),X3)),X2) ),
inference(resolution,[],[f60,f42]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2)) ),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2))
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f60,f68]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X1)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f41,f39]) ).
fof(f221,plain,
! [X0,X1] :
( intersect(X0,intersection(X1,X0))
| intersection(X0,X1) = empty_set ),
inference(superposition,[],[f149,f30]) ).
fof(f220,plain,
! [X0,X1] :
( intersect(X0,intersection(X1,X0))
| intersection(X0,X1) = empty_set ),
inference(superposition,[],[f149,f30]) ).
fof(f218,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,intersection(intersection(X0,X1),X2)) ),
inference(resolution,[],[f149,f93]) ).
fof(f217,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,intersection(intersection(X0,X1),X2)) ),
inference(resolution,[],[f149,f115]) ).
fof(f216,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(resolution,[],[f149,f92]) ).
fof(f215,plain,
! [X2,X0,X1] :
( empty_set = intersection(intersection(X0,X1),X2)
| intersect(X1,intersection(X1,X0)) ),
inference(resolution,[],[f149,f119]) ).
fof(f212,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(intersection(X0,X1),X0) ),
inference(resolution,[],[f149,f31]) ).
fof(f149,plain,
! [X0,X1] :
( intersect(X0,intersection(X0,X1))
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f131,f92]) ).
fof(f206,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2)) ),
inference(resolution,[],[f182,f93]) ).
fof(f205,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,intersection(X1,X2)) ),
inference(resolution,[],[f182,f115]) ).
fof(f204,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2)) ),
inference(resolution,[],[f182,f92]) ).
fof(f203,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,intersection(X2,X1)) ),
inference(resolution,[],[f182,f119]) ).
fof(f182,plain,
! [X0,X1] :
( intersect(X1,X1)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f148,f78]) ).
fof(f192,plain,
! [X0,X1] :
( intersect(X0,intersection(X1,X0))
| empty_set = intersection(X1,X0) ),
inference(superposition,[],[f148,f30]) ).
fof(f191,plain,
! [X0,X1] :
( intersect(X0,intersection(X1,X0))
| empty_set = intersection(X1,X0) ),
inference(superposition,[],[f148,f30]) ).
fof(f189,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,intersection(intersection(X1,X2),X0)) ),
inference(resolution,[],[f148,f93]) ).
fof(f188,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,intersection(intersection(X1,X2),X0)) ),
inference(resolution,[],[f148,f115]) ).
fof(f187,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X1,intersection(X1,X2)) ),
inference(resolution,[],[f148,f92]) ).
fof(f186,plain,
! [X2,X0,X1] :
( empty_set = intersection(X0,intersection(X1,X2))
| intersect(X2,intersection(X2,X1)) ),
inference(resolution,[],[f148,f119]) ).
fof(f183,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(intersection(X1,X0),X1) ),
inference(resolution,[],[f148,f31]) ).
fof(f181,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(intersection(X1,X0),intersection(X1,X0)) ),
inference(resolution,[],[f148,f82]) ).
fof(f148,plain,
! [X0,X1] :
( intersect(X1,intersection(X1,X0))
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f131,f119]) ).
fof(f147,plain,
! [X0] : empty_set = intersection(X0,empty_set),
inference(resolution,[],[f131,f94]) ).
fof(f157,plain,
! [X0] : empty_set = intersection(X0,empty_set),
inference(superposition,[],[f30,f146]) ).
fof(f156,plain,
! [X0] : empty_set = intersection(X0,empty_set),
inference(superposition,[],[f30,f146]) ).
fof(f154,plain,
! [X0] : empty_set = intersection(X0,empty_set),
inference(superposition,[],[f146,f30]) ).
fof(f153,plain,
! [X0] : empty_set = intersection(X0,empty_set),
inference(superposition,[],[f146,f30]) ).
fof(f146,plain,
! [X0] : empty_set = intersection(empty_set,X0),
inference(resolution,[],[f131,f86]) ).
fof(f151,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(X0,intersection(X0,X1)) ),
inference(resolution,[],[f131,f93]) ).
fof(f150,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(X1,intersection(X0,X1)) ),
inference(resolution,[],[f131,f115]) ).
fof(f131,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0 ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f123,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0
| empty_set = X0 ),
inference(resolution,[],[f110,f96]) ).
fof(f137,plain,
! [X2,X0,X1] :
( intersection(X1,X2) = X0
| ~ member(sK2(X0,intersection(X1,X2)),X0)
| ~ member(sK2(X0,intersection(X1,X2)),X2)
| ~ member(sK2(X0,intersection(X1,X2)),X1) ),
inference(resolution,[],[f35,f43]) ).
fof(f35,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f127,plain,
! [X2,X0,X1] :
( intersect(intersection(X0,X1),X2)
| empty_set = X2
| ~ member(sK2(X2,empty_set),X1)
| ~ member(sK2(X2,empty_set),X0) ),
inference(resolution,[],[f110,f43]) ).
fof(f132,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0 ),
inference(subsumption_resolution,[],[f129,f29]) ).
fof(f129,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0
| member(sK2(X0,empty_set),empty_set) ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f125,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0
| member(sK2(X0,empty_set),empty_set)
| empty_set = X0 ),
inference(resolution,[],[f110,f34]) ).
fof(f110,plain,
! [X0,X1] :
( ~ member(sK2(X0,empty_set),X1)
| intersect(X1,X0)
| empty_set = X0 ),
inference(resolution,[],[f96,f40]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X1,X0),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(superposition,[],[f92,f30]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X1,X0),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(superposition,[],[f92,f30]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1))
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[],[f59,f67]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X1,X0),X2)
| intersect(X0,X2) ),
inference(superposition,[],[f93,f30]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X1,X0),X2)
| intersect(X0,X2) ),
inference(superposition,[],[f93,f30]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X0,X1),X2)
| intersect(X0,X2) ),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ intersect(intersection(X0,X1),X2)
| intersect(X0,X2)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[],[f59,f68]) ).
fof(f114,plain,
! [X0,X1] :
( empty_set = X0
| intersect(X1,X0)
| ~ member(sK2(empty_set,X0),X1) ),
inference(resolution,[],[f100,f40]) ).
fof(f113,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| member(sK2(empty_set,intersection(X0,X1)),X0) ),
inference(resolution,[],[f100,f41]) ).
fof(f112,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| member(sK2(empty_set,intersection(X0,X1)),X1) ),
inference(resolution,[],[f100,f42]) ).
fof(f100,plain,
! [X0] :
( member(sK2(empty_set,X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f34,f29]) ).
fof(f109,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| member(sK2(intersection(X0,X1),empty_set),X0) ),
inference(resolution,[],[f96,f41]) ).
fof(f108,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| member(sK2(intersection(X0,X1),empty_set),X1) ),
inference(resolution,[],[f96,f42]) ).
fof(f96,plain,
! [X0] :
( member(sK2(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f34,f29]) ).
fof(f94,plain,
! [X0,X1] : ~ intersect(intersection(X0,empty_set),X1),
inference(superposition,[],[f86,f30]) ).
fof(f103,plain,
! [X2,X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| intersect(X2,X0)
| ~ member(sK2(X0,X1),X2) ),
inference(resolution,[],[f34,f40]) ).
fof(f102,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X0) ),
inference(resolution,[],[f34,f41]) ).
fof(f101,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X2)
| intersection(X0,X1) = X2
| member(sK2(intersection(X0,X1),X2),X1) ),
inference(resolution,[],[f34,f42]) ).
fof(f99,plain,
! [X2,X0,X1] :
( member(sK2(X0,X1),X0)
| X0 = X1
| intersect(X2,X1)
| ~ member(sK2(X0,X1),X2) ),
inference(resolution,[],[f34,f40]) ).
fof(f98,plain,
! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X1) ),
inference(resolution,[],[f34,f41]) ).
fof(f97,plain,
! [X2,X0,X1] :
( member(sK2(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0
| member(sK2(X0,intersection(X1,X2)),X2) ),
inference(resolution,[],[f34,f42]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f95,plain,
! [X0,X1] : ~ intersect(intersection(X0,empty_set),X1),
inference(superposition,[],[f86,f30]) ).
fof(f86,plain,
! [X0,X1] : ~ intersect(intersection(empty_set,X0),X1),
inference(resolution,[],[f59,f29]) ).
fof(f91,plain,
! [X2,X0,X1] :
( member(sK3(intersection(X1,X0),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(superposition,[],[f59,f30]) ).
fof(f90,plain,
! [X2,X0,X1] :
( member(sK3(intersection(X1,X0),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(superposition,[],[f59,f30]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ intersect(intersection(X0,X1),X2)
| intersect(X3,X0)
| ~ member(sK3(intersection(X0,X1),X2),X3) ),
inference(resolution,[],[f59,f40]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ intersect(intersection(intersection(X0,X1),X2),X3)
| member(sK3(intersection(intersection(X0,X1),X2),X3),X0) ),
inference(resolution,[],[f59,f41]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ intersect(intersection(intersection(X0,X1),X2),X3)
| member(sK3(intersection(intersection(X0,X1),X2),X3),X1) ),
inference(resolution,[],[f59,f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[],[f41,f38]) ).
fof(f82,plain,
! [X0,X1] :
( ~ intersect(X1,X0)
| intersect(X0,X0) ),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( intersect(X0,X0)
| ~ intersect(X1,X0)
| ~ intersect(X1,X0) ),
inference(resolution,[],[f68,f39]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( intersect(intersection(X0,X1),X2)
| ~ intersect(X3,X2)
| ~ member(sK3(X3,X2),X1)
| ~ member(sK3(X3,X2),X0) ),
inference(resolution,[],[f68,f43]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ member(sK3(X2,X1),X0)
| intersect(X0,X1)
| ~ intersect(X2,X1) ),
inference(resolution,[],[f40,f39]) ).
fof(f78,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X0,X0) ),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( intersect(X0,X0)
| ~ intersect(X0,X1)
| ~ intersect(X0,X1) ),
inference(resolution,[],[f67,f38]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( intersect(intersection(X0,X1),X2)
| ~ intersect(X2,X3)
| ~ member(sK3(X2,X3),X1)
| ~ member(sK3(X2,X3),X0) ),
inference(resolution,[],[f67,f43]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ member(sK3(X1,X2),X0)
| intersect(X0,X1)
| ~ intersect(X1,X2) ),
inference(resolution,[],[f40,f38]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| intersect(X3,intersection(X2,X1))
| ~ member(X0,X3) ),
inference(resolution,[],[f43,f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| intersect(X0,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X2)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f42,f39]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(sK3(intersection(X0,X1),X2),X1)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[],[f42,f38]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X1,X0))
| member(X2,X0) ),
inference(superposition,[],[f41,f30]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X1,X0))
| member(X2,X0) ),
inference(superposition,[],[f41,f30]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f58,plain,
! [X0] : ~ intersect(X0,empty_set),
inference(resolution,[],[f39,f29]) ).
fof(f57,plain,
! [X0] : ~ intersect(empty_set,X0),
inference(resolution,[],[f38,f29]) ).
fof(f30,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f55,plain,
( not_equal(intersection(sK0,sK1),empty_set)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f27,plain,
( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) )
& ( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
fof(f14,plain,
( ? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) )
=> ( ( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) )
& ( not_equal(intersection(sK0,sK1),empty_set)
| intersect(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).
fof(f46,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
( ~ not_equal(intersection(sK0,sK1),empty_set)
| ~ intersect(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f325,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f324,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f310,f46]) ).
fof(f310,plain,
( not_equal(empty_set,empty_set)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f55,f289]) ).
fof(f289,plain,
( empty_set = intersection(sK0,sK1)
| spl4_1 ),
inference(superposition,[],[f286,f30]) ).
fof(f286,plain,
( empty_set = intersection(sK1,sK0)
| spl4_1 ),
inference(resolution,[],[f250,f50]) ).
fof(f50,plain,
( ~ intersect(sK0,sK1)
| spl4_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f56,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f27,f53,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n025.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 : Tue Apr 30 01:49:41 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (28555)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (28558)WARNING: value z3 for option sas not known
% 0.15/0.38 % (28559)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (28557)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 % (28560)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 % (28558)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 % (28556)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (28561)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 % (28562)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [5]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 % (28558)First to succeed.
% 0.15/0.39 % (28558)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (28558)------------------------------
% 0.15/0.40 % (28558)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (28558)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (28558)Memory used [KB]: 904
% 0.15/0.40 % (28558)Time elapsed: 0.015 s
% 0.15/0.40 % (28558)Instructions burned: 21 (million)
% 0.15/0.40 % (28558)------------------------------
% 0.15/0.40 % (28558)------------------------------
% 0.15/0.40 % (28555)Success in time 0.032 s
%------------------------------------------------------------------------------