TSTP Solution File: COM003+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM003+3 : TPTP v8.1.2. Released v2.0.0.
% 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 04:47:10 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 170 ( 2 unt; 0 def)
% Number of atoms : 751 ( 0 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1014 ( 433 ~; 401 |; 127 &)
% ( 17 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 18 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 238 ( 191 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f267,plain,
$false,
inference(avatar_sat_refutation,[],[f70,f74,f79,f80,f87,f94,f98,f120,f125,f130,f148,f160,f182,f203,f206,f216,f233,f237,f243,f251,f260,f266]) ).
fof(f266,plain,
( ~ spl12_7
| ~ spl12_13 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f265,plain,
( $false
| ~ spl12_7
| ~ spl12_13 ),
inference(subsumption_resolution,[],[f263,f258]) ).
fof(f258,plain,
( program(sK10(sK4))
| ~ spl12_13 ),
inference(resolution,[],[f139,f58]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| program(X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X2,X1) )
& halts2(X2,X1)
& program(X2) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X0,X2,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) )
& halts2(X1,X2)
& program(X1) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X2,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) )
& halts2(X1,X2)
& program(X1) )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f139,plain,
( sP1(sK4,sK11(sK4),sK10(sK4))
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f137,plain,
( spl12_13
<=> sP1(sK4,sK11(sK4),sK10(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f263,plain,
( ~ program(sK10(sK4))
| ~ spl12_7
| ~ spl12_13 ),
inference(resolution,[],[f257,f90]) ).
fof(f90,plain,
( ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl12_7
<=> ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f257,plain,
( halts2(sK10(sK4),sK11(sK4))
| ~ spl12_13 ),
inference(resolution,[],[f139,f59]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| halts2(X2,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f260,plain,
( ~ spl12_13
| ~ spl12_14
| ~ spl12_22 ),
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f259,plain,
( $false
| ~ spl12_13
| ~ spl12_14
| ~ spl12_22 ),
inference(subsumption_resolution,[],[f256,f142]) ).
fof(f142,plain,
( halts3(sK4,sK10(sK4),sK11(sK4))
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f141,plain,
( spl12_14
<=> halts3(sK4,sK10(sK4),sK11(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f256,plain,
( ~ halts3(sK4,sK10(sK4),sK11(sK4))
| ~ spl12_13
| ~ spl12_22 ),
inference(resolution,[],[f139,f238]) ).
fof(f238,plain,
( ! [X0,X1] :
( ~ sP1(sK4,X1,X0)
| ~ halts3(sK4,X0,X1) )
| ~ spl12_22 ),
inference(resolution,[],[f211,f60]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ outputs(X0,good)
| ~ halts3(X0,X2,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
( outputs(sK4,good)
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f210,plain,
( spl12_22
<=> outputs(sK4,good) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).
fof(f251,plain,
( ~ spl12_4
| ~ spl12_5
| ~ spl12_14
| spl12_15
| ~ spl12_22 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f250,plain,
( $false
| ~ spl12_4
| ~ spl12_5
| ~ spl12_14
| spl12_15
| ~ spl12_22 ),
inference(subsumption_resolution,[],[f249,f78]) ).
fof(f78,plain,
( program(sK4)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f76,plain,
( spl12_4
<=> program(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f249,plain,
( ~ program(sK4)
| ~ spl12_5
| ~ spl12_14
| spl12_15
| ~ spl12_22 ),
inference(subsumption_resolution,[],[f248,f146]) ).
fof(f146,plain,
( ~ sP2(sK4)
| spl12_15 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl12_15
<=> sP2(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f248,plain,
( sP2(sK4)
| ~ program(sK4)
| ~ spl12_5
| ~ spl12_14
| ~ spl12_22 ),
inference(subsumption_resolution,[],[f247,f142]) ).
fof(f247,plain,
( ~ halts3(sK4,sK10(sK4),sK11(sK4))
| sP2(sK4)
| ~ program(sK4)
| ~ spl12_5
| ~ spl12_22 ),
inference(resolution,[],[f238,f229]) ).
fof(f229,plain,
( ! [X0] :
( sP1(X0,sK11(X0),sK10(X0))
| sP2(X0)
| ~ program(X0) )
| ~ spl12_5 ),
inference(subsumption_resolution,[],[f226,f133]) ).
fof(f133,plain,
! [X0] :
( program(sK10(X0))
| sP2(X0)
| ~ program(X0) ),
inference(subsumption_resolution,[],[f61,f58]) ).
fof(f61,plain,
! [X0] :
( sP2(X0)
| program(sK10(X0))
| sP1(X0,sK11(X0),sK10(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( sP2(X0)
| ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK10(X0),sK11(X0)) )
& ~ halts2(sK10(X0),sK11(X0))
& program(sK10(X0)) )
| sP1(X0,sK11(X0),sK10(X0))
| ~ program(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f21,f40]) ).
fof(f40,plain,
! [X0] :
( ? [X1,X2] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) )
& ~ halts2(X1,X2)
& program(X1) )
| sP1(X0,X2,X1) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK10(X0),sK11(X0)) )
& ~ halts2(sK10(X0),sK11(X0))
& program(sK10(X0)) )
| sP1(X0,sK11(X0),sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( sP2(X0)
| ? [X1,X2] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) )
& ~ halts2(X1,X2)
& program(X1) )
| sP1(X0,X2,X1) )
| ~ program(X0) ),
inference(definition_folding,[],[f16,f20,f19]) ).
fof(f20,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ( ( outputs(X3,bad)
& halts2(X3,X4) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4) )
& ( ~ halts2(X3,X4)
| ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4) ) )
& program(X3) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f16,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ( ( outputs(X3,bad)
& halts2(X3,X4) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4) )
& ( ~ halts2(X3,X4)
| ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4) ) )
& program(X3) )
| ? [X1,X2] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) )
& ~ halts2(X1,X2)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) )
& halts2(X1,X2)
& program(X1) ) )
| ~ program(X0) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ( ( outputs(X3,bad)
& halts2(X3,X4) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4) )
& ( ~ halts2(X3,X4)
| ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4) ) )
& program(X3) )
| ? [X1,X2] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X2) )
& ~ halts2(X1,X2)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X2) )
& halts2(X1,X2)
& program(X1) ) )
| ~ program(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ( ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X2) ) ) )
& program(X0) )
=> ? [X3] :
( ! [X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X4,X4)
& program(X4) )
=> ( outputs(X3,bad)
& halts2(X3,X4) ) )
& ( ( outputs(X0,good)
& halts3(X0,X4,X4)
& program(X4) )
=> ~ halts2(X3,X4) ) )
& program(X3) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3] :
( ( ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X3,bad)
& halts3(X3,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X3,good)
& halts3(X3,X1,X2) ) ) )
& program(X3) )
=> ? [X4] :
( ! [X1] :
( ( ( outputs(X3,bad)
& halts3(X3,X1,X1)
& program(X1) )
=> ( outputs(X4,bad)
& halts2(X4,X1) ) )
& ( ( outputs(X3,good)
& halts3(X3,X1,X1)
& program(X1) )
=> ~ halts2(X4,X1) ) )
& program(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f226,plain,
( ! [X0] :
( ~ program(sK10(X0))
| sP2(X0)
| sP1(X0,sK11(X0),sK10(X0))
| ~ program(X0) )
| ~ spl12_5 ),
inference(resolution,[],[f83,f62]) ).
fof(f62,plain,
! [X0] :
( ~ halts2(sK10(X0),sK11(X0))
| sP2(X0)
| sP1(X0,sK11(X0),sK10(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
( ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl12_5
<=> ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f243,plain,
( spl12_17
| ~ spl12_5
| ~ spl12_18
| ~ spl12_25 ),
inference(avatar_split_clause,[],[f242,f235,f185,f82,f171]) ).
fof(f171,plain,
( spl12_17
<=> ! [X0] : ~ program(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f185,plain,
( spl12_18
<=> program(sK9(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f235,plain,
( spl12_25
<=> ! [X0] :
( ~ program(X0)
| ~ halts2(sK9(sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).
fof(f242,plain,
( ! [X0] : ~ program(X0)
| ~ spl12_5
| ~ spl12_18
| ~ spl12_25 ),
inference(subsumption_resolution,[],[f241,f186]) ).
fof(f186,plain,
( program(sK9(sK4))
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f241,plain,
( ! [X0] :
( ~ program(X0)
| ~ program(sK9(sK4)) )
| ~ spl12_5
| ~ spl12_25 ),
inference(resolution,[],[f236,f83]) ).
fof(f236,plain,
( ! [X0] :
( ~ halts2(sK9(sK4),X0)
| ~ program(X0) )
| ~ spl12_25 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( spl12_25
| ~ spl12_22
| ~ spl12_12
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f207,f145,f117,f210,f235]) ).
fof(f117,plain,
( spl12_12
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f207,plain,
( ! [X0] :
( ~ outputs(sK4,good)
| ~ program(X0)
| ~ halts2(sK9(sK4),X0) )
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f163,f156]) ).
fof(f156,plain,
( ! [X0,X1] :
( halts3(sK4,X0,X1)
| ~ program(X0) )
| ~ spl12_12 ),
inference(resolution,[],[f155,f119]) ).
fof(f119,plain,
( sP0(sK4)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ sP0(X0)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(subsumption_resolution,[],[f50,f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ halts2(X1,X2)
| halts3(X0,X1,X2)
| ~ program(X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1,X2] :
( ( ( outputs(X0,bad)
& halts3(X0,X1,X2) )
| halts2(X1,X2)
| ~ program(X1) )
& ( ( outputs(X0,good)
& halts3(X0,X1,X2) )
| ~ halts2(X1,X2)
| ~ program(X1) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X3,X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ program(X3) )
& ( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ program(X3) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] :
( ! [X3,X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ program(X3) )
& ( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ program(X3) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f50,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| halts2(X1,X2)
| ~ program(X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f163,plain,
( ! [X0] :
( ~ outputs(sK4,good)
| ~ halts3(sK4,X0,X0)
| ~ program(X0)
| ~ halts2(sK9(sK4),X0) )
| ~ spl12_15 ),
inference(resolution,[],[f147,f55]) ).
fof(f55,plain,
! [X2,X0] :
( ~ sP2(X0)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| ~ halts2(sK9(X0),X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( ! [X2] :
( ( ( outputs(sK9(X0),bad)
& halts2(sK9(X0),X2) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2) )
& ( ~ halts2(sK9(X0),X2)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2) ) )
& program(sK9(X0)) )
| ~ sP2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f35,f36]) ).
fof(f36,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ( ( outputs(X1,bad)
& halts2(X1,X2) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2) )
& ( ~ halts2(X1,X2)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2) ) )
& program(X1) )
=> ( ! [X2] :
( ( ( outputs(sK9(X0),bad)
& halts2(sK9(X0),X2) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2) )
& ( ~ halts2(sK9(X0),X2)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2) ) )
& program(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ( ( outputs(X1,bad)
& halts2(X1,X2) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2) )
& ( ~ halts2(X1,X2)
| ~ outputs(X0,good)
| ~ halts3(X0,X2,X2)
| ~ program(X2) ) )
& program(X1) )
| ~ sP2(X0) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ( ( outputs(X3,bad)
& halts2(X3,X4) )
| ~ outputs(X0,bad)
| ~ halts3(X0,X4,X4)
| ~ program(X4) )
& ( ~ halts2(X3,X4)
| ~ outputs(X0,good)
| ~ halts3(X0,X4,X4)
| ~ program(X4) ) )
& program(X3) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f20]) ).
fof(f147,plain,
( sP2(sK4)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f233,plain,
( spl12_22
| ~ spl12_8
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f230,f117,f92,f210]) ).
fof(f92,plain,
( spl12_8
<=> ! [X0] :
( outputs(X0,good)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f230,plain,
( outputs(sK4,good)
| ~ spl12_8
| ~ spl12_12 ),
inference(resolution,[],[f93,f119]) ).
fof(f93,plain,
( ! [X0] :
( ~ sP0(X0)
| outputs(X0,good) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f216,plain,
( spl12_17
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_15
| ~ spl12_18 ),
inference(avatar_split_clause,[],[f215,f185,f145,f117,f89,f85,f171]) ).
fof(f85,plain,
( spl12_6
<=> ! [X0] :
( outputs(X0,bad)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f215,plain,
( ! [X0] : ~ program(X0)
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_15
| ~ spl12_18 ),
inference(subsumption_resolution,[],[f214,f186]) ).
fof(f214,plain,
( ! [X0] :
( ~ program(sK9(sK4))
| ~ program(X0) )
| ~ spl12_6
| ~ spl12_7
| ~ spl12_12
| ~ spl12_15 ),
inference(resolution,[],[f90,f175]) ).
fof(f175,plain,
( ! [X0] :
( halts2(sK9(sK4),X0)
| ~ program(X0) )
| ~ spl12_6
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f174,f156]) ).
fof(f174,plain,
( ! [X0] :
( ~ halts3(sK4,X0,X0)
| ~ program(X0)
| halts2(sK9(sK4),X0) )
| ~ spl12_6
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f162,f132]) ).
fof(f132,plain,
( outputs(sK4,bad)
| ~ spl12_6
| ~ spl12_12 ),
inference(resolution,[],[f119,f86]) ).
fof(f86,plain,
( ! [X0] :
( ~ sP0(X0)
| outputs(X0,bad) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f162,plain,
( ! [X0] :
( ~ outputs(sK4,bad)
| ~ halts3(sK4,X0,X0)
| ~ program(X0)
| halts2(sK9(sK4),X0) )
| ~ spl12_15 ),
inference(resolution,[],[f147,f56]) ).
fof(f56,plain,
! [X2,X0] :
( ~ sP2(X0)
| ~ outputs(X0,bad)
| ~ halts3(X0,X2,X2)
| ~ program(X2)
| halts2(sK9(X0),X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f206,plain,
( spl12_17
| ~ spl12_6
| ~ spl12_8
| ~ spl12_12
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f205,f145,f117,f92,f85,f171]) ).
fof(f205,plain,
( ! [X0] : ~ program(X0)
| ~ spl12_6
| ~ spl12_8
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f177,f175]) ).
fof(f177,plain,
( ! [X0] :
( ~ program(X0)
| ~ halts2(sK9(sK4),X0) )
| ~ spl12_8
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f176,f156]) ).
fof(f176,plain,
( ! [X0] :
( ~ halts3(sK4,X0,X0)
| ~ program(X0)
| ~ halts2(sK9(sK4),X0) )
| ~ spl12_8
| ~ spl12_12
| ~ spl12_15 ),
inference(subsumption_resolution,[],[f163,f153]) ).
fof(f153,plain,
( outputs(sK4,good)
| ~ spl12_8
| ~ spl12_12 ),
inference(resolution,[],[f93,f119]) ).
fof(f203,plain,
( ~ spl12_15
| spl12_18 ),
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f202,plain,
( $false
| ~ spl12_15
| spl12_18 ),
inference(subsumption_resolution,[],[f201,f147]) ).
fof(f201,plain,
( ~ sP2(sK4)
| spl12_18 ),
inference(resolution,[],[f187,f54]) ).
fof(f54,plain,
! [X0] :
( program(sK9(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f187,plain,
( ~ program(sK9(sK4))
| spl12_18 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f182,plain,
( ~ spl12_4
| ~ spl12_17 ),
inference(avatar_contradiction_clause,[],[f178]) ).
fof(f178,plain,
( $false
| ~ spl12_4
| ~ spl12_17 ),
inference(resolution,[],[f172,f78]) ).
fof(f172,plain,
( ! [X0] : ~ program(X0)
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f160,plain,
( spl12_15
| ~ spl12_4
| ~ spl12_12
| spl12_14 ),
inference(avatar_split_clause,[],[f159,f141,f117,f76,f145]) ).
fof(f159,plain,
( sP2(sK4)
| ~ spl12_4
| ~ spl12_12
| spl12_14 ),
inference(subsumption_resolution,[],[f158,f78]) ).
fof(f158,plain,
( sP2(sK4)
| ~ program(sK4)
| ~ spl12_12
| spl12_14 ),
inference(resolution,[],[f157,f133]) ).
fof(f157,plain,
( ~ program(sK10(sK4))
| ~ spl12_12
| spl12_14 ),
inference(resolution,[],[f156,f143]) ).
fof(f143,plain,
( ~ halts3(sK4,sK10(sK4),sK11(sK4))
| spl12_14 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f148,plain,
( spl12_13
| ~ spl12_14
| spl12_15
| ~ spl12_4
| ~ spl12_6
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f135,f117,f85,f76,f145,f141,f137]) ).
fof(f135,plain,
( sP2(sK4)
| ~ halts3(sK4,sK10(sK4),sK11(sK4))
| sP1(sK4,sK11(sK4),sK10(sK4))
| ~ spl12_4
| ~ spl12_6
| ~ spl12_12 ),
inference(subsumption_resolution,[],[f134,f78]) ).
fof(f134,plain,
( sP2(sK4)
| ~ halts3(sK4,sK10(sK4),sK11(sK4))
| sP1(sK4,sK11(sK4),sK10(sK4))
| ~ program(sK4)
| ~ spl12_6
| ~ spl12_12 ),
inference(resolution,[],[f63,f132]) ).
fof(f63,plain,
! [X0] :
( ~ outputs(X0,bad)
| sP2(X0)
| ~ halts3(X0,sK10(X0),sK11(X0))
| sP1(X0,sK11(X0),sK10(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f130,plain,
( ~ spl12_1
| ~ spl12_3 ),
inference(avatar_contradiction_clause,[],[f129]) ).
fof(f129,plain,
( $false
| ~ spl12_1
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f128,f42]) ).
fof(f42,plain,
algorithm(sK3),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ! [X1] :
( ! [X2] : decides(sK3,X1,X2)
| ~ program(X1) )
& algorithm(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f11,f22]) ).
fof(f22,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& algorithm(X0) )
=> ( ! [X1] :
( ! [X2] : decides(sK3,X1,X2)
| ~ program(X1) )
& algorithm(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& algorithm(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(flattening,[],[f6]) ).
fof(f6,plain,
~ ~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(rectify,[],[f5]) ).
fof(f5,negated_conjecture,
~ ~ ? [X5] :
( ! [X6] :
( program(X6)
=> ! [X7] : decides(X5,X6,X7) )
& algorithm(X5) ),
inference(negated_conjecture,[],[f4]) ).
fof(f4,conjecture,
~ ? [X5] :
( ! [X6] :
( program(X6)
=> ! [X7] : decides(X5,X6,X7) )
& algorithm(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f128,plain,
( ~ algorithm(sK3)
| ~ spl12_1
| ~ spl12_3 ),
inference(resolution,[],[f127,f73]) ).
fof(f73,plain,
( ! [X3] :
( program(sK5(X3))
| ~ algorithm(X3) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl12_3
<=> ! [X3] :
( program(sK5(X3))
| ~ algorithm(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f127,plain,
( ~ program(sK5(sK3))
| ~ spl12_1 ),
inference(resolution,[],[f126,f43]) ).
fof(f43,plain,
! [X2,X1] :
( decides(sK3,X1,X2)
| ~ program(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f126,plain,
( ~ decides(sK3,sK5(sK3),sK6(sK3))
| ~ spl12_1 ),
inference(resolution,[],[f66,f42]) ).
fof(f66,plain,
( ! [X3] :
( ~ algorithm(X3)
| ~ decides(X3,sK5(X3),sK6(X3)) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f65,plain,
( spl12_1
<=> ! [X3] :
( ~ decides(X3,sK5(X3),sK6(X3))
| ~ algorithm(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f125,plain,
( ~ spl12_4
| spl12_12
| spl12_11 ),
inference(avatar_split_clause,[],[f122,f113,f117,f76]) ).
fof(f113,plain,
( spl12_11
<=> program(sK7(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f122,plain,
( sP0(sK4)
| ~ program(sK4)
| spl12_11 ),
inference(resolution,[],[f115,f52]) ).
fof(f52,plain,
! [X0] :
( program(sK7(X0))
| sP0(X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( sP0(X0)
| ( ~ decides(X0,sK7(X0),sK8(X0))
& program(sK7(X0)) )
| ~ program(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f18,f32,f31]) ).
fof(f31,plain,
! [X0] :
( ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
=> ( ? [X2] : ~ decides(X0,sK7(X0),X2)
& program(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0] :
( ? [X2] : ~ decides(X0,sK7(X0),X2)
=> ~ decides(X0,sK7(X0),sK8(X0)) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
( sP0(X0)
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
| ~ program(X0) ),
inference(definition_folding,[],[f14,f17]) ).
fof(f14,plain,
! [X0] :
( ! [X3,X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ program(X3) )
& ( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ program(X3) ) )
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
| ~ program(X0) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
! [X0] :
( ! [X3,X4] :
( ( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ program(X3) )
& ( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ program(X3) ) )
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
| ~ program(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0] :
( ( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& program(X0) )
=> ! [X3,X4] :
( ( ( ~ halts2(X3,X4)
& program(X3) )
=> ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( ( halts2(X3,X4)
& program(X3) )
=> ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3] :
( ( ! [X1] :
( program(X1)
=> ! [X2] : decides(X3,X1,X2) )
& program(X3) )
=> ! [X1,X2] :
( ( ( ~ halts2(X1,X2)
& program(X1) )
=> ( outputs(X3,bad)
& halts3(X3,X1,X2) ) )
& ( ( halts2(X1,X2)
& program(X1) )
=> ( outputs(X3,good)
& halts3(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f115,plain,
( ~ program(sK7(sK4))
| spl12_11 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f120,plain,
( ~ spl12_11
| spl12_12
| ~ spl12_2
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f111,f76,f68,f117,f113]) ).
fof(f68,plain,
( spl12_2
<=> ! [X2,X1] :
( decides(sK4,X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f111,plain,
( sP0(sK4)
| ~ program(sK7(sK4))
| ~ spl12_2
| ~ spl12_4 ),
inference(subsumption_resolution,[],[f100,f78]) ).
fof(f100,plain,
( sP0(sK4)
| ~ program(sK4)
| ~ program(sK7(sK4))
| ~ spl12_2 ),
inference(resolution,[],[f53,f69]) ).
fof(f69,plain,
( ! [X2,X1] :
( decides(sK4,X1,X2)
| ~ program(X1) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f53,plain,
! [X0] :
( ~ decides(X0,sK7(X0),sK8(X0))
| sP0(X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f98,plain,
( ~ spl12_4
| ~ spl12_5
| ~ spl12_7 ),
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f96,plain,
( $false
| ~ spl12_4
| ~ spl12_5
| ~ spl12_7 ),
inference(resolution,[],[f95,f78]) ).
fof(f95,plain,
( ! [X1] : ~ program(X1)
| ~ spl12_5
| ~ spl12_7 ),
inference(subsumption_resolution,[],[f90,f83]) ).
fof(f94,plain,
( spl12_7
| spl12_8 ),
inference(avatar_split_clause,[],[f49,f92,f89]) ).
fof(f49,plain,
! [X2,X0,X1] :
( outputs(X0,good)
| ~ halts2(X1,X2)
| ~ program(X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f87,plain,
( spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f51,f85,f82]) ).
fof(f51,plain,
! [X2,X0,X1] :
( outputs(X0,bad)
| halts2(X1,X2)
| ~ program(X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f80,plain,
( spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f44,f76,f72]) ).
fof(f44,plain,
! [X3] :
( program(sK4)
| program(sK5(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ( ! [X1] :
( ! [X2] : decides(sK4,X1,X2)
| ~ program(X1) )
& program(sK4) )
| ! [X3] :
( ( ~ decides(X3,sK5(X3),sK6(X3))
& program(sK5(X3)) )
| ~ algorithm(X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f24,f27,f26,f25]) ).
fof(f25,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& program(X0) )
=> ( ! [X1] :
( ! [X2] : decides(sK4,X1,X2)
| ~ program(X1) )
& program(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X3] :
( ? [X4] :
( ? [X5] : ~ decides(X3,X4,X5)
& program(X4) )
=> ( ? [X5] : ~ decides(X3,sK5(X3),X5)
& program(sK5(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X3] :
( ? [X5] : ~ decides(X3,sK5(X3),X5)
=> ~ decides(X3,sK5(X3),sK6(X3)) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& program(X0) )
| ! [X3] :
( ? [X4] :
( ? [X5] : ~ decides(X3,X4,X5)
& program(X4) )
| ~ algorithm(X3) ) ),
inference(rectify,[],[f12]) ).
fof(f12,plain,
( ? [X3] :
( ! [X4] :
( ! [X5] : decides(X3,X4,X5)
| ~ program(X4) )
& program(X3) )
| ! [X0] :
( ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
| ~ algorithm(X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
( ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) )
=> ? [X3] :
( ! [X4] :
( program(X4)
=> ! [X5] : decides(X3,X4,X5) )
& program(X3) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
( ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) )
=> ? [X3] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X3,X1,X2) )
& program(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f79,plain,
( spl12_1
| spl12_4 ),
inference(avatar_split_clause,[],[f45,f76,f65]) ).
fof(f45,plain,
! [X3] :
( program(sK4)
| ~ decides(X3,sK5(X3),sK6(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f74,plain,
( spl12_3
| spl12_2 ),
inference(avatar_split_clause,[],[f46,f68,f72]) ).
fof(f46,plain,
! [X2,X3,X1] :
( decides(sK4,X1,X2)
| ~ program(X1)
| program(sK5(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f70,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f47,f68,f65]) ).
fof(f47,plain,
! [X2,X3,X1] :
( decides(sK4,X1,X2)
| ~ program(X1)
| ~ decides(X3,sK5(X3),sK6(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM003+3 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 21:23:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (14439)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (14443)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.36 TRYING [1,1,1]
% 0.13/0.36 TRYING [2,1,1]
% 0.13/0.36 TRYING [2,2,1]
% 0.13/0.36 TRYING [2,1,2]
% 0.13/0.36 TRYING [2,2,2]
% 0.13/0.36 TRYING [3,1,3]
% 0.13/0.36 TRYING [3,2,3]
% 0.13/0.36 % (14440)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36 % (14441)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (14444)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.36 % (14442)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.36 % (14445)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.36 TRYING [3,3,1]
% 0.13/0.36 % (14446)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 TRYING [3,3,3]
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [1,1,1]
% 0.13/0.37 TRYING [2,1,1]
% 0.13/0.37 % (14445)First to succeed.
% 0.13/0.37 TRYING [4,1,4]
% 0.13/0.37 TRYING [2,2,1]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [4,2,4]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [4,3,4]
% 0.13/0.37 TRYING [2,1,2]
% 0.13/0.37 % (14445)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14439"
% 0.13/0.37 TRYING [2,2,2]
% 0.13/0.37 % (14445)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (14445)------------------------------
% 0.13/0.37 % (14445)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37 % (14445)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (14445)Memory used [KB]: 890
% 0.13/0.37 % (14445)Time elapsed: 0.010 s
% 0.13/0.37 % (14445)Instructions burned: 11 (million)
% 0.13/0.37 % (14439)Success in time 0.015 s
%------------------------------------------------------------------------------