TSTP Solution File: COM003+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM003+1 : 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 : n003.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 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 54
% Syntax : Number of formulae : 262 ( 2 unt; 0 def)
% Number of atoms : 1155 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1537 ( 644 ~; 623 |; 189 &)
% ( 33 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 46 ( 45 usr; 36 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 282 ( 223 !; 59 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f480,plain,
$false,
inference(avatar_sat_refutation,[],[f98,f102,f107,f108,f124,f128,f133,f137,f141,f145,f153,f157,f161,f165,f172,f177,f182,f189,f196,f240,f244,f268,f271,f314,f317,f366,f369,f376,f381,f410,f419,f441,f448,f468,f471,f479]) ).
fof(f479,plain,
( ~ spl16_4
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23
| ~ spl16_26
| ~ spl16_32 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f478,plain,
( $false
| ~ spl16_4
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23
| ~ spl16_26
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f477,f106]) ).
fof(f106,plain,
( program(sK7)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl16_4
<=> program(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f477,plain,
( ~ program(sK7)
| ~ spl16_4
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f474,f185]) ).
fof(f185,plain,
( ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f184,plain,
( spl16_23
<=> ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
fof(f474,plain,
( ~ halts2(sK7,sK11(sK7))
| ~ spl16_4
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23
| ~ spl16_26
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f473,f106]) ).
fof(f473,plain,
( ~ halts2(sK7,sK11(sK7))
| ~ program(sK7)
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f462,f454]) ).
fof(f454,plain,
( ! [X0] :
( sP0(X0,sK11(X0))
| ~ program(X0) )
| ~ spl16_12
| ~ spl16_13
| ~ spl16_23 ),
inference(subsumption_resolution,[],[f451,f241]) ).
fof(f241,plain,
( ! [X0] :
( program(sK11(X0))
| ~ program(X0) )
| ~ spl16_13 ),
inference(subsumption_resolution,[],[f144,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| program(X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,X1) )
& halts2(X1,X1)
& program(X1) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,X1) )
& halts2(X1,X1)
& program(X1) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f144,plain,
( ! [X0] :
( program(sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f143,plain,
( spl16_13
<=> ! [X0] :
( program(sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
fof(f451,plain,
( ! [X0] :
( ~ program(sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) )
| ~ spl16_12
| ~ spl16_23 ),
inference(resolution,[],[f185,f140]) ).
fof(f140,plain,
( ! [X0] :
( ~ halts2(sK11(X0),sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f139,plain,
( spl16_12
<=> ! [X0] :
( ~ halts2(sK11(X0),sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_12])]) ).
fof(f462,plain,
( ! [X0] :
( ~ sP0(sK7,X0)
| ~ halts2(sK7,X0) )
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f456,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ outputs(X0,good)
| ~ halts2(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f456,plain,
( outputs(sK7,good)
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f195,f267]) ).
fof(f267,plain,
( sP5(sK7)
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl16_32
<=> sP5(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_32])]) ).
fof(f195,plain,
( ! [X0] :
( ~ sP5(X0)
| outputs(X0,good) )
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f194,plain,
( spl16_26
<=> ! [X0] :
( outputs(X0,good)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_26])]) ).
fof(f471,plain,
( spl16_37
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f469,f416,f305]) ).
fof(f305,plain,
( spl16_37
<=> halts2(sK12(sK7),sK12(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_37])]) ).
fof(f416,plain,
( spl16_45
<=> sP2(sK7,sK12(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_45])]) ).
fof(f469,plain,
( halts2(sK12(sK7),sK12(sK7))
| ~ spl16_45 ),
inference(resolution,[],[f418,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| halts2(X1,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) )
& halts2(X1,X1)
& program(X1) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) )
& halts2(X1,X1)
& program(X1) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f418,plain,
( sP2(sK7,sK12(sK7))
| ~ spl16_45 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f468,plain,
( ~ spl16_4
| ~ spl16_16
| ~ spl16_17
| ~ spl16_23
| spl16_45 ),
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f467,plain,
( $false
| ~ spl16_4
| ~ spl16_16
| ~ spl16_17
| ~ spl16_23
| spl16_45 ),
inference(subsumption_resolution,[],[f466,f106]) ).
fof(f466,plain,
( ~ program(sK7)
| ~ spl16_16
| ~ spl16_17
| ~ spl16_23
| spl16_45 ),
inference(resolution,[],[f455,f417]) ).
fof(f417,plain,
( ~ sP2(sK7,sK12(sK7))
| spl16_45 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f455,plain,
( ! [X0] :
( sP2(X0,sK12(X0))
| ~ program(X0) )
| ~ spl16_16
| ~ spl16_17
| ~ spl16_23 ),
inference(subsumption_resolution,[],[f452,f420]) ).
fof(f420,plain,
( ! [X0] :
( program(sK12(X0))
| ~ program(X0) )
| ~ spl16_17 ),
inference(subsumption_resolution,[],[f160,f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| program(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f160,plain,
( ! [X0] :
( program(sK12(X0))
| ~ program(X0)
| sP2(X0,sK12(X0)) )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f159,plain,
( spl16_17
<=> ! [X0] :
( program(sK12(X0))
| ~ program(X0)
| sP2(X0,sK12(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_17])]) ).
fof(f452,plain,
( ! [X0] :
( ~ program(sK12(X0))
| ~ program(X0)
| sP2(X0,sK12(X0)) )
| ~ spl16_16
| ~ spl16_23 ),
inference(resolution,[],[f185,f156]) ).
fof(f156,plain,
( ! [X0] :
( ~ halts2(sK12(X0),sK12(X0))
| ~ program(X0)
| sP2(X0,sK12(X0)) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f155,plain,
( spl16_16
<=> ! [X0] :
( ~ halts2(sK12(X0),sK12(X0))
| ~ program(X0)
| sP2(X0,sK12(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_16])]) ).
fof(f448,plain,
( ~ spl16_25
| ~ spl16_37
| ~ spl16_38 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f447,plain,
( $false
| ~ spl16_25
| ~ spl16_37
| ~ spl16_38 ),
inference(subsumption_resolution,[],[f446,f310]) ).
fof(f310,plain,
( program(sK12(sK7))
| ~ spl16_38 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f309,plain,
( spl16_38
<=> program(sK12(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_38])]) ).
fof(f446,plain,
( ~ program(sK12(sK7))
| ~ spl16_25
| ~ spl16_37 ),
inference(resolution,[],[f306,f192]) ).
fof(f192,plain,
( ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) )
| ~ spl16_25 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f191,plain,
( spl16_25
<=> ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_25])]) ).
fof(f306,plain,
( halts2(sK12(sK7),sK12(sK7))
| ~ spl16_37 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f441,plain,
( ~ spl16_32
| ~ spl16_38
| spl16_44 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f440,plain,
( $false
| ~ spl16_32
| ~ spl16_38
| spl16_44 ),
inference(subsumption_resolution,[],[f439,f267]) ).
fof(f439,plain,
( ~ sP5(sK7)
| ~ spl16_38
| spl16_44 ),
inference(subsumption_resolution,[],[f438,f310]) ).
fof(f438,plain,
( ~ program(sK12(sK7))
| ~ sP5(sK7)
| spl16_44 ),
inference(resolution,[],[f414,f272]) ).
fof(f272,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ sP5(X0) ),
inference(subsumption_resolution,[],[f88,f86]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ sP5(X0)
| ~ halts2(X1,X2)
| ~ program(X1)
| halts3(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,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) ) )
| ~ sP5(X0) ),
inference(rectify,[],[f53]) ).
fof(f53,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) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,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) ) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f88,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| halts2(X1,X2)
| ~ program(X1)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f414,plain,
( ~ halts3(sK7,sK12(sK7),sK12(sK7))
| spl16_44 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f412,plain,
( spl16_44
<=> halts3(sK7,sK12(sK7),sK12(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_44])]) ).
fof(f419,plain,
( ~ spl16_44
| spl16_45
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_32 ),
inference(avatar_split_clause,[],[f353,f265,f187,f151,f104,f416,f412]) ).
fof(f151,plain,
( spl16_15
<=> ! [X0] :
( ~ outputs(X0,bad)
| ~ program(X0)
| sP2(X0,sK12(X0))
| ~ halts3(X0,sK12(X0),sK12(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_15])]) ).
fof(f187,plain,
( spl16_24
<=> ! [X0] :
( outputs(X0,bad)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
fof(f353,plain,
( sP2(sK7,sK12(sK7))
| ~ halts3(sK7,sK12(sK7),sK12(sK7))
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f352,f106]) ).
fof(f352,plain,
( ~ program(sK7)
| sP2(sK7,sK12(sK7))
| ~ halts3(sK7,sK12(sK7),sK12(sK7))
| ~ spl16_15
| ~ spl16_24
| ~ spl16_32 ),
inference(resolution,[],[f351,f152]) ).
fof(f152,plain,
( ! [X0] :
( ~ outputs(X0,bad)
| ~ program(X0)
| sP2(X0,sK12(X0))
| ~ halts3(X0,sK12(X0),sK12(X0)) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f351,plain,
( outputs(sK7,bad)
| ~ spl16_24
| ~ spl16_32 ),
inference(resolution,[],[f188,f267]) ).
fof(f188,plain,
( ! [X0] :
( ~ sP5(X0)
| outputs(X0,bad) )
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f410,plain,
( ~ spl16_6
| ~ spl16_12
| ~ spl16_13
| ~ spl16_22
| spl16_41 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f409,plain,
( $false
| ~ spl16_6
| ~ spl16_12
| ~ spl16_13
| ~ spl16_22
| spl16_41 ),
inference(subsumption_resolution,[],[f407,f181]) ).
fof(f181,plain,
( program(sK13)
| ~ spl16_22 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f179,plain,
( spl16_22
<=> program(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
fof(f407,plain,
( ~ program(sK13)
| ~ spl16_6
| ~ spl16_12
| ~ spl16_13
| spl16_41 ),
inference(resolution,[],[f395,f360]) ).
fof(f360,plain,
( ~ sP0(sK13,sK11(sK13))
| spl16_41 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f359,plain,
( spl16_41
<=> sP0(sK13,sK11(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
fof(f395,plain,
( ! [X0] :
( sP0(X0,sK11(X0))
| ~ program(X0) )
| ~ spl16_6
| ~ spl16_12
| ~ spl16_13 ),
inference(subsumption_resolution,[],[f391,f241]) ).
fof(f391,plain,
( ! [X0] :
( ~ program(sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0)) )
| ~ spl16_6
| ~ spl16_12 ),
inference(resolution,[],[f115,f140]) ).
fof(f115,plain,
( ! [X1] :
( halts2(X1,X1)
| ~ program(X1) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f114,plain,
( spl16_6
<=> ! [X1] :
( halts2(X1,X1)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f381,plain,
( ~ spl16_19
| ~ spl16_21
| ~ spl16_22 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f380,plain,
( $false
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22 ),
inference(subsumption_resolution,[],[f379,f181]) ).
fof(f379,plain,
( ~ program(sK13)
| ~ spl16_19
| ~ spl16_21 ),
inference(duplicate_literal_removal,[],[f377]) ).
fof(f377,plain,
( ~ program(sK13)
| ~ program(sK13)
| ~ spl16_19
| ~ spl16_21 ),
inference(resolution,[],[f168,f334]) ).
fof(f334,plain,
( ! [X0] :
( halts2(sK13,X0)
| ~ program(X0) )
| ~ spl16_21 ),
inference(resolution,[],[f176,f246]) ).
fof(f246,plain,
! [X0,X1] :
( ~ sP3(X0)
| ~ program(X1)
| halts2(X0,X1) ),
inference(subsumption_resolution,[],[f79,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sP3(X0)
| ~ halts2(X1,X1)
| ~ program(X1)
| halts2(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( ( outputs(X0,bad)
& halts2(X0,X1) )
| halts2(X1,X1)
| ~ program(X1) )
& ( ( outputs(X0,good)
& halts2(X0,X1) )
| ~ halts2(X1,X1)
| ~ program(X1) ) )
| ~ sP3(X0) ),
inference(rectify,[],[f47]) ).
fof(f47,plain,
! [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ( outputs(X2,good)
& halts2(X2,X3) )
| ~ halts2(X3,X3)
| ~ program(X3) ) )
| ~ sP3(X2) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ( outputs(X2,good)
& halts2(X2,X3) )
| ~ halts2(X3,X3)
| ~ program(X3) ) )
| ~ sP3(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f79,plain,
! [X0,X1] :
( halts2(X0,X1)
| halts2(X1,X1)
| ~ program(X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f176,plain,
( sP3(sK13)
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f174,plain,
( spl16_21
<=> sP3(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_21])]) ).
fof(f168,plain,
( ! [X1] :
( ~ halts2(X1,X1)
| ~ program(X1) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f167,plain,
( spl16_19
<=> ! [X1] :
( ~ halts2(X1,X1)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_19])]) ).
fof(f376,plain,
( ~ spl16_20
| ~ spl16_21
| ~ spl16_41
| ~ spl16_42 ),
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f375,plain,
( $false
| ~ spl16_20
| ~ spl16_21
| ~ spl16_41
| ~ spl16_42 ),
inference(subsumption_resolution,[],[f374,f364]) ).
fof(f364,plain,
( program(sK11(sK13))
| ~ spl16_42 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f363,plain,
( spl16_42
<=> program(sK11(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f374,plain,
( ~ program(sK11(sK13))
| ~ spl16_20
| ~ spl16_21
| ~ spl16_41 ),
inference(resolution,[],[f373,f334]) ).
fof(f373,plain,
( ~ halts2(sK13,sK11(sK13))
| ~ spl16_20
| ~ spl16_21
| ~ spl16_41 ),
inference(resolution,[],[f339,f361]) ).
fof(f361,plain,
( sP0(sK13,sK11(sK13))
| ~ spl16_41 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f339,plain,
( ! [X0] :
( ~ sP0(sK13,X0)
| ~ halts2(sK13,X0) )
| ~ spl16_20
| ~ spl16_21 ),
inference(resolution,[],[f336,f70]) ).
fof(f336,plain,
( outputs(sK13,good)
| ~ spl16_20
| ~ spl16_21 ),
inference(resolution,[],[f176,f171]) ).
fof(f171,plain,
( ! [X0] :
( ~ sP3(X0)
| outputs(X0,good) )
| ~ spl16_20 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f170,plain,
( spl16_20
<=> ! [X0] :
( outputs(X0,good)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_20])]) ).
fof(f369,plain,
( ~ spl16_13
| ~ spl16_22
| spl16_42 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f368,plain,
( $false
| ~ spl16_13
| ~ spl16_22
| spl16_42 ),
inference(subsumption_resolution,[],[f367,f181]) ).
fof(f367,plain,
( ~ program(sK13)
| ~ spl16_13
| spl16_42 ),
inference(resolution,[],[f365,f241]) ).
fof(f365,plain,
( ~ program(sK11(sK13))
| spl16_42 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
( spl16_41
| ~ spl16_42
| ~ spl16_11
| ~ spl16_18
| ~ spl16_21
| ~ spl16_22 ),
inference(avatar_split_clause,[],[f357,f179,f174,f163,f135,f363,f359]) ).
fof(f135,plain,
( spl16_11
<=> ! [X0] :
( ~ outputs(X0,bad)
| ~ program(X0)
| sP0(X0,sK11(X0))
| ~ halts2(X0,sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
fof(f163,plain,
( spl16_18
<=> ! [X0] :
( outputs(X0,bad)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_18])]) ).
fof(f357,plain,
( ~ program(sK11(sK13))
| sP0(sK13,sK11(sK13))
| ~ spl16_11
| ~ spl16_18
| ~ spl16_21
| ~ spl16_22 ),
inference(subsumption_resolution,[],[f356,f337]) ).
fof(f337,plain,
( outputs(sK13,bad)
| ~ spl16_18
| ~ spl16_21 ),
inference(resolution,[],[f176,f164]) ).
fof(f164,plain,
( ! [X0] :
( ~ sP3(X0)
| outputs(X0,bad) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f356,plain,
( ~ program(sK11(sK13))
| sP0(sK13,sK11(sK13))
| ~ outputs(sK13,bad)
| ~ spl16_11
| ~ spl16_21
| ~ spl16_22 ),
inference(subsumption_resolution,[],[f355,f181]) ).
fof(f355,plain,
( ~ program(sK11(sK13))
| ~ program(sK13)
| sP0(sK13,sK11(sK13))
| ~ outputs(sK13,bad)
| ~ spl16_11
| ~ spl16_21 ),
inference(resolution,[],[f334,f136]) ).
fof(f136,plain,
( ! [X0] :
( ~ halts2(X0,sK11(X0))
| ~ program(X0)
| sP0(X0,sK11(X0))
| ~ outputs(X0,bad) )
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f317,plain,
( ~ spl16_4
| ~ spl16_17
| spl16_38 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f316,plain,
( $false
| ~ spl16_4
| ~ spl16_17
| spl16_38 ),
inference(subsumption_resolution,[],[f315,f106]) ).
fof(f315,plain,
( ~ program(sK7)
| ~ spl16_17
| spl16_38 ),
inference(resolution,[],[f311,f245]) ).
fof(f245,plain,
( ! [X0] :
( program(sK12(X0))
| ~ program(X0) )
| ~ spl16_17 ),
inference(subsumption_resolution,[],[f160,f81]) ).
fof(f311,plain,
( ~ program(sK12(sK7))
| spl16_38 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f314,plain,
( ~ spl16_38
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_26
| ~ spl16_32 ),
inference(avatar_split_clause,[],[f313,f265,f194,f187,f151,f104,f309]) ).
fof(f313,plain,
( ~ program(sK12(sK7))
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_26
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f303,f267]) ).
fof(f303,plain,
( ~ program(sK12(sK7))
| ~ sP5(sK7)
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f291,f272]) ).
fof(f291,plain,
( ~ halts3(sK7,sK12(sK7),sK12(sK7))
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_26
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f290,f276]) ).
fof(f276,plain,
( ! [X0] :
( ~ sP2(sK7,X0)
| ~ halts3(sK7,X0,X0) )
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f274,f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f274,plain,
( outputs(sK7,good)
| ~ spl16_26
| ~ spl16_32 ),
inference(resolution,[],[f267,f195]) ).
fof(f290,plain,
( sP2(sK7,sK12(sK7))
| ~ halts3(sK7,sK12(sK7),sK12(sK7))
| ~ spl16_4
| ~ spl16_15
| ~ spl16_24
| ~ spl16_32 ),
inference(subsumption_resolution,[],[f279,f106]) ).
fof(f279,plain,
( ~ program(sK7)
| sP2(sK7,sK12(sK7))
| ~ halts3(sK7,sK12(sK7),sK12(sK7))
| ~ spl16_15
| ~ spl16_24
| ~ spl16_32 ),
inference(resolution,[],[f152,f275]) ).
fof(f275,plain,
( outputs(sK7,bad)
| ~ spl16_24
| ~ spl16_32 ),
inference(resolution,[],[f267,f188]) ).
fof(f271,plain,
( spl16_32
| ~ spl16_4
| spl16_31 ),
inference(avatar_split_clause,[],[f270,f261,f104,f265]) ).
fof(f261,plain,
( spl16_31
<=> program(sK14(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_31])]) ).
fof(f270,plain,
( sP5(sK7)
| ~ spl16_4
| spl16_31 ),
inference(subsumption_resolution,[],[f269,f106]) ).
fof(f269,plain,
( sP5(sK7)
| ~ program(sK7)
| spl16_31 ),
inference(resolution,[],[f263,f90]) ).
fof(f90,plain,
! [X0] :
( program(sK14(X0))
| sP5(X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( sP5(X0)
| ( ~ decides(X0,sK14(X0),sK15(X0))
& program(sK14(X0)) )
| ~ program(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f29,f56,f55]) ).
fof(f55,plain,
! [X0] :
( ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
=> ( ? [X2] : ~ decides(X0,sK14(X0),X2)
& program(sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ? [X2] : ~ decides(X0,sK14(X0),X2)
=> ~ decides(X0,sK14(X0),sK15(X0)) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( sP5(X0)
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) )
| ~ program(X0) ),
inference(definition_folding,[],[f20,f28]) ).
fof(f20,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,[],[f19]) ).
fof(f19,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,[],[f12]) ).
fof(f12,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(f263,plain,
( ~ program(sK14(sK7))
| spl16_31 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f268,plain,
( ~ spl16_31
| spl16_32
| ~ spl16_2
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f259,f104,f96,f265,f261]) ).
fof(f96,plain,
( spl16_2
<=> ! [X2,X1] :
( decides(sK7,X1,X2)
| ~ program(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f259,plain,
( sP5(sK7)
| ~ program(sK14(sK7))
| ~ spl16_2
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f248,f106]) ).
fof(f248,plain,
( sP5(sK7)
| ~ program(sK7)
| ~ program(sK14(sK7))
| ~ spl16_2 ),
inference(resolution,[],[f91,f97]) ).
fof(f97,plain,
( ! [X2,X1] :
( decides(sK7,X1,X2)
| ~ program(X1) )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f91,plain,
! [X0] :
( ~ decides(X0,sK14(X0),sK15(X0))
| sP5(X0)
| ~ program(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f244,plain,
( ~ spl16_1
| ~ spl16_3 ),
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f243,plain,
( $false
| ~ spl16_1
| ~ spl16_3 ),
inference(subsumption_resolution,[],[f242,f58]) ).
fof(f58,plain,
algorithm(sK6),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ! [X1] :
( ! [X2] : decides(sK6,X1,X2)
| ~ program(X1) )
& algorithm(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f13,f30]) ).
fof(f30,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& algorithm(X0) )
=> ( ! [X1] :
( ! [X2] : decides(sK6,X1,X2)
| ~ program(X1) )
& algorithm(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [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) ),
inference(flattening,[],[f7]) ).
fof(f7,plain,
~ ~ ? [X0] :
( ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) )
& algorithm(X0) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ~ ? [X6] :
( ! [X7] :
( program(X7)
=> ! [X8] : decides(X6,X7,X8) )
& algorithm(X6) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
~ ? [X6] :
( ! [X7] :
( program(X7)
=> ! [X8] : decides(X6,X7,X8) )
& algorithm(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f242,plain,
( ~ algorithm(sK6)
| ~ spl16_1
| ~ spl16_3 ),
inference(resolution,[],[f236,f101]) ).
fof(f101,plain,
( ! [X3] :
( program(sK8(X3))
| ~ algorithm(X3) )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f100,plain,
( spl16_3
<=> ! [X3] :
( program(sK8(X3))
| ~ algorithm(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f236,plain,
( ~ program(sK8(sK6))
| ~ spl16_1 ),
inference(resolution,[],[f235,f59]) ).
fof(f59,plain,
! [X2,X1] :
( decides(sK6,X1,X2)
| ~ program(X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f235,plain,
( ~ decides(sK6,sK8(sK6),sK9(sK6))
| ~ spl16_1 ),
inference(resolution,[],[f94,f58]) ).
fof(f94,plain,
( ! [X3] :
( ~ algorithm(X3)
| ~ decides(X3,sK8(X3),sK9(X3)) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl16_1
<=> ! [X3] :
( ~ decides(X3,sK8(X3),sK9(X3))
| ~ algorithm(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f240,plain,
( ~ spl16_8
| ~ spl16_9
| ~ spl16_10 ),
inference(avatar_contradiction_clause,[],[f239]) ).
fof(f239,plain,
( $false
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10 ),
inference(subsumption_resolution,[],[f238,f224]) ).
fof(f224,plain,
( halts2(sK10,sK10)
| ~ spl16_8
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f222,plain,
( halts2(sK10,sK10)
| halts2(sK10,sK10)
| ~ spl16_8
| ~ spl16_10 ),
inference(resolution,[],[f123,f132]) ).
fof(f132,plain,
( program(sK10)
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f130,plain,
( spl16_10
<=> program(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f123,plain,
( ! [X1] :
( ~ program(X1)
| halts2(sK10,X1)
| halts2(X1,X1) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f122,plain,
( spl16_8
<=> ! [X1] :
( halts2(sK10,X1)
| ~ program(X1)
| halts2(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f238,plain,
( ~ halts2(sK10,sK10)
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10 ),
inference(subsumption_resolution,[],[f237,f132]) ).
fof(f237,plain,
( ~ program(sK10)
| ~ halts2(sK10,sK10)
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10 ),
inference(resolution,[],[f127,f224]) ).
fof(f127,plain,
( ! [X1] :
( ~ halts2(sK10,X1)
| ~ program(X1)
| ~ halts2(X1,X1) )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f126,plain,
( spl16_9
<=> ! [X1] :
( ~ halts2(sK10,X1)
| ~ program(X1)
| ~ halts2(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f196,plain,
( spl16_25
| spl16_26 ),
inference(avatar_split_clause,[],[f87,f194,f191]) ).
fof(f87,plain,
! [X2,X0,X1] :
( outputs(X0,good)
| ~ halts2(X1,X2)
| ~ program(X1)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f189,plain,
( spl16_23
| spl16_24 ),
inference(avatar_split_clause,[],[f89,f187,f184]) ).
fof(f89,plain,
! [X2,X0,X1] :
( outputs(X0,bad)
| halts2(X1,X2)
| ~ program(X1)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f182,plain,
( spl16_14
| spl16_22 ),
inference(avatar_split_clause,[],[f84,f179,f147]) ).
fof(f147,plain,
( spl16_14
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
fof(f84,plain,
( program(sK13)
| sP4 ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( ( sP3(sK13)
& program(sK13) )
| sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f50,f51]) ).
fof(f51,plain,
( ? [X0] :
( sP3(X0)
& program(X0) )
=> ( sP3(sK13)
& program(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
( ? [X0] :
( sP3(X0)
& program(X0) )
| sP4 ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
( ? [X2] :
( sP3(X2)
& program(X2) )
| sP4 ),
inference(definition_folding,[],[f18,f26,f25,f24]) ).
fof(f26,plain,
( ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| sP2(X0,X1) )
| ~ program(X0) )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f18,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ( outputs(X2,good)
& halts2(X2,X3) )
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) )
& halts2(X1,X1)
& program(X1) ) )
| ~ program(X0) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ( outputs(X2,good)
& halts2(X2,X3) )
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,X1) )
& halts2(X1,X1)
& program(X1) ) )
| ~ program(X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts3(X0,X1,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts3(X0,X1,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( ( ( ~ halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ( halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,good)
& halts2(X2,X3) ) ) )
& program(X2) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
( ? [X3] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X3,bad)
& halts3(X3,X1,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X3,good)
& halts3(X3,X1,X1) ) ) )
& program(X3) )
=> ? [X4] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X4,bad)
& halts2(X4,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X4,good)
& halts2(X4,X1) ) ) )
& program(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f177,plain,
( spl16_14
| spl16_21 ),
inference(avatar_split_clause,[],[f85,f174,f147]) ).
fof(f85,plain,
( sP3(sK13)
| sP4 ),
inference(cnf_transformation,[],[f52]) ).
fof(f172,plain,
( spl16_19
| spl16_20 ),
inference(avatar_split_clause,[],[f78,f170,f167]) ).
fof(f78,plain,
! [X0,X1] :
( outputs(X0,good)
| ~ halts2(X1,X1)
| ~ program(X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f165,plain,
( spl16_6
| spl16_18 ),
inference(avatar_split_clause,[],[f80,f163,f114]) ).
fof(f80,plain,
! [X0,X1] :
( outputs(X0,bad)
| halts2(X1,X1)
| ~ program(X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f161,plain,
( ~ spl16_14
| spl16_17 ),
inference(avatar_split_clause,[],[f74,f159,f147]) ).
fof(f74,plain,
! [X0] :
( program(sK12(X0))
| sP2(X0,sK12(X0))
| ~ program(X0)
| ~ sP4 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
( ! [X0] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),sK12(X0)) )
& ~ halts2(sK12(X0),sK12(X0))
& program(sK12(X0)) )
| sP2(X0,sK12(X0))
| ~ program(X0) )
| ~ sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f44,f45]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| sP2(X0,X1) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),sK12(X0)) )
& ~ halts2(sK12(X0),sK12(X0))
& program(sK12(X0)) )
| sP2(X0,sK12(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
( ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| sP2(X0,X1) )
| ~ program(X0) )
| ~ sP4 ),
inference(nnf_transformation,[],[f26]) ).
fof(f157,plain,
( ~ spl16_14
| spl16_16 ),
inference(avatar_split_clause,[],[f75,f155,f147]) ).
fof(f75,plain,
! [X0] :
( ~ halts2(sK12(X0),sK12(X0))
| sP2(X0,sK12(X0))
| ~ program(X0)
| ~ sP4 ),
inference(cnf_transformation,[],[f46]) ).
fof(f153,plain,
( ~ spl16_14
| spl16_15 ),
inference(avatar_split_clause,[],[f76,f151,f147]) ).
fof(f76,plain,
! [X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),sK12(X0))
| sP2(X0,sK12(X0))
| ~ program(X0)
| ~ sP4 ),
inference(cnf_transformation,[],[f46]) ).
fof(f145,plain,
( spl16_13
| spl16_5 ),
inference(avatar_split_clause,[],[f71,f110,f143]) ).
fof(f110,plain,
( spl16_5
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f71,plain,
! [X0] :
( sP1
| program(sK11(X0))
| sP0(X0,sK11(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
( sP1
| ! [X0] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,sK11(X0)) )
& ~ halts2(sK11(X0),sK11(X0))
& program(sK11(X0)) )
| sP0(X0,sK11(X0))
| ~ program(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f23,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| sP0(X0,X1) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,sK11(X0)) )
& ~ halts2(sK11(X0),sK11(X0))
& program(sK11(X0)) )
| sP0(X0,sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( sP1
| ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| sP0(X0,X1) )
| ~ program(X0) ) ),
inference(definition_folding,[],[f16,f22,f21]) ).
fof(f22,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ~ halts2(X2,X3)
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f16,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ~ halts2(X2,X3)
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts2(X0,X1) )
& halts2(X1,X1)
& program(X1) ) )
| ~ program(X0) ) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ~ halts2(X2,X3)
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ! [X0] :
( ? [X1] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,X1) )
& ~ halts2(X1,X1)
& program(X1) )
| ( ( ~ outputs(X0,good)
| ~ halts2(X0,X1) )
& halts2(X1,X1)
& program(X1) ) )
| ~ program(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
( ? [X0] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,bad)
& halts2(X0,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X0,good)
& halts2(X0,X1) ) ) )
& program(X0) )
=> ? [X2] :
( ! [X3] :
( ( ( ~ halts2(X3,X3)
& program(X3) )
=> ( outputs(X2,bad)
& halts2(X2,X3) ) )
& ( ( halts2(X3,X3)
& program(X3) )
=> ~ halts2(X2,X3) ) )
& program(X2) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
( ? [X4] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X4,bad)
& halts2(X4,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ( outputs(X4,good)
& halts2(X4,X1) ) ) )
& program(X4) )
=> ? [X5] :
( ! [X1] :
( ( ( ~ halts2(X1,X1)
& program(X1) )
=> ( outputs(X5,bad)
& halts2(X5,X1) ) )
& ( ( halts2(X1,X1)
& program(X1) )
=> ~ halts2(X5,X1) ) )
& program(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f141,plain,
( spl16_12
| spl16_5 ),
inference(avatar_split_clause,[],[f72,f110,f139]) ).
fof(f72,plain,
! [X0] :
( sP1
| ~ halts2(sK11(X0),sK11(X0))
| sP0(X0,sK11(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f137,plain,
( spl16_11
| spl16_5 ),
inference(avatar_split_clause,[],[f73,f110,f135]) ).
fof(f73,plain,
! [X0] :
( sP1
| ~ outputs(X0,bad)
| ~ halts2(X0,sK11(X0))
| sP0(X0,sK11(X0))
| ~ program(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f133,plain,
( ~ spl16_5
| spl16_10 ),
inference(avatar_split_clause,[],[f64,f130,f110]) ).
fof(f64,plain,
( program(sK10)
| ~ sP1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( ! [X1] :
( ( ( outputs(sK10,bad)
& halts2(sK10,X1) )
| halts2(X1,X1)
| ~ program(X1) )
& ( ~ halts2(sK10,X1)
| ~ halts2(X1,X1)
| ~ program(X1) ) )
& program(sK10) )
| ~ sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f38,f39]) ).
fof(f39,plain,
( ? [X0] :
( ! [X1] :
( ( ( outputs(X0,bad)
& halts2(X0,X1) )
| halts2(X1,X1)
| ~ program(X1) )
& ( ~ halts2(X0,X1)
| ~ halts2(X1,X1)
| ~ program(X1) ) )
& program(X0) )
=> ( ! [X1] :
( ( ( outputs(sK10,bad)
& halts2(sK10,X1) )
| halts2(X1,X1)
| ~ program(X1) )
& ( ~ halts2(sK10,X1)
| ~ halts2(X1,X1)
| ~ program(X1) ) )
& program(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ? [X0] :
( ! [X1] :
( ( ( outputs(X0,bad)
& halts2(X0,X1) )
| halts2(X1,X1)
| ~ program(X1) )
& ( ~ halts2(X0,X1)
| ~ halts2(X1,X1)
| ~ program(X1) ) )
& program(X0) )
| ~ sP1 ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
( ? [X2] :
( ! [X3] :
( ( ( outputs(X2,bad)
& halts2(X2,X3) )
| halts2(X3,X3)
| ~ program(X3) )
& ( ~ halts2(X2,X3)
| ~ halts2(X3,X3)
| ~ program(X3) ) )
& program(X2) )
| ~ sP1 ),
inference(nnf_transformation,[],[f22]) ).
fof(f128,plain,
( ~ spl16_5
| spl16_9 ),
inference(avatar_split_clause,[],[f65,f126,f110]) ).
fof(f65,plain,
! [X1] :
( ~ halts2(sK10,X1)
| ~ halts2(X1,X1)
| ~ program(X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f124,plain,
( ~ spl16_5
| spl16_8 ),
inference(avatar_split_clause,[],[f66,f122,f110]) ).
fof(f66,plain,
! [X1] :
( halts2(sK10,X1)
| halts2(X1,X1)
| ~ program(X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f108,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f60,f104,f100]) ).
fof(f60,plain,
! [X3] :
( program(sK7)
| program(sK8(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ( ! [X1] :
( ! [X2] : decides(sK7,X1,X2)
| ~ program(X1) )
& program(sK7) )
| ! [X3] :
( ( ~ decides(X3,sK8(X3),sK9(X3))
& program(sK8(X3)) )
| ~ algorithm(X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f32,f35,f34,f33]) ).
fof(f33,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) )
& program(X0) )
=> ( ! [X1] :
( ! [X2] : decides(sK7,X1,X2)
| ~ program(X1) )
& program(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X3] :
( ? [X4] :
( ? [X5] : ~ decides(X3,X4,X5)
& program(X4) )
=> ( ? [X5] : ~ decides(X3,sK8(X3),X5)
& program(sK8(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X3] :
( ? [X5] : ~ decides(X3,sK8(X3),X5)
=> ~ decides(X3,sK8(X3),sK9(X3)) ),
introduced(choice_axiom,[]) ).
fof(f32,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,[],[f14]) ).
fof(f14,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,[],[f9]) ).
fof(f9,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(f107,plain,
( spl16_1
| spl16_4 ),
inference(avatar_split_clause,[],[f61,f104,f93]) ).
fof(f61,plain,
! [X3] :
( program(sK7)
| ~ decides(X3,sK8(X3),sK9(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f102,plain,
( spl16_3
| spl16_2 ),
inference(avatar_split_clause,[],[f62,f96,f100]) ).
fof(f62,plain,
! [X2,X3,X1] :
( decides(sK7,X1,X2)
| ~ program(X1)
| program(sK8(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f36]) ).
fof(f98,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f63,f96,f93]) ).
fof(f63,plain,
! [X2,X3,X1] :
( decides(sK7,X1,X2)
| ~ program(X1)
| ~ decides(X3,sK8(X3),sK9(X3))
| ~ algorithm(X3) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM003+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 21:26:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (672)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (679)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37 % (675)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (676)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (677)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)
% 0.13/0.37 % (678)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.37 % (680)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37 % (681)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)
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [1,1,1]
% 0.13/0.38 TRYING [1,1,1]
% 0.13/0.38 TRYING [2,1,1]
% 0.13/0.38 TRYING [2,2,1]
% 0.13/0.38 TRYING [2,1,1]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 TRYING [2,2,1]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 TRYING [2,1,2]
% 0.13/0.38 % (680)First to succeed.
% 0.13/0.38 TRYING [2,2,2]
% 0.13/0.38 TRYING [2,1,2]
% 0.13/0.38 TRYING [2,2,2]
% 0.13/0.38 TRYING [3,1,3]
% 0.13/0.38 TRYING [4]
% 0.13/0.38 TRYING [3,2,3]
% 0.13/0.38 TRYING [4]
% 0.13/0.38 % (680)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-672"
% 0.13/0.38 % (677)Also succeeded, but the first one will report.
% 0.13/0.38 TRYING [3,3,1]
% 0.13/0.38 TRYING [3,1,3]
% 0.13/0.39 % (680)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39 % (680)------------------------------
% 0.13/0.39 % (680)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39 % (680)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (680)Memory used [KB]: 976
% 0.13/0.39 % (680)Time elapsed: 0.012 s
% 0.13/0.39 % (680)Instructions burned: 17 (million)
% 0.13/0.39 % (672)Success in time 0.029 s
%------------------------------------------------------------------------------