TSTP Solution File: COM003+2 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n008.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 : Wed Aug 31 15:53:01 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 115 ( 7 unt; 0 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 472 ( 195 ~; 171 |; 68 &)
% ( 20 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 25 ( 24 usr; 12 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 164 ( 135 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f306,plain,
$false,
inference(avatar_sat_refutation,[],[f131,f138,f143,f150,f155,f159,f163,f165,f190,f194,f283,f305]) ).
fof(f305,plain,
( ~ spl8_5
| ~ spl8_9
| ~ spl8_18 ),
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f304,plain,
( $false
| ~ spl8_5
| ~ spl8_9
| ~ spl8_18 ),
inference(subsumption_resolution,[],[f303,f262]) ).
fof(f262,plain,
( halts2(sK5,sK5)
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f260,plain,
( spl8_18
<=> halts2(sK5,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f303,plain,
( ~ halts2(sK5,sK5)
| ~ spl8_5
| ~ spl8_9
| ~ spl8_18 ),
inference(resolution,[],[f290,f158]) ).
fof(f158,plain,
( ! [X1] :
( ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f157,plain,
( spl8_9
<=> ! [X1] :
( ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f290,plain,
( program_halts2(sK5,sK5)
| ~ spl8_5
| ~ spl8_18 ),
inference(subsumption_resolution,[],[f288,f142]) ).
fof(f142,plain,
( program(sK5)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl8_5
<=> program(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f288,plain,
( program_halts2(sK5,sK5)
| ~ program(sK5)
| ~ spl8_18 ),
inference(resolution,[],[f262,f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ halts2(X1,X0)
| program_halts2(X1,X0)
| ~ program(X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( program_halts2(X1,X0)
| ~ halts2(X1,X0)
| ~ program(X1) )
& ( ( halts2(X1,X0)
& program(X1) )
| ~ program_halts2(X1,X0) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( program_halts2(X1,X0)
| ~ halts2(X1,X0)
| ~ program(X1) )
& ( ( halts2(X1,X0)
& program(X1) )
| ~ program_halts2(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( program_halts2(X1,X0)
<=> ( halts2(X1,X0)
& program(X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( program_halts2(X0,X1)
<=> ( program(X0)
& halts2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_def) ).
fof(f283,plain,
( spl8_18
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_split_clause,[],[f282,f140,f136,f260]) ).
fof(f136,plain,
( spl8_4
<=> ! [X1] : program_not_halts2_halts2_outputs(sK5,X1,good) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f282,plain,
( halts2(sK5,sK5)
| ~ spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f267,f86]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ halts2_outputs(X0,X2,X1)
| halts2(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ( halts2(X0,X2)
& outputs(X0,X1) )
| ~ halts2_outputs(X0,X2,X1) )
& ( halts2_outputs(X0,X2,X1)
| ~ halts2(X0,X2)
| ~ outputs(X0,X1) ) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ( ( halts2(X2,X1)
& outputs(X2,X0) )
| ~ halts2_outputs(X2,X1,X0) )
& ( halts2_outputs(X2,X1,X0)
| ~ halts2(X2,X1)
| ~ outputs(X2,X0) ) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ( ( halts2(X2,X1)
& outputs(X2,X0) )
| ~ halts2_outputs(X2,X1,X0) )
& ( halts2_outputs(X2,X1,X0)
| ~ halts2(X2,X1)
| ~ outputs(X2,X0) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ( halts2(X2,X1)
& outputs(X2,X0) )
<=> halts2_outputs(X2,X1,X0) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X3,X1,X0] :
( ( outputs(X0,X3)
& halts2(X0,X1) )
<=> halts2_outputs(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs_def) ).
fof(f267,plain,
( halts2_outputs(sK5,sK5,good)
| halts2(sK5,sK5)
| ~ spl8_4
| ~ spl8_5 ),
inference(resolution,[],[f235,f142]) ).
fof(f235,plain,
( ! [X3] :
( ~ program(X3)
| halts2(X3,X3)
| halts2_outputs(sK5,X3,good) )
| ~ spl8_4 ),
inference(resolution,[],[f230,f110]) ).
fof(f110,plain,
! [X0,X1] :
( program_not_halts2(X1,X0)
| ~ program(X1)
| halts2(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ( program_not_halts2(X1,X0)
| ~ program(X1)
| halts2(X1,X0) )
& ( ( program(X1)
& ~ halts2(X1,X0) )
| ~ program_not_halts2(X1,X0) ) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X1,X0] :
( ( program_not_halts2(X0,X1)
| ~ program(X0)
| halts2(X0,X1) )
& ( ( program(X0)
& ~ halts2(X0,X1) )
| ~ program_not_halts2(X0,X1) ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X1,X0] :
( ( program_not_halts2(X0,X1)
| ~ program(X0)
| halts2(X0,X1) )
& ( ( program(X0)
& ~ halts2(X0,X1) )
| ~ program_not_halts2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( program_not_halts2(X0,X1)
<=> ( program(X0)
& ~ halts2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_def) ).
fof(f230,plain,
( ! [X15] :
( ~ program_not_halts2(X15,X15)
| halts2_outputs(sK5,X15,good) )
| ~ spl8_4 ),
inference(resolution,[],[f104,f137]) ).
fof(f137,plain,
( ! [X1] : program_not_halts2_halts2_outputs(sK5,X1,good)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ program_not_halts2_halts2_outputs(X1,X0,X2)
| ~ program_not_halts2(X0,X0)
| halts2_outputs(X1,X0,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ~ program_not_halts2(X0,X0)
| halts2_outputs(X1,X0,X2)
| ~ program_not_halts2_halts2_outputs(X1,X0,X2) )
& ( program_not_halts2_halts2_outputs(X1,X0,X2)
| ( program_not_halts2(X0,X0)
& ~ halts2_outputs(X1,X0,X2) ) ) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ~ program_not_halts2(X0,X0)
| halts2_outputs(X1,X0,X2)
| ~ program_not_halts2_halts2_outputs(X1,X0,X2) )
& ( program_not_halts2_halts2_outputs(X1,X0,X2)
| ( program_not_halts2(X0,X0)
& ~ halts2_outputs(X1,X0,X2) ) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ~ program_not_halts2(X0,X0)
| halts2_outputs(X1,X0,X2) )
<=> program_not_halts2_halts2_outputs(X1,X0,X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X2,X1,X0] :
( program_not_halts2_halts2_outputs(X1,X0,X2)
<=> ( program_not_halts2(X0,X0)
=> halts2_outputs(X1,X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X0,X3] :
( program_not_halts2_halts2_outputs(X0,X1,X3)
<=> ( program_not_halts2(X1,X1)
=> halts2_outputs(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
fof(f194,plain,
( ~ spl8_3
| ~ spl8_6
| ~ spl8_8
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| ~ spl8_3
| ~ spl8_6
| ~ spl8_8
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f192,f162]) ).
fof(f162,plain,
( ! [X3] : program_halts2_halts2_outputs(sK3,X3,good)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl8_10
<=> ! [X3] : program_halts2_halts2_outputs(sK3,X3,good) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f192,plain,
( ~ program_halts2_halts2_outputs(sK3,sK6(sK3),good)
| ~ spl8_3
| ~ spl8_6
| ~ spl8_8 ),
inference(subsumption_resolution,[],[f191,f154]) ).
fof(f154,plain,
( program(sK3)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl8_8
<=> program(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f191,plain,
( ~ program_halts2_halts2_outputs(sK3,sK6(sK3),good)
| ~ program(sK3)
| ~ spl8_3
| ~ spl8_6 ),
inference(resolution,[],[f146,f134]) ).
fof(f134,plain,
( ! [X2] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f133,plain,
( spl8_3
<=> ! [X2] :
( ~ program(X2)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f146,plain,
( ! [X3] : program_not_halts2_halts2_outputs(sK3,X3,bad)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl8_6
<=> ! [X3] : program_not_halts2_halts2_outputs(sK3,X3,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f190,plain,
( ~ spl8_1
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| ~ spl8_1
| ~ spl8_7 ),
inference(resolution,[],[f187,f127]) ).
fof(f127,plain,
( program_program_decides(sK4)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f125,plain,
( spl8_1
<=> program_program_decides(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f187,plain,
( ! [X0] : ~ program_program_decides(X0)
| ~ spl8_7 ),
inference(subsumption_resolution,[],[f186,f115]) ).
fof(f115,plain,
! [X2,X0,X1] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ~ program_program_decides(X0)
| ! [X1,X2] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
& program_halts2_halts3_outputs(X0,X1,X2,good) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ~ program_program_decides(X0)
| ! [X2,X1] :
( program_not_halts2_halts3_outputs(X0,X2,X1,bad)
& program_halts2_halts3_outputs(X0,X2,X1,good) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] :
( program_program_decides(X0)
=> ! [X2,X1] :
( program_not_halts2_halts3_outputs(X0,X2,X1,bad)
& program_halts2_halts3_outputs(X0,X2,X1,good) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( program_program_decides(X3)
=> ! [X2,X1] :
( program_halts2_halts3_outputs(X3,X1,X2,good)
& program_not_halts2_halts3_outputs(X3,X1,X2,bad) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f186,plain,
( ! [X0] :
( ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program_program_decides(X0) )
| ~ spl8_7 ),
inference(subsumption_resolution,[],[f183,f106]) ).
fof(f106,plain,
! [X0] :
( ~ program_program_decides(X0)
| program(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( ( program_decides(X0)
& program(X0) )
| ~ program_program_decides(X0) )
& ( program_program_decides(X0)
| ~ program_decides(X0)
| ~ program(X0) ) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( ( program_decides(X0)
& program(X0) )
| ~ program_program_decides(X0) )
& ( program_program_decides(X0)
| ~ program_decides(X0)
| ~ program(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( program_decides(X0)
& program(X0) )
<=> program_program_decides(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(f183,plain,
( ! [X0] :
( ~ program_program_decides(X0)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program(X0) )
| ~ spl8_7 ),
inference(resolution,[],[f149,f116]) ).
fof(f116,plain,
! [X2,X0,X1] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f149,plain,
( ! [X0] :
( ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program(X0) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl8_7
<=> ! [X0] :
( ~ program(X0)
| ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f165,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f164]) ).
fof(f164,plain,
( $false
| ~ spl8_2 ),
inference(resolution,[],[f130,f123]) ).
fof(f123,plain,
algorithm_program_decides(sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
algorithm_program_decides(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f79]) ).
fof(f79,plain,
( ? [X0] : algorithm_program_decides(X0)
=> algorithm_program_decides(sK7) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0] : algorithm_program_decides(X0),
inference(flattening,[],[f17]) ).
fof(f17,negated_conjecture,
~ ~ ? [X0] : algorithm_program_decides(X0),
inference(negated_conjecture,[],[f16]) ).
fof(f16,conjecture,
~ ? [X0] : algorithm_program_decides(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f130,plain,
( ! [X1] : ~ algorithm_program_decides(X1)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl8_2
<=> ! [X1] : ~ algorithm_program_decides(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f163,plain,
( spl8_10
| spl8_7 ),
inference(avatar_split_clause,[],[f112,f148,f161]) ).
fof(f112,plain,
! [X3,X0] :
( ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad)
| program_halts2_halts2_outputs(sK3,X3,good)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0] :
( ~ program(X0)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad) )
| ( program(sK3)
& ! [X3] :
( program_halts2_halts2_outputs(sK3,X3,good)
& program_not_halts2_halts2_outputs(sK3,X3,bad) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f33,f66,f65]) ).
fof(f65,plain,
! [X0] :
( ? [X1] :
( ~ program_halts2_halts3_outputs(X0,X1,X1,good)
| ~ program_not_halts2_halts3_outputs(X0,X1,X1,bad) )
=> ( ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( program_halts2_halts2_outputs(X2,X3,good)
& program_not_halts2_halts2_outputs(X2,X3,bad) ) )
=> ( program(sK3)
& ! [X3] :
( program_halts2_halts2_outputs(sK3,X3,good)
& program_not_halts2_halts2_outputs(sK3,X3,bad) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ! [X0] :
( ~ program(X0)
| ? [X1] :
( ~ program_halts2_halts3_outputs(X0,X1,X1,good)
| ~ program_not_halts2_halts3_outputs(X0,X1,X1,bad) ) )
| ? [X2] :
( program(X2)
& ! [X3] :
( program_halts2_halts2_outputs(X2,X3,good)
& program_not_halts2_halts2_outputs(X2,X3,bad) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts3_outputs(X0,X1,X1,bad)
& program_halts2_halts3_outputs(X0,X1,X1,good) )
& program(X0) )
=> ? [X2] :
( program(X2)
& ! [X3] :
( program_halts2_halts2_outputs(X2,X3,good)
& program_not_halts2_halts2_outputs(X2,X3,bad) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
( ? [X3] :
( program(X3)
& ! [X1] :
( program_not_halts2_halts3_outputs(X3,X1,X1,bad)
& program_halts2_halts3_outputs(X3,X1,X1,good) ) )
=> ? [X4] :
( program(X4)
& ! [X1] :
( program_halts2_halts2_outputs(X4,X1,good)
& program_not_halts2_halts2_outputs(X4,X1,bad) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f159,plain,
( spl8_9
| spl8_3 ),
inference(avatar_split_clause,[],[f120,f133,f157]) ).
fof(f120,plain,
! [X2,X1] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program(X2)
| ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ( program(sK5)
& ! [X1] :
( program_not_halts2_halts2_outputs(sK5,X1,good)
& ( ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1) ) ) )
| ! [X2] :
( ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f75,f77,f76]) ).
fof(f76,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,good)
& ( ~ halts2(X0,X1)
| ~ program_halts2(X1,X1) ) ) )
=> ( program(sK5)
& ! [X1] :
( program_not_halts2_halts2_outputs(sK5,X1,good)
& ( ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X2] :
( ? [X3] :
( ~ program_halts2_halts2_outputs(X2,X3,good)
| ~ program_not_halts2_halts2_outputs(X2,X3,bad) )
=> ( ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,good)
& ( ~ halts2(X0,X1)
| ~ program_halts2(X1,X1) ) ) )
| ! [X2] :
( ~ program(X2)
| ? [X3] :
( ~ program_halts2_halts2_outputs(X2,X3,good)
| ~ program_not_halts2_halts2_outputs(X2,X3,bad) ) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( program_not_halts2_halts2_outputs(X2,X3,good)
& ( ~ halts2(X2,X3)
| ~ program_halts2(X3,X3) ) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ~ program_halts2_halts2_outputs(X0,X1,good)
| ~ program_not_halts2_halts2_outputs(X0,X1,bad) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
( ? [X0] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X0,X1,bad)
& program_halts2_halts2_outputs(X0,X1,good) )
& program(X0) )
=> ? [X2] :
( program(X2)
& ! [X3] :
( ( program_halts2(X3,X3)
=> ~ halts2(X2,X3) )
& program_not_halts2_halts2_outputs(X2,X3,good) ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
( ? [X4] :
( ! [X1] :
( program_halts2_halts2_outputs(X4,X1,good)
& program_not_halts2_halts2_outputs(X4,X1,bad) )
& program(X4) )
=> ? [X5] :
( ! [X1] :
( program_not_halts2_halts2_outputs(X5,X1,good)
& ( program_halts2(X1,X1)
=> ~ halts2(X5,X1) ) )
& program(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f155,plain,
( spl8_8
| spl8_7 ),
inference(avatar_split_clause,[],[f113,f148,f152]) ).
fof(f113,plain,
! [X0] :
( ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad)
| ~ program(X0)
| program(sK3)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good) ),
inference(cnf_transformation,[],[f67]) ).
fof(f150,plain,
( spl8_6
| spl8_7 ),
inference(avatar_split_clause,[],[f111,f148,f145]) ).
fof(f111,plain,
! [X3,X0] :
( ~ program(X0)
| program_not_halts2_halts2_outputs(sK3,X3,bad)
| ~ program_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),good)
| ~ program_not_halts2_halts3_outputs(X0,sK2(X0),sK2(X0),bad) ),
inference(cnf_transformation,[],[f67]) ).
fof(f143,plain,
( spl8_3
| spl8_5 ),
inference(avatar_split_clause,[],[f122,f140,f133]) ).
fof(f122,plain,
! [X2] :
( program(sK5)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f121,f136,f133]) ).
fof(f121,plain,
! [X2,X1] :
( program_not_halts2_halts2_outputs(sK5,X1,good)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ),
inference(cnf_transformation,[],[f78]) ).
fof(f131,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f114,f129,f125]) ).
fof(f114,plain,
! [X1] :
( ~ algorithm_program_decides(X1)
| program_program_decides(sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( program_program_decides(sK4)
| ! [X1] : ~ algorithm_program_decides(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f68,f69]) ).
fof(f69,plain,
( ? [X0] : program_program_decides(X0)
=> program_program_decides(sK4) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X0] : program_program_decides(X0)
| ! [X1] : ~ algorithm_program_decides(X1) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
( ? [X1] : program_program_decides(X1)
| ! [X0] : ~ algorithm_program_decides(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
( ? [X0] : algorithm_program_decides(X0)
=> ? [X1] : program_program_decides(X1) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
( ? [X0] : algorithm_program_decides(X0)
=> ? [X3] : program_program_decides(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 17:05:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % (13166)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50 % (13173)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.50 % (13166)Refutation not found, incomplete strategy% (13166)------------------------------
% 0.19/0.50 % (13166)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (13166)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (13166)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (13166)Memory used [KB]: 5884
% 0.19/0.50 % (13166)Time elapsed: 0.002 s
% 0.19/0.50 % (13166)Instructions burned: 1 (million)
% 0.19/0.50 % (13166)------------------------------
% 0.19/0.50 % (13166)------------------------------
% 0.19/0.50 % (13189)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (13177)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51 % (13189)First to succeed.
% 0.19/0.51 % (13187)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.51 % (13189)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (13189)------------------------------
% 0.19/0.51 % (13189)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (13189)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (13189)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (13189)Memory used [KB]: 6012
% 0.19/0.51 % (13189)Time elapsed: 0.108 s
% 0.19/0.51 % (13189)Instructions burned: 6 (million)
% 0.19/0.51 % (13189)------------------------------
% 0.19/0.51 % (13189)------------------------------
% 0.19/0.51 % (13164)Success in time 0.171 s
%------------------------------------------------------------------------------