TSTP Solution File: COM003_1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : COM003_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : n009.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 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 143 ( 7 unt; 20 typ; 0 def)
% Number of atoms : 431 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 560 ( 252 ~; 221 |; 40 &)
% ( 19 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 24 ( 23 usr; 20 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 174 ( 151 !; 23 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
program: $tType ).
tff(type_def_6,type,
algorithm: $tType ).
tff(type_def_7,type,
input: $tType ).
tff(type_def_8,type,
output: $tType ).
tff(func_def_0,type,
bad: output ).
tff(func_def_1,type,
good: output ).
tff(func_def_2,type,
algorithm_of: program > algorithm ).
tff(func_def_3,type,
as_input: program > input ).
tff(func_def_4,type,
sK0: program ).
tff(func_def_5,type,
sK1: algorithm > program ).
tff(func_def_6,type,
sK2: algorithm > input ).
tff(func_def_7,type,
sK3: program ).
tff(func_def_8,type,
sK4: program > program ).
tff(func_def_9,type,
sK5: program ).
tff(func_def_10,type,
sK6: program > program ).
tff(func_def_11,type,
sK7: algorithm ).
tff(pred_def_1,type,
decides: ( algorithm * program * input ) > $o ).
tff(pred_def_2,type,
halts2: ( program * input ) > $o ).
tff(pred_def_3,type,
halts3: ( program * program * input ) > $o ).
tff(pred_def_4,type,
outputs: ( program * output ) > $o ).
tff(f221,plain,
$false,
inference(avatar_sat_refutation,[],[f61,f65,f76,f84,f91,f92,f105,f106,f110,f117,f124,f126,f136,f141,f148,f171,f172,f179,f186,f193,f204,f206,f209,f218,f220]) ).
tff(f220,plain,
( ~ spl8_4
| ~ spl8_21 ),
inference(avatar_contradiction_clause,[],[f219]) ).
tff(f219,plain,
( $false
| ~ spl8_4
| ~ spl8_21 ),
inference(subsumption_resolution,[],[f57,f123]) ).
tff(f123,plain,
( ! [X3: program,X4: input] : ~ halts2(X3,X4)
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f122]) ).
tff(f122,plain,
( spl8_21
<=> ! [X4: input,X3: program] : ~ halts2(X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
tff(f57,plain,
( ! [X3: program,X4: input] : halts2(X3,X4)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f56,plain,
( spl8_4
<=> ! [X4: input,X3: program] : halts2(X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f218,plain,
( ~ spl8_25
| ~ spl8_12
| ~ spl8_18
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f215,f122,f112,f86,f199]) ).
tff(f199,plain,
( spl8_25
<=> outputs(sK0,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f86,plain,
( spl8_12
<=> ! [X0: program] :
( halts2(sK4(X0),as_input(sK4(X0)))
| ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,bad) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f112,plain,
( spl8_18
<=> ! [X4: program,X5: input] : decides(algorithm_of(sK0),X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f215,plain,
( ~ outputs(sK0,bad)
| ~ spl8_12
| ~ spl8_18
| ~ spl8_21 ),
inference(resolution,[],[f214,f207]) ).
tff(f207,plain,
( ! [X0: program,X1: input] : halts3(sK0,X0,X1)
| ~ spl8_18 ),
inference(resolution,[],[f113,f174]) ).
tff(f174,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| halts3(X2,X3,X4) ),
inference(subsumption_resolution,[],[f21,f18]) ).
tff(f18,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| halts3(X2,X3,X4)
| halts2(X3,X4) ),
inference(cnf_transformation,[],[f14]) ).
tff(f14,plain,
! [X1: program,X0: input,X2: program] :
( ! [X3: program,X4: input] :
( ( halts2(X3,X4)
| ( outputs(X2,bad)
& halts3(X2,X3,X4) ) )
& ( ~ halts2(X3,X4)
| ( halts3(X2,X3,X4)
& outputs(X2,good) ) ) )
| ~ decides(algorithm_of(X2),X1,X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
! [X2: program,X1: program,X0: input] :
( decides(algorithm_of(X2),X1,X0)
=> ! [X4: input,X3: program] :
( ( ~ halts2(X3,X4)
=> ( outputs(X2,bad)
& halts3(X2,X3,X4) ) )
& ( halts2(X3,X4)
=> ( halts3(X2,X3,X4)
& outputs(X2,good) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X2: input,X1: program,X3: program] :
( decides(algorithm_of(X3),X1,X2)
=> ! [X1: program,X2: input] :
( ( ~ halts2(X1,X2)
=> ( outputs(X3,bad)
& halts3(X3,X1,X2) ) )
& ( halts2(X1,X2)
=> ( halts3(X3,X1,X2)
& outputs(X3,good) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
tff(f21,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ halts2(X3,X4)
| ~ decides(algorithm_of(X2),X1,X0)
| halts3(X2,X3,X4) ),
inference(cnf_transformation,[],[f14]) ).
tff(f113,plain,
( ! [X4: program,X5: input] : decides(algorithm_of(sK0),X4,X5)
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f112]) ).
tff(f214,plain,
( ! [X0: program] :
( ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,bad) )
| ~ spl8_12
| ~ spl8_21 ),
inference(subsumption_resolution,[],[f87,f123]) ).
tff(f87,plain,
( ! [X0: program] :
( ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| halts2(sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,bad) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f86]) ).
tff(f209,plain,
( spl8_25
| ~ spl8_5
| ~ spl8_18 ),
inference(avatar_split_clause,[],[f208,f112,f59,f199]) ).
tff(f59,plain,
( spl8_5
<=> ! [X2: program,X0: input,X1: program] :
( ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,bad) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
tff(f208,plain,
( outputs(sK0,bad)
| ~ spl8_5
| ~ spl8_18 ),
inference(resolution,[],[f60,f113]) ).
tff(f60,plain,
( ! [X2: program,X0: input,X1: program] :
( ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,bad) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f206,plain,
~ spl8_19,
inference(avatar_contradiction_clause,[],[f205]) ).
tff(f205,plain,
( $false
| ~ spl8_19 ),
inference(resolution,[],[f116,f43]) ).
tff(f43,plain,
! [X2: program,X1: input] : decides(sK7,X2,X1),
inference(cnf_transformation,[],[f8]) ).
tff(f8,plain,
? [X0: algorithm] :
! [X2: program,X1: input] : decides(X0,X2,X1),
inference(flattening,[],[f7]) ).
tff(f7,plain,
~ ~ ? [X0: algorithm] :
! [X2: program,X1: input] : decides(X0,X2,X1),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ~ ? [X6: algorithm] :
! [X8: input,X7: program] : decides(X6,X7,X8),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
~ ? [X6: algorithm] :
! [X8: input,X7: program] : decides(X6,X7,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(f116,plain,
( ! [X0: algorithm] : ~ decides(X0,sK1(X0),sK2(X0))
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f115]) ).
tff(f115,plain,
( spl8_19
<=> ! [X0: algorithm] : ~ decides(X0,sK1(X0),sK2(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f204,plain,
( ~ spl8_8
| ~ spl8_13
| ~ spl8_21 ),
inference(avatar_contradiction_clause,[],[f203]) ).
tff(f203,plain,
( $false
| ~ spl8_8
| ~ spl8_13
| ~ spl8_21 ),
inference(subsumption_resolution,[],[f144,f123]) ).
tff(f144,plain,
( ! [X3: program] : halts2(sK3,as_input(X3))
| ~ spl8_8
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f90,f72]) ).
tff(f72,plain,
( ! [X3: program] :
( halts2(sK3,as_input(X3))
| halts2(X3,as_input(X3)) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f71,plain,
( spl8_8
<=> ! [X3: program] :
( halts2(X3,as_input(X3))
| halts2(sK3,as_input(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f90,plain,
( ! [X3: program] :
( ~ halts2(X3,as_input(X3))
| halts2(sK3,as_input(X3)) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f89]) ).
tff(f89,plain,
( spl8_13
<=> ! [X3: program] :
( ~ halts2(X3,as_input(X3))
| halts2(sK3,as_input(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f193,plain,
( ~ spl8_4
| ~ spl8_17
| ~ spl8_18
| ~ spl8_20 ),
inference(avatar_contradiction_clause,[],[f190]) ).
tff(f190,plain,
( $false
| ~ spl8_4
| ~ spl8_17
| ~ spl8_18
| ~ spl8_20 ),
inference(resolution,[],[f189,f149]) ).
tff(f149,plain,
( outputs(sK0,good)
| ~ spl8_18
| ~ spl8_20 ),
inference(resolution,[],[f120,f113]) ).
tff(f120,plain,
( ! [X2: program,X0: input,X1: program] :
( ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,good) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f119]) ).
tff(f119,plain,
( spl8_20
<=> ! [X2: program,X0: input,X1: program] :
( ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,good) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f189,plain,
( ! [X0: program] : ~ outputs(X0,good)
| ~ spl8_4
| ~ spl8_17 ),
inference(subsumption_resolution,[],[f188,f57]) ).
tff(f188,plain,
( ! [X0: program] :
( ~ outputs(X0,good)
| ~ halts2(sK6(X0),as_input(sK6(X0))) )
| ~ spl8_4
| ~ spl8_17 ),
inference(subsumption_resolution,[],[f109,f57]) ).
tff(f109,plain,
( ! [X0: program] :
( ~ halts2(X0,as_input(sK6(X0)))
| ~ halts2(sK6(X0),as_input(sK6(X0)))
| ~ outputs(X0,good) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f108]) ).
tff(f108,plain,
( spl8_17
<=> ! [X0: program] :
( ~ halts2(sK6(X0),as_input(sK6(X0)))
| ~ halts2(X0,as_input(sK6(X0)))
| ~ outputs(X0,good) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
tff(f186,plain,
( ~ spl8_5
| ~ spl8_9
| ~ spl8_18
| ~ spl8_20 ),
inference(avatar_contradiction_clause,[],[f185]) ).
tff(f185,plain,
( $false
| ~ spl8_5
| ~ spl8_9
| ~ spl8_18
| ~ spl8_20 ),
inference(subsumption_resolution,[],[f184,f137]) ).
tff(f137,plain,
( outputs(sK0,bad)
| ~ spl8_5
| ~ spl8_18 ),
inference(resolution,[],[f60,f113]) ).
tff(f184,plain,
( ~ outputs(sK0,bad)
| ~ spl8_9
| ~ spl8_18
| ~ spl8_20 ),
inference(subsumption_resolution,[],[f183,f149]) ).
tff(f183,plain,
( ~ outputs(sK0,bad)
| ~ outputs(sK0,good)
| ~ spl8_9
| ~ spl8_18 ),
inference(resolution,[],[f75,f175]) ).
tff(f175,plain,
( ! [X0: program,X1: input] : halts3(sK0,X0,X1)
| ~ spl8_18 ),
inference(resolution,[],[f174,f113]) ).
tff(f75,plain,
( ! [X0: program] :
( ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,good)
| ~ outputs(X0,bad) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f74,plain,
( spl8_9
<=> ! [X0: program] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,good) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f179,plain,
( ~ spl8_3
| ~ spl8_8
| ~ spl8_10
| ~ spl8_13
| ~ spl8_17 ),
inference(avatar_contradiction_clause,[],[f178]) ).
tff(f178,plain,
( $false
| ~ spl8_3
| ~ spl8_8
| ~ spl8_10
| ~ spl8_13
| ~ spl8_17 ),
inference(subsumption_resolution,[],[f177,f80]) ).
tff(f80,plain,
( outputs(sK3,good)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f78,plain,
( spl8_10
<=> outputs(sK3,good) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
tff(f177,plain,
( ~ outputs(sK3,good)
| ~ spl8_3
| ~ spl8_8
| ~ spl8_13
| ~ spl8_17 ),
inference(resolution,[],[f176,f144]) ).
tff(f176,plain,
( ! [X0: program] :
( ~ halts2(X0,as_input(sK6(X0)))
| ~ outputs(X0,good) )
| ~ spl8_3
| ~ spl8_17 ),
inference(subsumption_resolution,[],[f109,f53]) ).
tff(f53,plain,
( ! [X3: program] : halts2(X3,as_input(X3))
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f52,plain,
( spl8_3
<=> ! [X3: program] : halts2(X3,as_input(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f172,plain,
( ~ spl8_10
| ~ spl8_14
| ~ spl8_2
| ~ spl8_8
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f151,f89,f71,f49,f94,f78]) ).
tff(f94,plain,
( spl8_14
<=> outputs(sK3,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f49,plain,
( spl8_2
<=> ! [X0: program] :
( ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK6(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f151,plain,
( ~ outputs(sK3,bad)
| ~ outputs(sK3,good)
| ~ spl8_2
| ~ spl8_8
| ~ spl8_13 ),
inference(resolution,[],[f50,f144]) ).
tff(f50,plain,
( ! [X0: program] :
( ~ halts2(X0,as_input(sK6(X0)))
| ~ outputs(X0,bad)
| ~ outputs(X0,good) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f171,plain,
( ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f169]) ).
tff(f169,plain,
( $false
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(resolution,[],[f83,f144]) ).
tff(f83,plain,
( ! [X3: program] : ~ halts2(X3,as_input(X3))
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f82]) ).
tff(f82,plain,
( spl8_11
<=> ! [X3: program] : ~ halts2(X3,as_input(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f148,plain,
( ~ spl8_6
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f147]) ).
tff(f147,plain,
( $false
| ~ spl8_6
| ~ spl8_16 ),
inference(subsumption_resolution,[],[f146,f142]) ).
tff(f142,plain,
( halts2(sK5,as_input(sK5))
| ~ spl8_6 ),
inference(factoring,[],[f64]) ).
tff(f64,plain,
( ! [X3: program] :
( halts2(sK5,as_input(X3))
| halts2(X3,as_input(X3)) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f63]) ).
tff(f63,plain,
( spl8_6
<=> ! [X3: program] :
( halts2(sK5,as_input(X3))
| halts2(X3,as_input(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
tff(f146,plain,
( ~ halts2(sK5,as_input(sK5))
| ~ spl8_6
| ~ spl8_16 ),
inference(resolution,[],[f103,f142]) ).
tff(f103,plain,
( ! [X3: program] :
( ~ halts2(sK5,as_input(X3))
| ~ halts2(X3,as_input(X3)) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f102]) ).
tff(f102,plain,
( spl8_16
<=> ! [X3: program] :
( ~ halts2(X3,as_input(X3))
| ~ halts2(sK5,as_input(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f141,plain,
( ~ spl8_3
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f140]) ).
tff(f140,plain,
( $false
| ~ spl8_3
| ~ spl8_16 ),
inference(resolution,[],[f139,f53]) ).
tff(f139,plain,
( ! [X3: program] : ~ halts2(sK5,as_input(X3))
| ~ spl8_3
| ~ spl8_16 ),
inference(subsumption_resolution,[],[f103,f53]) ).
tff(f136,plain,
( ~ spl8_4
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f135]) ).
tff(f135,plain,
( $false
| ~ spl8_4
| ~ spl8_16 ),
inference(subsumption_resolution,[],[f134,f57]) ).
tff(f134,plain,
( ! [X3: program] : ~ halts2(X3,as_input(X3))
| ~ spl8_4
| ~ spl8_16 ),
inference(subsumption_resolution,[],[f103,f57]) ).
tff(f126,plain,
( spl8_3
| spl8_14
| spl8_9 ),
inference(avatar_split_clause,[],[f28,f74,f94,f52]) ).
tff(f28,plain,
! [X3: program,X0: program] :
( ~ outputs(X0,good)
| outputs(sK3,bad)
| ~ outputs(X0,bad)
| ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| halts2(X3,as_input(X3)) ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ halts3(X0,X1,as_input(X1))
| ~ outputs(X0,good) )
& halts2(X1,as_input(X1)) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) ) ) )
| ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
| ( halts2(X2,as_input(X3))
& outputs(X2,good) ) )
& ( halts2(X3,as_input(X3))
| ( halts2(X2,as_input(X3))
& outputs(X2,bad) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
( ? [X0: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ( halts3(X0,X1,as_input(X1))
& outputs(X0,good) ) )
& ( ~ halts2(X1,as_input(X1))
=> ( halts3(X0,X1,as_input(X1))
& outputs(X0,bad) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( halts2(X2,as_input(X3))
& outputs(X2,bad) ) )
& ( halts2(X3,as_input(X3))
=> ( halts2(X2,as_input(X3))
& outputs(X2,good) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
( ? [X3: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ( halts3(X3,X1,as_input(X1))
& outputs(X3,good) ) )
& ( ~ halts2(X1,as_input(X1))
=> ( outputs(X3,bad)
& halts3(X3,X1,as_input(X1)) ) ) )
=> ? [X4: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,good) ) )
& ( ~ halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,bad) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f124,plain,
( spl8_20
| spl8_21 ),
inference(avatar_split_clause,[],[f20,f122,f119]) ).
tff(f20,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ halts2(X3,X4)
| ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,good) ),
inference(cnf_transformation,[],[f14]) ).
tff(f117,plain,
( spl8_18
| spl8_19 ),
inference(avatar_split_clause,[],[f17,f115,f112]) ).
tff(f17,plain,
! [X0: algorithm,X4: program,X5: input] :
( ~ decides(X0,sK1(X0),sK2(X0))
| decides(algorithm_of(sK0),X4,X5) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,plain,
( ! [X0: algorithm] :
? [X2: program,X1: input] : ~ decides(X0,X2,X1)
| ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
( ? [X0: algorithm] :
! [X2: program,X1: input] : decides(X0,X2,X1)
=> ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( ? [X0: algorithm] :
! [X2: input,X1: program] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X1: program,X2: input] : decides(algorithm_of(X3),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f110,plain,
( spl8_16
| spl8_17 ),
inference(avatar_split_clause,[],[f40,f108,f102]) ).
tff(f40,plain,
! [X3: program,X0: program] :
( ~ halts2(sK6(X0),as_input(sK6(X0)))
| ~ halts2(sK5,as_input(X3))
| ~ outputs(X0,good)
| ~ halts2(X3,as_input(X3))
| ~ halts2(X0,as_input(sK6(X0))) ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,plain,
( ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X2,as_input(X3))
| ~ halts2(X3,as_input(X3)) )
& ( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3)) ) )
| ! [X0: program] :
? [X1: program] :
( ( halts2(X1,as_input(X1))
& ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) ) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ halts2(X0,as_input(X1))
| ~ outputs(X0,bad) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( halts2(X0,as_input(X1))
& outputs(X0,bad) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
=> ~ halts2(X2,as_input(X3)) )
& ( ~ halts2(X3,as_input(X3))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
( ? [X4: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,bad) ) )
& ( halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,good) ) ) )
=> ? [X5: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ~ halts2(X5,as_input(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(f106,plain,
( spl8_2
| spl8_16 ),
inference(avatar_split_clause,[],[f41,f102,f49]) ).
tff(f41,plain,
! [X3: program,X0: program] :
( ~ halts2(X3,as_input(X3))
| ~ halts2(X0,as_input(sK6(X0)))
| ~ halts2(sK5,as_input(X3))
| ~ outputs(X0,bad)
| ~ outputs(X0,good) ),
inference(cnf_transformation,[],[f13]) ).
tff(f105,plain,
( spl8_13
| spl8_9 ),
inference(avatar_split_clause,[],[f27,f74,f89]) ).
tff(f27,plain,
! [X3: program,X0: program] :
( ~ outputs(X0,good)
| ~ halts2(X3,as_input(X3))
| ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| halts2(sK3,as_input(X3))
| ~ outputs(X0,bad) ),
inference(cnf_transformation,[],[f15]) ).
tff(f92,plain,
( spl8_8
| spl8_12 ),
inference(avatar_split_clause,[],[f30,f86,f71]) ).
tff(f30,plain,
! [X3: program,X0: program] :
( ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,bad)
| halts2(sK3,as_input(X3))
| halts2(sK4(X0),as_input(sK4(X0)))
| halts2(X3,as_input(X3)) ),
inference(cnf_transformation,[],[f15]) ).
tff(f91,plain,
( spl8_12
| spl8_13 ),
inference(avatar_split_clause,[],[f32,f89,f86]) ).
tff(f32,plain,
! [X3: program,X0: program] :
( ~ halts2(X3,as_input(X3))
| halts2(sK3,as_input(X3))
| halts2(sK4(X0),as_input(sK4(X0)))
| ~ outputs(X0,bad)
| ~ halts3(X0,sK4(X0),as_input(sK4(X0))) ),
inference(cnf_transformation,[],[f15]) ).
tff(f84,plain,
( spl8_10
| spl8_11
| spl8_9 ),
inference(avatar_split_clause,[],[f26,f74,f82,f78]) ).
tff(f26,plain,
! [X3: program,X0: program] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK4(X0),as_input(sK4(X0)))
| ~ halts2(X3,as_input(X3))
| ~ outputs(X0,good)
| outputs(sK3,good) ),
inference(cnf_transformation,[],[f15]) ).
tff(f76,plain,
( spl8_8
| spl8_9 ),
inference(avatar_split_clause,[],[f29,f74,f71]) ).
tff(f29,plain,
! [X3: program,X0: program] :
( ~ outputs(X0,bad)
| ~ outputs(X0,good)
| halts2(X3,as_input(X3))
| halts2(sK3,as_input(X3))
| ~ halts3(X0,sK4(X0),as_input(sK4(X0))) ),
inference(cnf_transformation,[],[f15]) ).
tff(f65,plain,
( spl8_6
| spl8_2 ),
inference(avatar_split_clause,[],[f36,f49,f63]) ).
tff(f36,plain,
! [X3: program,X0: program] :
( ~ halts2(X0,as_input(sK6(X0)))
| halts2(sK5,as_input(X3))
| halts2(X3,as_input(X3))
| ~ outputs(X0,good)
| ~ outputs(X0,bad) ),
inference(cnf_transformation,[],[f13]) ).
tff(f61,plain,
( spl8_4
| spl8_5 ),
inference(avatar_split_clause,[],[f19,f59,f56]) ).
tff(f19,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| halts2(X3,X4)
| outputs(X2,bad) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM003_1 : TPTP v8.1.0. Released v5.0.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 16:58:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50 % (19016)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.51 % (19008)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.51 % (19008)First to succeed.
% 0.19/0.51 % (19016)Refutation not found, incomplete strategy% (19016)------------------------------
% 0.19/0.51 % (19016)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (19008)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (19008)------------------------------
% 0.19/0.52 % (19008)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (19008)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (19008)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (19008)Memory used [KB]: 6012
% 0.19/0.52 % (19008)Time elapsed: 0.089 s
% 0.19/0.52 % (19008)Instructions burned: 5 (million)
% 0.19/0.52 % (19008)------------------------------
% 0.19/0.52 % (19008)------------------------------
% 0.19/0.52 % (18987)Success in time 0.169 s
%------------------------------------------------------------------------------