%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:38:59 AM UTC 2026
% Result : Theorem 0.64s 0.71s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 138 ( 21 unt; 13 def)
% Number of atoms : 413 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 485 ( 210 ~; 193 |; 54 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 14 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 150 ( 0 sgn 127 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( program_program_decides(X0)
<=> ( program(X0)
& program_decides(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(f4,axiom,
! [X0,X1] :
( program_halts2(X0,X1)
<=> ( program(X0)
& halts2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_def) ).
fof(f6,axiom,
! [X0,X1] :
( program_not_halts2(X0,X1)
<=> ( program(X0)
& ~ halts2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_def) ).
fof(f7,axiom,
! [X0,X1,X2] :
( halts2_outputs(X0,X1,X2)
<=> ( halts2(X0,X1)
& outputs(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs_def) ).
fof(f11,axiom,
! [X0,X1,X2] :
( program_not_halts2_halts2_outputs(X0,X1,X2)
<=> ( program_not_halts2(X1,X1)
=> halts2_outputs(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
fof(f12,axiom,
( ? [X0] : algorithm_program_decides(X0)
=> ? [X1] : program_program_decides(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f13,axiom,
! [X0] :
( program_program_decides(X0)
=> ! [X1,X2] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
& program_not_halts2_halts3_outputs(X0,X1,X2,bad) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f14,axiom,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_halts2_halts3_outputs(X0,X1,X1,good)
& program_not_halts2_halts3_outputs(X0,X1,X1,bad) ) )
=> ? [X2] :
( program(X2)
& ! [X1] :
( program_halts2_halts2_outputs(X2,X1,good)
& program_not_halts2_halts2_outputs(X2,X1,bad) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f15,axiom,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_halts2_halts2_outputs(X0,X1,good)
& program_not_halts2_halts2_outputs(X0,X1,bad) ) )
=> ? [X2] :
( program(X2)
& ! [X1] :
( ( program_halts2(X1,X1)
=> ~ halts2(X2,X1) )
& program_not_halts2_halts2_outputs(X2,X1,good) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f16,conjecture,
~ ? [X0] : algorithm_program_decides(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f17,negated_conjecture,
~ ~ ? [X0] : algorithm_program_decides(X0),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,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(rectify,[],[f14]) ).
fof(f19,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_halts2_halts2_outputs(X0,X1,good)
& program_not_halts2_halts2_outputs(X0,X1,bad) ) )
=> ? [X2] :
( program(X2)
& ! [X3] :
( ( program_halts2(X3,X3)
=> ~ halts2(X2,X3) )
& program_not_halts2_halts2_outputs(X2,X3,good) ) ) ),
inference(rectify,[],[f15]) ).
fof(f20,plain,
? [X0] : algorithm_program_decides(X0),
inference(flattening,[],[f17]) ).
fof(f25,plain,
! [X0,X1,X2] :
( program_not_halts2_halts2_outputs(X0,X1,X2)
<=> ( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f26,plain,
( ? [X1] : program_program_decides(X1)
| ! [X0] : ~ algorithm_program_decides(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0] :
( ! [X1,X2] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
& program_not_halts2_halts3_outputs(X0,X1,X2,bad) )
| ~ program_program_decides(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f28,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( program_halts2_halts2_outputs(X2,X3,good)
& program_not_halts2_halts2_outputs(X2,X3,bad) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ~ program_halts2_halts3_outputs(X0,X1,X1,good)
| ~ program_not_halts2_halts3_outputs(X0,X1,X1,bad) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( ( ~ halts2(X2,X3)
| ~ program_halts2(X3,X3) )
& program_not_halts2_halts2_outputs(X2,X3,good) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ~ program_halts2_halts2_outputs(X0,X1,good)
| ~ program_not_halts2_halts2_outputs(X0,X1,bad) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0] :
( ( program_program_decides(X0)
| ~ program(X0)
| ~ program_decides(X0) )
& ( ( program(X0)
& program_decides(X0) )
| ~ program_program_decides(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] :
( ( program_program_decides(X0)
| ~ program(X0)
| ~ program_decides(X0) )
& ( ( program(X0)
& program_decides(X0) )
| ~ program_program_decides(X0) ) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( ( program_halts2(X0,X1)
| ~ program(X0)
| ~ halts2(X0,X1) )
& ( ( program(X0)
& halts2(X0,X1) )
| ~ program_halts2(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0,X1] :
( ( program_halts2(X0,X1)
| ~ program(X0)
| ~ halts2(X0,X1) )
& ( ( program(X0)
& halts2(X0,X1) )
| ~ program_halts2(X0,X1) ) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ( 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(f42,plain,
! [X0,X1] :
( ( program_not_halts2(X0,X1)
| ~ program(X0)
| halts2(X0,X1) )
& ( ( program(X0)
& ~ halts2(X0,X1) )
| ~ program_not_halts2(X0,X1) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( halts2_outputs(X0,X1,X2)
| ~ halts2(X0,X1)
| ~ outputs(X0,X2) )
& ( ( halts2(X0,X1)
& outputs(X0,X2) )
| ~ halts2_outputs(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( halts2_outputs(X0,X1,X2)
| ~ halts2(X0,X1)
| ~ outputs(X0,X2) )
& ( ( halts2(X0,X1)
& outputs(X0,X2) )
| ~ halts2_outputs(X0,X1,X2) ) ),
inference(flattening,[],[f43]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( program_not_halts2_halts2_outputs(X0,X1,X2)
| ( ~ halts2_outputs(X0,X1,X2)
& program_not_halts2(X1,X1) ) )
& ( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( program_not_halts2_halts2_outputs(X0,X1,X2)
| ( ~ halts2_outputs(X0,X1,X2)
& program_not_halts2(X1,X1) ) )
& ( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
( ? [X0] : program_program_decides(X0)
| ! [X1] : ~ algorithm_program_decides(X1) ),
inference(rectify,[],[f26]) ).
fof(f54,plain,
( program_program_decides(sK2)
| ! [X1] : ~ algorithm_program_decides(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f53]) ).
fof(f55,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( program_halts2_halts2_outputs(X0,X1,good)
& program_not_halts2_halts2_outputs(X0,X1,bad) ) )
| ! [X2] :
( ~ program(X2)
| ? [X3] :
( ~ program_halts2_halts3_outputs(X2,X3,X3,good)
| ~ program_not_halts2_halts3_outputs(X2,X3,X3,bad) ) ) ),
inference(rectify,[],[f28]) ).
fof(f56,plain,
( ( program(sK3)
& ! [X1] :
( program_halts2_halts2_outputs(sK3,X1,good)
& program_not_halts2_halts2_outputs(sK3,X1,bad) ) )
| ! [X2] :
( ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X3,sK4(X2))],[f55]) ).
fof(f57,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( ( ~ halts2(X0,X1)
| ~ program_halts2(X1,X1) )
& program_not_halts2_halts2_outputs(X0,X1,good) ) )
| ! [X2] :
( ~ program(X2)
| ? [X3] :
( ~ program_halts2_halts2_outputs(X2,X3,good)
| ~ program_not_halts2_halts2_outputs(X2,X3,bad) ) ) ),
inference(rectify,[],[f29]) ).
fof(f58,plain,
( ( program(sK5)
& ! [X1] :
( ( ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1) )
& program_not_halts2_halts2_outputs(sK5,X1,good) ) )
| ! [X2] :
( ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X3,sK6(X2))],[f57]) ).
fof(f59,plain,
algorithm_program_decides(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f20]) ).
fof(f64,plain,
! [X0] :
( program(X0)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0,X1] :
( ~ halts2(X0,X1)
| ~ program(X0)
| program_halts2(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f77,plain,
! [X0,X1] :
( program_not_halts2(X0,X1)
| ~ program(X0)
| halts2(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ halts2_outputs(X0,X1,X2)
| halts2(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ program_not_halts2(X1,X1)
| halts2_outputs(X0,X1,X2)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X1] :
( program_program_decides(sK2)
| ~ algorithm_program_decides(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f94,plain,
! [X2,X0,X1] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f95,plain,
! [X2,X0,X1] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f96,plain,
! [X2,X1] :
( program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad) ),
inference(cnf_transformation,[],[f56]) ).
fof(f97,plain,
! [X2,X1] :
( program_halts2_halts2_outputs(sK3,X1,good)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad) ),
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
! [X2] :
( program(sK3)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,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,[],[f58]) ).
fof(f100,plain,
! [X2,X1] :
( ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ),
inference(cnf_transformation,[],[f58]) ).
fof(f101,plain,
! [X2] :
( program(sK5)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad) ),
inference(cnf_transformation,[],[f58]) ).
fof(f102,plain,
algorithm_program_decides(sK7),
inference(cnf_transformation,[],[f59]) ).
fof(f104,definition,
( spl8_1
<=> ! [X2] :
( ~ program(X2)
| ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f105,plain,
( ! [X2] :
( ~ program_not_halts2_halts2_outputs(X2,sK6(X2),bad)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,sK6(X2),good) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl8_2
<=> ! [X1] : program_not_halts2_halts2_outputs(sK5,X1,good) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f108,plain,
( ! [X1] : program_not_halts2_halts2_outputs(sK5,X1,good)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f99,f107,f104]) ).
fof(f111,definition,
( spl8_3
<=> ! [X1] :
( ~ halts2(sK5,X1)
| ~ program_halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f112,plain,
( ! [X1] :
( ~ program_halts2(X1,X1)
| ~ halts2(sK5,X1) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f100,f111,f104]) ).
fof(f115,definition,
( spl8_4
<=> program(sK5) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f117,plain,
( program(sK5)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[],[f101,f115,f104]) ).
fof(f120,definition,
( spl8_5
<=> ! [X2] :
( ~ program(X2)
| ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
fof(f121,plain,
( ! [X2] :
( ~ program_not_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),bad)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,sK4(X2),sK4(X2),good) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,definition,
( spl8_6
<=> ! [X1] : program_not_halts2_halts2_outputs(sK3,X1,bad) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
fof(f124,plain,
( ! [X1] : program_not_halts2_halts2_outputs(sK3,X1,bad)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( spl8_5
| spl8_6 ),
inference(avatar_split_clause,[],[f96,f123,f120]) ).
fof(f127,definition,
( spl8_7
<=> ! [X1] : program_halts2_halts2_outputs(sK3,X1,good) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f128,plain,
( ! [X1] : program_halts2_halts2_outputs(sK3,X1,good)
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f129,plain,
( spl8_5
| spl8_7 ),
inference(avatar_split_clause,[],[f97,f127,f120]) ).
fof(f131,definition,
( spl8_8
<=> program(sK3) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f133,plain,
( program(sK3)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl8_5
| spl8_8 ),
inference(avatar_split_clause,[],[f98,f131,f120]) ).
fof(f136,definition,
( spl8_9
<=> ! [X1] : ~ algorithm_program_decides(X1) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f137,plain,
( ! [X1] : ~ algorithm_program_decides(X1)
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl8_10
<=> program_program_decides(sK2) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f141,plain,
( program_program_decides(sK2)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl8_9
| spl8_10 ),
inference(avatar_split_clause,[],[f93,f139,f136]) ).
fof(f143,plain,
( $false
| ~ spl8_9 ),
inference(resolution,[],[f137,f102]) ).
fof(f144,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f143]) ).
fof(f147,plain,
( ! [X0] :
( ~ program(X0)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good)
| ~ program_program_decides(X0) )
| ~ spl8_5 ),
inference(resolution,[],[f121,f94]) ).
fof(f150,plain,
( ! [X0] :
( ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good)
| ~ program_program_decides(X0) )
| ~ spl8_5 ),
inference(forward_subsumption_resolution,[],[f147,f64]) ).
fof(f151,plain,
( ! [X0] : ~ program_program_decides(X0)
| ~ spl8_5 ),
inference(forward_subsumption_resolution,[],[f150,f95]) ).
fof(f152,plain,
( $false
| ~ spl8_5
| ~ spl8_10 ),
inference(resolution,[],[f151,f141]) ).
fof(f154,plain,
( ~ spl8_5
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f156,plain,
! [X2,X0,X1] :
( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2)
| ~ program(X1)
| halts2(X1,X1) ),
inference(resolution,[],[f90,f77]) ).
fof(f157,plain,
! [X2,X0,X1] :
( halts2(X1,X1)
| ~ program(X1)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2)
| halts2(X0,X1) ),
inference(resolution,[],[f156,f79]) ).
fof(f175,definition,
( spl8_11
<=> ! [X2,X3] :
( ~ program_not_halts2_halts2_outputs(X2,sK5,X3)
| halts2(X2,sK5) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
fof(f176,plain,
( ! [X2,X3] :
( halts2(X2,sK5)
| ~ program_not_halts2_halts2_outputs(X2,sK5,X3) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f183,plain,
( ~ program(sK3)
| ~ program_halts2_halts2_outputs(sK3,sK6(sK3),good)
| ~ spl8_1
| ~ spl8_6 ),
inference(resolution,[],[f105,f124]) ).
fof(f184,plain,
( ~ program_halts2_halts2_outputs(sK3,sK6(sK3),good)
| ~ spl8_1
| ~ spl8_6
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f183,f133]) ).
fof(f185,plain,
( $false
| ~ spl8_1
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f184,f128]) ).
fof(f186,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f199,definition,
( spl8_14
<=> ! [X0] : ~ program_not_halts2_halts2_outputs(sK5,sK5,X0) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
fof(f200,plain,
( ! [X0] : ~ program_not_halts2_halts2_outputs(sK5,sK5,X0)
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f203,definition,
( spl8_15
<=> halts2(sK5,sK5) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f204,plain,
( halts2(sK5,sK5)
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( ~ halts2(sK5,sK5)
| spl8_15 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f214,plain,
( ! [X0,X1] :
( ~ program(sK5)
| ~ program_not_halts2_halts2_outputs(X0,sK5,X1)
| halts2(X0,sK5) )
| spl8_15 ),
inference(resolution,[],[f205,f157]) ).
fof(f215,plain,
( ! [X0,X1] :
( ~ program_not_halts2_halts2_outputs(X0,sK5,X1)
| halts2(X0,sK5) )
| ~ spl8_4
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f214,f117]) ).
fof(f216,plain,
( spl8_11
| ~ spl8_4
| spl8_15 ),
inference(avatar_split_clause,[],[f215,f203,f115,f175]) ).
fof(f220,plain,
( ~ program(sK5)
| program_halts2(sK5,sK5)
| ~ spl8_15 ),
inference(resolution,[],[f204,f71]) ).
fof(f221,plain,
( program_halts2(sK5,sK5)
| ~ spl8_4
| ~ spl8_15 ),
inference(forward_subsumption_resolution,[],[f220,f117]) ).
fof(f223,plain,
( ~ halts2(sK5,sK5)
| ~ spl8_3
| ~ spl8_4
| ~ spl8_15 ),
inference(resolution,[],[f221,f112]) ).
fof(f228,plain,
( $false
| ~ spl8_3
| ~ spl8_4
| ~ spl8_15 ),
inference(forward_subsumption_resolution,[],[f223,f204]) ).
fof(f229,plain,
( ~ spl8_3
| ~ spl8_4
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f236,plain,
( ! [X0] : ~ program_not_halts2_halts2_outputs(sK5,sK5,X0)
| ~ spl8_11
| spl8_15 ),
inference(resolution,[],[f176,f205]) ).
fof(f238,plain,
( spl8_14
| ~ spl8_11
| spl8_15 ),
inference(avatar_split_clause,[],[f236,f203,f175,f199]) ).
fof(f249,plain,
( $false
| ~ spl8_2
| ~ spl8_14 ),
inference(resolution,[],[f200,f108]) ).
fof(f252,plain,
( ~ spl8_2
| ~ spl8_14 ),
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s5,plain,
( spl8_5
| spl8_7 ),
inference(sat_conversion,[],[f129]) ).
cnf(s6,plain,
( spl8_5
| spl8_8 ),
inference(sat_conversion,[],[f134]) ).
cnf(s7,plain,
( spl8_9
| spl8_10 ),
inference(sat_conversion,[],[f142]) ).
cnf(s8,plain,
~ spl8_9,
inference(sat_conversion,[],[f144]) ).
cnf(s9,plain,
( ~ spl8_5
| ~ spl8_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s11,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(sat_conversion,[],[f186]) ).
cnf(s14,plain,
( ~ spl8_4
| spl8_11
| spl8_15 ),
inference(sat_conversion,[],[f216]) ).
cnf(s16,plain,
( ~ spl8_3
| ~ spl8_4
| ~ spl8_15 ),
inference(sat_conversion,[],[f229]) ).
cnf(s18,plain,
( ~ spl8_11
| spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f238]) ).
cnf(s20,plain,
( ~ spl8_2
| ~ spl8_14 ),
inference(sat_conversion,[],[f252]) ).
cnf(s21,plain,
spl8_10,
inference(rat,[],[s7,s8]) ).
cnf(s22,plain,
~ spl8_5,
inference(rat,[],[s9,s21]) ).
cnf(s23,plain,
spl8_8,
inference(rat,[],[s6,s22]) ).
cnf(s24,plain,
spl8_7,
inference(rat,[],[s5,s22]) ).
cnf(s25,plain,
spl8_6,
inference(rat,[],[s4,s22]) ).
cnf(s26,plain,
~ spl8_1,
inference(rat,[],[s11,s23,s24,s25]) ).
cnf(s27,plain,
spl8_4,
inference(rat,[],[s3,s26]) ).
cnf(s28,plain,
spl8_3,
inference(rat,[],[s2,s26]) ).
cnf(s29,plain,
~ spl8_15,
inference(rat,[],[s16,s27,s28]) ).
cnf(s30,plain,
spl8_11,
inference(rat,[],[s14,s27,s29]) ).
cnf(s31,plain,
spl8_14,
inference(rat,[],[s18,s29,s30]) ).
cnf(s32,plain,
~ spl8_2,
inference(rat,[],[s20,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s32,s26]) ).
fof(f253,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:43:38 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.71 % (1218550)Detected formulas, will run a generic FOF schedule.
% 0.64/0.71 % (1218560)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3624998811:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/0.71 % (1218560)First to succeed.
% 0.64/0.71 % (1218560)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1218550"
% 0.64/0.71 % (1218557)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3814808756:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/0.71 % (1218556)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2310931760:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/0.71 % (1218561)dis-21_1_sil=8000:lcm=predicate:random_seed=737378440:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.64/0.71 % (1218558)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=609442339:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/0.71 % (1218555)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4284647191:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/0.71 % (1218559)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3673582673:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/0.71 % (1218558)Refutation not found, incomplete strategy
% 0.64/0.71 % (1218558)------------------------------
% 0.64/0.71 % (1218558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/0.71 % (1218558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.71 % (1218558)CaDiCaL version: 2.1.3
% 0.64/0.71 % (1218558)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.71 % (1218558)Time elapsed: 0.001 s
% 0.64/0.71 % (1218558)Peak memory usage: 86 MB
% 0.64/0.71 % (1218561)Also succeeded, but the first one will report.
% 0.64/0.71 % (1218559)Refutation not found, incomplete strategy
% 0.64/0.71 % (1218559)------------------------------
% 0.64/0.71 % (1218559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/0.71 % (1218559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.71 % (1218559)CaDiCaL version: 2.1.3
% 0.64/0.71 % (1218559)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.71 % (1218559)Time elapsed: 0.006 s
% 0.64/0.71 % (1218559)Peak memory usage: 88 MB
% 0.64/0.71 % (1218559)Instructions burned: 10 (million)
% 0.64/0.71 % (1218560)Refutation found. Thanks to Tanya!
% 0.64/0.71 % SZS status Theorem for theBenchmark
% 0.64/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.80 % (1218560)------------------------------
% 0.18/0.80 % (1218560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.80 % (1218560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.80 % (1218560)CaDiCaL version: 2.1.3
% 0.18/0.80 % (1218560)Termination reason: Refutation
% 0.18/0.80 % (1218560)Time elapsed: 0.004 s
% 0.18/0.80 % (1218560)Peak memory usage: 90 MB
% 0.18/0.80 % (1218560)Instructions burned: 8 (million)
% 0.18/0.80 % (1218560)------------------------------
% 0.18/0.80 % (1218560)------------------------------
% 0.18/0.80 % (1218550)Success in time 0.296 s
% 0.18/0.80 % Vampire exiting
%------------------------------------------------------------------------------