%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 09:40:05 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 39
% Syntax : Number of formulae : 315 ( 18 unt; 34 def)
% Number of atoms : 1268 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1680 ( 727 ~; 776 |; 106 &)
% ( 34 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 43 ( 42 usr; 35 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 235 ( 0 sgn 204 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) )
=> ? [X3] :
( program(X3)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ( program(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) )
=> ! [X1,X2] :
( ( ( program(X1)
& halts2(X1,X2) )
=> ( halts3(X0,X1,X2)
& outputs(X0,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X2) )
=> ( halts3(X0,X1,X2)
& outputs(X0,bad) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
( ? [X0] :
( program(X0)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ( halts3(X0,X1,X1)
& outputs(X0,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts3(X0,X1,X1)
& outputs(X0,bad) ) ) ) )
=> ? [X2] :
( program(X2)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ( halts2(X2,X1)
& outputs(X2,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts2(X2,X1)
& outputs(X2,bad) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
( ? [X0] :
( program(X0)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ( halts2(X0,X1)
& outputs(X0,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts2(X0,X1)
& outputs(X0,bad) ) ) ) )
=> ? [X2] :
( program(X2)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ~ halts2(X2,X1) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts2(X2,X1)
& outputs(X2,bad) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f5,conjecture,
~ ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f6,negated_conjecture,
~ ~ ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
( ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) )
=> ? [X3] :
( program(X3)
& ! [X4] :
( program(X4)
=> ! [X5] : decides(X3,X4,X5) ) ) ),
inference(rectify,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ( program(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) )
=> ! [X3,X4] :
( ( ( program(X3)
& halts2(X3,X4) )
=> ( halts3(X0,X3,X4)
& outputs(X0,good) ) )
& ( ( program(X3)
& ~ halts2(X3,X4) )
=> ( halts3(X0,X3,X4)
& outputs(X0,bad) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f9,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ( halts3(X0,X1,X1)
& outputs(X0,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts3(X0,X1,X1)
& outputs(X0,bad) ) ) ) )
=> ? [X2] :
( program(X2)
& ! [X3] :
( ( ( program(X3)
& halts2(X3,X3) )
=> ( halts2(X2,X3)
& outputs(X2,good) ) )
& ( ( program(X3)
& ~ halts2(X3,X3) )
=> ( halts2(X2,X3)
& outputs(X2,bad) ) ) ) ) ),
inference(rectify,[],[f3]) ).
fof(f10,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( ( ( program(X1)
& halts2(X1,X1) )
=> ( halts2(X0,X1)
& outputs(X0,good) ) )
& ( ( program(X1)
& ~ halts2(X1,X1) )
=> ( halts2(X0,X1)
& outputs(X0,bad) ) ) ) )
=> ? [X2] :
( program(X2)
& ! [X3] :
( ( ( program(X3)
& halts2(X3,X3) )
=> ~ halts2(X2,X3) )
& ( ( program(X3)
& ~ halts2(X3,X3) )
=> ( halts2(X2,X3)
& outputs(X2,bad) ) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f11,plain,
? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
inference(flattening,[],[f6]) ).
fof(f12,plain,
( ? [X3] :
( program(X3)
& ! [X4] :
( ! [X5] : decides(X3,X4,X5)
| ~ program(X4) ) )
| ! [X0] :
( ~ algorithm(X0)
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0] :
( ! [X3,X4] :
( ( ( halts3(X0,X3,X4)
& outputs(X0,good) )
| ~ program(X3)
| ~ halts2(X3,X4) )
& ( ( halts3(X0,X3,X4)
& outputs(X0,bad) )
| ~ program(X3)
| halts2(X3,X4) ) )
| ~ program(X0)
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0] :
( ! [X3,X4] :
( ( ( halts3(X0,X3,X4)
& outputs(X0,good) )
| ~ program(X3)
| ~ halts2(X3,X4) )
& ( ( halts3(X0,X3,X4)
& outputs(X0,bad) )
| ~ program(X3)
| halts2(X3,X4) ) )
| ~ program(X0)
| ? [X1] :
( ? [X2] : ~ decides(X0,X1,X2)
& program(X1) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( ( ( halts2(X2,X3)
& outputs(X2,good) )
| ~ program(X3)
| ~ halts2(X3,X3) )
& ( ( halts2(X2,X3)
& outputs(X2,bad) )
| ~ program(X3)
| halts2(X3,X3) ) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ( ( ~ halts3(X0,X1,X1)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X1) )
| ( ( ~ halts3(X0,X1,X1)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X1) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( ( ( halts2(X2,X3)
& outputs(X2,good) )
| ~ program(X3)
| ~ halts2(X3,X3) )
& ( ( halts2(X2,X3)
& outputs(X2,bad) )
| ~ program(X3)
| halts2(X3,X3) ) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ( ( ~ halts3(X0,X1,X1)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X1) )
| ( ( ~ halts3(X0,X1,X1)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X1) ) ) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( ( ~ halts2(X2,X3)
| ~ program(X3)
| ~ halts2(X3,X3) )
& ( ( halts2(X2,X3)
& outputs(X2,bad) )
| ~ program(X3)
| halts2(X3,X3) ) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ( ( ~ halts2(X0,X1)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X1) )
| ( ( ~ halts2(X0,X1)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X1) ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f18,plain,
( ? [X2] :
( program(X2)
& ! [X3] :
( ( ~ halts2(X2,X3)
| ~ program(X3)
| ~ halts2(X3,X3) )
& ( ( halts2(X2,X3)
& outputs(X2,bad) )
| ~ program(X3)
| halts2(X3,X3) ) ) )
| ! [X0] :
( ~ program(X0)
| ? [X1] :
( ( ( ~ halts2(X0,X1)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X1) )
| ( ( ~ halts2(X0,X1)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X1) ) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0] :
( algorithm(X0)
& ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0,X4,X5] :
( ~ decides(X0,sK1(X0),sK2(X0))
| ~ algorithm(X0)
| ~ program(X4)
| decides(sK0,X4,X5) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X4,X5] :
( program(sK1(X0))
| ~ algorithm(X0)
| ~ program(X4)
| decides(sK0,X4,X5) ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
! [X0] :
( program(sK1(X0))
| ~ algorithm(X0)
| program(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X0] :
( ~ decides(X0,sK1(X0),sK2(X0))
| ~ algorithm(X0)
| program(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X3,X0,X4] :
( ~ decides(X0,sK3(X0),sK4(X0))
| ~ program(X0)
| ~ halts2(X3,X4)
| ~ program(X3)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X3,X0,X4] :
( ~ decides(X0,sK3(X0),sK4(X0))
| ~ program(X0)
| ~ halts2(X3,X4)
| ~ program(X3)
| halts3(X0,X3,X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X3,X0,X4] :
( program(sK3(X0))
| ~ program(X0)
| ~ halts2(X3,X4)
| ~ program(X3)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X3,X0,X4] :
( halts3(X0,X3,X4)
| ~ program(X0)
| ~ halts2(X3,X4)
| ~ program(X3)
| program(sK3(X0)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X3,X0,X4] :
( ~ decides(X0,sK3(X0),sK4(X0))
| ~ program(X0)
| halts2(X3,X4)
| ~ program(X3)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X3,X0,X4] :
( ~ decides(X0,sK3(X0),sK4(X0))
| ~ program(X0)
| halts2(X3,X4)
| ~ program(X3)
| halts3(X0,X3,X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X3,X0,X4] :
( program(sK3(X0))
| ~ program(X0)
| halts2(X3,X4)
| ~ program(X3)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X3,X0,X4] :
( program(sK3(X0))
| ~ program(X0)
| halts2(X3,X4)
| ~ program(X3)
| halts3(X0,X3,X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0,X1] :
( ~ halts3(X0,X1,X1)
| ~ outputs(X0,good)
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X3,X0] :
( program(sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| outputs(sK5,good) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X3,X0] :
( program(sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| halts2(sK5,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK6(X0),sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| outputs(sK5,good) ),
inference(cnf_transformation,[],[f16]) ).
fof(f38,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK6(X0),sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| halts2(sK5,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X3,X0] :
( program(sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| outputs(sK5,bad) ),
inference(cnf_transformation,[],[f16]) ).
fof(f42,plain,
! [X3,X0] :
( program(sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| halts2(sK5,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK6(X0),sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| outputs(sK5,bad) ),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK6(X0),sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| halts2(sK5,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sP7(X1,X0)
| halts2(X1,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP7(X1,X0)
| program(X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f47,plain,
! [X0] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK6(X0),sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| program(sK5) ),
inference(cnf_transformation,[],[f16]) ).
fof(f49,plain,
! [X0] :
( program(sK6(X0))
| sP7(sK6(X0),X0)
| ~ program(X0)
| program(sK5) ),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sP10(X1,X0)
| ~ halts2(X0,X1)
| ~ outputs(X0,good) ),
inference(cnf_transformation,[],[f18]) ).
fof(f52,plain,
! [X3,X0] :
( ~ halts2(sK9(X0),sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f54,plain,
! [X3,X0] :
( program(sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f56,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| halts2(X3,X3)
| ~ program(X3)
| halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sP10(X1,X0)
| program(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0] :
( ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| program(sK8) ),
inference(cnf_transformation,[],[f18]) ).
fof(f60,plain,
! [X3,X0] :
( ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f61,plain,
! [X3,X0] :
( program(sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f62,plain,
! [X3,X0] :
( ~ halts2(sK9(X0),sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(sK8,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f63,plain,
! [X0] :
( ~ halts2(sK9(X0),sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| program(sK8) ),
inference(cnf_transformation,[],[f18]) ).
fof(f64,plain,
! [X0] :
( program(sK9(X0))
| sP10(sK9(X0),X0)
| ~ program(X0)
| program(sK8) ),
inference(cnf_transformation,[],[f18]) ).
fof(f65,plain,
! [X2,X1] :
( decides(sK11,X1,X2)
| ~ program(X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
algorithm(sK11),
inference(cnf_transformation,[],[f19]) ).
fof(f72,definition,
( spl12_2
<=> ! [X3] :
( halts2(X3,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( halts2(X3,X3)
| ~ program(X3) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl12_3
<=> ! [X0] :
( ~ halts2(sK9(X0),sK9(X0))
| ~ program(X0)
| sP10(sK9(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f76,plain,
( ! [X0] :
( sP10(sK9(X0),X0)
| ~ program(X0)
| ~ halts2(sK9(X0),sK9(X0)) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl12_4
<=> ! [X3] :
( halts2(X3,X3)
| halts2(sK8,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X3] :
( halts2(X3,X3)
| halts2(sK8,X3)
| ~ program(X3) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( spl12_4
| spl12_3 ),
inference(avatar_split_clause,[],[f52,f75,f79]) ).
fof(f83,definition,
( spl12_5
<=> ! [X0] :
( program(sK9(X0))
| ~ program(X0)
| sP10(sK9(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f84,plain,
( ! [X0] :
( program(sK9(X0))
| ~ program(X0)
| sP10(sK9(X0),X0) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl12_4
| spl12_5 ),
inference(avatar_split_clause,[],[f54,f83,f79]) ).
fof(f88,definition,
( spl12_6
<=> ! [X0] :
( ~ outputs(X0,bad)
| ~ program(X0)
| sP10(sK9(X0),X0)
| ~ halts2(X0,sK9(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f89,plain,
( ! [X0] :
( sP10(sK9(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0)) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl12_4
| spl12_6 ),
inference(avatar_split_clause,[],[f56,f88,f79]) ).
fof(f93,definition,
( spl12_7
<=> program(sK8) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f95,plain,
( program(sK8)
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl12_7
| spl12_6 ),
inference(avatar_split_clause,[],[f59,f88,f93]) ).
fof(f98,definition,
( spl12_8
<=> ! [X3] :
( ~ halts2(X3,X3)
| ~ halts2(sK8,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f99,plain,
( ! [X3] :
( ~ halts2(X3,X3)
| ~ halts2(sK8,X3)
| ~ program(X3) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( spl12_8
| spl12_6 ),
inference(avatar_split_clause,[],[f60,f88,f98]) ).
fof(f101,plain,
! [X3,X0] :
( program(sK9(X0))
| ~ program(X0)
| ~ halts2(X3,X3)
| ~ program(X3)
| ~ halts2(sK8,X3) ),
inference(forward_subsumption_resolution,[],[f61,f58]) ).
fof(f102,plain,
( spl12_8
| spl12_3 ),
inference(avatar_split_clause,[],[f62,f75,f98]) ).
fof(f103,plain,
( spl12_7
| spl12_3 ),
inference(avatar_split_clause,[],[f63,f75,f93]) ).
fof(f104,plain,
! [X0] :
( program(sK9(X0))
| ~ program(X0)
| program(sK8) ),
inference(forward_subsumption_resolution,[],[f64,f58]) ).
fof(f106,definition,
( spl12_9
<=> outputs(sK5,good) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f108,plain,
( outputs(sK5,good)
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl12_10
<=> ! [X3] :
( ~ halts2(X3,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f111,plain,
( ! [X3] :
( ~ halts2(X3,X3)
| ~ program(X3) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f117,definition,
( spl12_12
<=> ! [X3] :
( ~ halts2(X3,X3)
| halts2(sK5,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f118,plain,
( ! [X3] :
( ~ halts2(X3,X3)
| halts2(sK5,X3)
| ~ program(X3) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f121,definition,
( spl12_13
<=> ! [X0] :
( program(sK6(X0))
| ~ program(X0)
| sP7(sK6(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f122,plain,
( ! [X0] :
( program(sK6(X0))
| ~ program(X0)
| sP7(sK6(X0),X0) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( spl12_9
| spl12_10
| spl12_13 ),
inference(avatar_split_clause,[],[f35,f121,f110,f106]) ).
fof(f124,plain,
( spl12_12
| spl12_13 ),
inference(avatar_split_clause,[],[f36,f121,f117]) ).
fof(f126,definition,
( spl12_14
<=> ! [X0] :
( ~ outputs(X0,bad)
| ~ program(X0)
| sP7(sK6(X0),X0)
| ~ halts3(X0,sK6(X0),sK6(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
fof(f127,plain,
( ! [X0] :
( ~ halts3(X0,sK6(X0),sK6(X0))
| ~ program(X0)
| sP7(sK6(X0),X0)
| ~ outputs(X0,bad) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( spl12_9
| spl12_10
| spl12_14 ),
inference(avatar_split_clause,[],[f37,f126,f110,f106]) ).
fof(f129,plain,
( spl12_12
| spl12_14 ),
inference(avatar_split_clause,[],[f38,f126,f117]) ).
fof(f131,definition,
( spl12_15
<=> outputs(sK5,bad) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f133,plain,
( outputs(sK5,bad)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f136,definition,
( spl12_16
<=> ! [X3] :
( halts2(X3,X3)
| halts2(sK5,X3)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
fof(f137,plain,
( ! [X3] :
( halts2(X3,X3)
| halts2(sK5,X3)
| ~ program(X3) )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl12_15
| spl12_2
| spl12_13 ),
inference(avatar_split_clause,[],[f41,f121,f72,f131]) ).
fof(f140,plain,
( spl12_16
| spl12_13 ),
inference(avatar_split_clause,[],[f42,f121,f136]) ).
fof(f141,plain,
( spl12_15
| spl12_2
| spl12_14 ),
inference(avatar_split_clause,[],[f43,f126,f72,f131]) ).
fof(f142,plain,
( spl12_16
| spl12_14 ),
inference(avatar_split_clause,[],[f44,f126,f136]) ).
fof(f144,definition,
( spl12_17
<=> program(sK5) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
fof(f146,plain,
( program(sK5)
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl12_17
| spl12_14 ),
inference(avatar_split_clause,[],[f47,f126,f144]) ).
fof(f149,plain,
! [X0] :
( program(sK6(X0))
| ~ program(X0)
| program(sK5) ),
inference(forward_subsumption_resolution,[],[f49,f46]) ).
fof(f151,definition,
( spl12_18
<=> ! [X4,X3] :
( ~ halts2(X3,X4)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
fof(f152,plain,
( ! [X3,X4] :
( ~ halts2(X3,X4)
| ~ program(X3) )
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,definition,
( spl12_19
<=> ! [X0] :
( ~ decides(X0,sK3(X0),sK4(X0))
| outputs(X0,good)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
fof(f155,plain,
( ! [X0] :
( ~ decides(X0,sK3(X0),sK4(X0))
| outputs(X0,good)
| ~ program(X0) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f156,plain,
( spl12_18
| spl12_19 ),
inference(avatar_split_clause,[],[f24,f154,f151]) ).
fof(f158,definition,
( spl12_20
<=> ! [X0] :
( program(sK3(X0))
| outputs(X0,good)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
fof(f159,plain,
( ! [X0] :
( outputs(X0,good)
| program(sK3(X0))
| ~ program(X0) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( spl12_18
| spl12_20 ),
inference(avatar_split_clause,[],[f26,f158,f151]) ).
fof(f162,definition,
( spl12_21
<=> ! [X4,X3] :
( halts2(X3,X4)
| ~ program(X3) ) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
fof(f163,plain,
( ! [X3,X4] :
( halts2(X3,X4)
| ~ program(X3) )
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,definition,
( spl12_22
<=> ! [X0] :
( ~ decides(X0,sK3(X0),sK4(X0))
| outputs(X0,bad)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition]) ).
fof(f166,plain,
( ! [X0] :
( ~ decides(X0,sK3(X0),sK4(X0))
| outputs(X0,bad)
| ~ program(X0) )
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f167,plain,
( spl12_21
| spl12_22 ),
inference(avatar_split_clause,[],[f28,f165,f162]) ).
fof(f168,plain,
! [X3,X0,X4] :
( ~ decides(X0,sK3(X0),sK4(X0))
| ~ program(X0)
| ~ program(X3)
| halts3(X0,X3,X4) ),
inference(forward_subsumption_resolution,[],[f29,f25]) ).
fof(f170,definition,
( spl12_23
<=> ! [X0] :
( program(sK3(X0))
| outputs(X0,bad)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
fof(f171,plain,
( ! [X0] :
( outputs(X0,bad)
| program(sK3(X0))
| ~ program(X0) )
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( spl12_21
| spl12_23 ),
inference(avatar_split_clause,[],[f30,f170,f162]) ).
fof(f173,plain,
! [X3,X0,X4] :
( halts3(X0,X3,X4)
| ~ program(X0)
| ~ program(X3)
| program(sK3(X0)) ),
inference(forward_subsumption_resolution,[],[f31,f27]) ).
fof(f175,definition,
( spl12_24
<=> ! [X4,X5] :
( ~ program(X4)
| decides(sK0,X4,X5) ) ),
introduced(definition,[new_symbols(definition,[spl12_24])],[avatar_definition]) ).
fof(f176,plain,
( ! [X4,X5] :
( decides(sK0,X4,X5)
| ~ program(X4) )
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,definition,
( spl12_25
<=> ! [X0] :
( ~ decides(X0,sK1(X0),sK2(X0))
| ~ algorithm(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_25])],[avatar_definition]) ).
fof(f179,plain,
( ! [X0] :
( ~ algorithm(X0)
| ~ decides(X0,sK1(X0),sK2(X0)) )
| ~ spl12_25 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
( spl12_24
| spl12_25 ),
inference(avatar_split_clause,[],[f20,f178,f175]) ).
fof(f182,definition,
( spl12_26
<=> ! [X0] :
( program(sK1(X0))
| ~ algorithm(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_26])],[avatar_definition]) ).
fof(f183,plain,
( ! [X0] :
( ~ algorithm(X0)
| program(sK1(X0)) )
| ~ spl12_26 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f184,plain,
( spl12_24
| spl12_26 ),
inference(avatar_split_clause,[],[f21,f182,f175]) ).
fof(f186,definition,
( spl12_27
<=> program(sK0) ),
introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition]) ).
fof(f188,plain,
( program(sK0)
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f189,plain,
( spl12_27
| spl12_26 ),
inference(avatar_split_clause,[],[f22,f182,f186]) ).
fof(f190,plain,
( spl12_27
| spl12_25 ),
inference(avatar_split_clause,[],[f23,f178,f186]) ).
fof(f192,definition,
( spl12_28
<=> ! [X0] :
( program(sK9(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_28])],[avatar_definition]) ).
fof(f193,plain,
( ! [X0] :
( program(sK9(X0))
| ~ program(X0) )
| ~ spl12_28 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f194,plain,
( spl12_8
| spl12_28 ),
inference(avatar_split_clause,[],[f101,f192,f98]) ).
fof(f195,plain,
( spl12_7
| spl12_28 ),
inference(avatar_split_clause,[],[f104,f192,f93]) ).
fof(f197,definition,
( spl12_29
<=> ! [X0] :
( program(sK6(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_29])],[avatar_definition]) ).
fof(f198,plain,
( ! [X0] :
( program(sK6(X0))
| ~ program(X0) )
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( spl12_17
| spl12_29 ),
inference(avatar_split_clause,[],[f149,f197,f144]) ).
fof(f201,plain,
( ! [X0] :
( program(sK6(X0))
| ~ program(X0) )
| ~ spl12_13 ),
inference(forward_subsumption_resolution,[],[f122,f46]) ).
fof(f202,plain,
( ! [X3] : ~ program(X3)
| ~ spl12_18
| ~ spl12_21 ),
inference(forward_subsumption_resolution,[],[f163,f152]) ).
fof(f203,plain,
( spl12_29
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f201,f121,f197]) ).
fof(f209,plain,
( program(sK1(sK11))
| ~ spl12_26 ),
inference(resolution,[],[f183,f66]) ).
fof(f225,plain,
( ! [X3] :
( halts2(sK5,X3)
| ~ program(X3) )
| ~ spl12_12
| ~ spl12_16 ),
inference(forward_subsumption_resolution,[],[f137,f118]) ).
fof(f226,plain,
( halts2(sK8,sK8)
| ~ program(sK8)
| ~ spl12_4 ),
inference(factoring,[],[f80]) ).
fof(f227,plain,
( halts2(sK8,sK8)
| ~ spl12_4
| ~ spl12_7 ),
inference(forward_subsumption_resolution,[],[f226,f95]) ).
fof(f229,plain,
( ~ halts2(sK8,sK8)
| ~ program(sK8)
| ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(resolution,[],[f99,f227]) ).
fof(f235,plain,
( ~ program(sK8)
| ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(forward_subsumption_resolution,[],[f229,f227]) ).
fof(f238,plain,
( $false
| ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(forward_subsumption_resolution,[],[f235,f95]) ).
fof(f239,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f243,plain,
( ~ decides(sK11,sK1(sK11),sK2(sK11))
| ~ spl12_25 ),
inference(resolution,[],[f179,f66]) ).
fof(f244,plain,
( ~ program(sK1(sK11))
| ~ spl12_25 ),
inference(resolution,[],[f243,f65]) ).
fof(f245,plain,
( $false
| ~ spl12_25
| ~ spl12_26 ),
inference(forward_subsumption_resolution,[],[f244,f209]) ).
fof(f246,plain,
( ~ spl12_25
| ~ spl12_26 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f247,plain,
( ! [X0] :
( ~ outputs(X0,good)
| ~ halts2(sK9(X0),sK9(X0))
| ~ halts2(X0,sK9(X0))
| ~ program(X0) )
| ~ spl12_3 ),
inference(resolution,[],[f76,f50]) ).
fof(f253,plain,
( outputs(sK0,good)
| ~ program(sK0)
| ~ program(sK3(sK0))
| ~ spl12_19
| ~ spl12_24 ),
inference(resolution,[],[f155,f176]) ).
fof(f254,plain,
( outputs(sK0,good)
| ~ program(sK0)
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24 ),
inference(forward_subsumption_resolution,[],[f253,f159]) ).
fof(f256,plain,
( outputs(sK0,good)
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f254,f188]) ).
fof(f267,plain,
( outputs(sK0,bad)
| ~ program(sK0)
| ~ program(sK3(sK0))
| ~ spl12_22
| ~ spl12_24 ),
inference(resolution,[],[f166,f176]) ).
fof(f268,plain,
( outputs(sK0,bad)
| ~ program(sK0)
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24 ),
inference(forward_subsumption_resolution,[],[f267,f171]) ).
fof(f270,plain,
( outputs(sK0,bad)
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f268,f188]) ).
fof(f274,plain,
( ! [X0] :
( ~ program(X0)
| ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0))
| ~ halts2(X0,sK9(X0))
| ~ outputs(X0,good) )
| ~ spl12_6 ),
inference(resolution,[],[f89,f50]) ).
fof(f277,plain,
( ! [X0] :
( ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ halts2(X0,sK9(X0))
| ~ program(X0) )
| ~ spl12_6 ),
inference(duplicate_literal_removal,[],[f274]) ).
fof(f285,plain,
( ! [X0,X1] :
( ~ program(sK0)
| ~ program(X0)
| halts3(sK0,X0,X1)
| ~ program(sK3(sK0)) )
| ~ spl12_24 ),
inference(resolution,[],[f168,f176]) ).
fof(f286,plain,
( ! [X0,X1] :
( ~ program(sK0)
| ~ program(X0)
| halts3(sK0,X0,X1) )
| ~ spl12_24 ),
inference(forward_subsumption_resolution,[],[f285,f173]) ).
fof(f288,plain,
( ! [X0,X1] :
( halts3(sK0,X0,X1)
| ~ program(X0) )
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f286,f188]) ).
fof(f289,plain,
( ! [X0] :
( ~ program(X0)
| ~ outputs(sK0,good)
| ~ sP7(X0,sK0) )
| ~ spl12_24
| ~ spl12_27 ),
inference(resolution,[],[f288,f32]) ).
fof(f290,plain,
( ! [X0] :
( ~ outputs(sK0,good)
| ~ sP7(X0,sK0) )
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f289,f46]) ).
fof(f291,plain,
( ! [X0] : ~ sP7(X0,sK0)
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f290,f256]) ).
fof(f294,plain,
( ~ program(sK0)
| sP7(sK6(sK0),sK0)
| ~ outputs(sK0,bad)
| ~ program(sK6(sK0))
| ~ spl12_14
| ~ spl12_24
| ~ spl12_27 ),
inference(resolution,[],[f127,f288]) ).
fof(f297,plain,
( sP7(sK6(sK0),sK0)
| ~ outputs(sK0,bad)
| ~ program(sK6(sK0))
| ~ spl12_14
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f294,f188]) ).
fof(f299,plain,
( ~ outputs(sK0,bad)
| ~ program(sK6(sK0))
| ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f297,f291]) ).
fof(f301,plain,
( ~ program(sK6(sK0))
| ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f299,f270]) ).
fof(f311,plain,
( ~ outputs(sK5,bad)
| ~ halts2(sK5,sK9(sK5))
| ~ program(sK5)
| ~ spl12_6
| ~ spl12_9 ),
inference(resolution,[],[f277,f108]) ).
fof(f313,plain,
( ~ halts2(sK5,sK9(sK5))
| ~ program(sK5)
| ~ spl12_6
| ~ spl12_9
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f311,f133]) ).
fof(f316,plain,
( ~ halts2(sK5,sK9(sK5))
| ~ spl12_6
| ~ spl12_9
| ~ spl12_15
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f313,f146]) ).
fof(f318,plain,
( ~ program(sK9(sK5))
| ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17 ),
inference(resolution,[],[f316,f225]) ).
fof(f320,plain,
( ~ halts2(sK9(sK0),sK9(sK0))
| ~ halts2(sK0,sK9(sK0))
| ~ program(sK0)
| ~ spl12_3
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(resolution,[],[f247,f256]) ).
fof(f321,plain,
( ~ halts2(sK9(sK5),sK9(sK5))
| ~ halts2(sK5,sK9(sK5))
| ~ program(sK5)
| ~ spl12_3
| ~ spl12_9 ),
inference(resolution,[],[f247,f108]) ).
fof(f323,plain,
( ~ program(sK5)
| ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28 ),
inference(resolution,[],[f318,f193]) ).
fof(f324,plain,
( $false
| ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28 ),
inference(forward_subsumption_resolution,[],[f323,f146]) ).
fof(f325,plain,
( ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f326,plain,
( ~ halts2(sK9(sK5),sK9(sK5))
| ~ halts2(sK5,sK9(sK5))
| ~ spl12_3
| ~ spl12_9
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f321,f146]) ).
fof(f328,definition,
( spl12_32
<=> halts2(sK5,sK9(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_32])],[avatar_definition]) ).
fof(f330,plain,
( ~ halts2(sK5,sK9(sK5))
| spl12_32 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f332,definition,
( spl12_33
<=> halts2(sK9(sK5),sK9(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_33])],[avatar_definition]) ).
fof(f334,plain,
( ~ halts2(sK9(sK5),sK9(sK5))
| spl12_33 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f356,plain,
( ~ program(sK9(sK5))
| ~ spl12_12
| ~ spl12_16
| spl12_32 ),
inference(resolution,[],[f330,f225]) ).
fof(f357,plain,
( ~ program(sK5)
| ~ spl12_12
| ~ spl12_16
| ~ spl12_28
| spl12_32 ),
inference(resolution,[],[f356,f193]) ).
fof(f358,plain,
( $false
| ~ spl12_12
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28
| spl12_32 ),
inference(forward_subsumption_resolution,[],[f357,f146]) ).
fof(f359,plain,
( ~ spl12_12
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28
| spl12_32 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f360,plain,
( ~ program(sK9(sK5))
| ~ spl12_2
| spl12_33 ),
inference(resolution,[],[f334,f73]) ).
fof(f363,definition,
( spl12_36
<=> program(sK9(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_36])],[avatar_definition]) ).
fof(f364,plain,
( program(sK9(sK5))
| ~ spl12_36 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( ~ program(sK9(sK5))
| spl12_36 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f371,plain,
( ~ spl12_36
| ~ spl12_2
| spl12_33 ),
inference(avatar_split_clause,[],[f360,f332,f72,f363]) ).
fof(f375,plain,
( ~ program(sK5)
| ~ spl12_28
| spl12_36 ),
inference(resolution,[],[f365,f193]) ).
fof(f376,plain,
( $false
| ~ spl12_17
| ~ spl12_28
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f375,f146]) ).
fof(f377,plain,
( ~ spl12_17
| ~ spl12_28
| spl12_36 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f378,plain,
( ~ program(sK0)
| ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27
| ~ spl12_29 ),
inference(resolution,[],[f198,f301]) ).
fof(f379,plain,
( $false
| ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27
| ~ spl12_29 ),
inference(forward_subsumption_resolution,[],[f378,f188]) ).
fof(f380,plain,
( ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27
| ~ spl12_29 ),
inference(avatar_contradiction_clause,[],[f379]) ).
fof(f389,plain,
( sP7(sK6(sK0),sK0)
| ~ program(sK6(sK0))
| ~ spl12_14
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f297,f270]) ).
fof(f391,definition,
( spl12_40
<=> program(sK6(sK0)) ),
introduced(definition,[new_symbols(definition,[spl12_40])],[avatar_definition]) ).
fof(f392,plain,
( program(sK6(sK0))
| ~ spl12_40 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f393,plain,
( ~ program(sK6(sK0))
| spl12_40 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f395,definition,
( spl12_41
<=> sP7(sK6(sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl12_41])],[avatar_definition]) ).
fof(f397,plain,
( sP7(sK6(sK0),sK0)
| ~ spl12_41 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f423,plain,
( ~ halts2(sK9(sK0),sK9(sK0))
| ~ halts2(sK0,sK9(sK0))
| ~ spl12_3
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f320,f188]) ).
fof(f429,definition,
( spl12_42
<=> halts2(sK0,sK9(sK0)) ),
introduced(definition,[new_symbols(definition,[spl12_42])],[avatar_definition]) ).
fof(f431,plain,
( ~ halts2(sK0,sK9(sK0))
| spl12_42 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f438,definition,
( spl12_44
<=> halts2(sK9(sK0),sK9(sK0)) ),
introduced(definition,[new_symbols(definition,[spl12_44])],[avatar_definition]) ).
fof(f440,plain,
( ~ halts2(sK9(sK0),sK9(sK0))
| spl12_44 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f441,plain,
( ~ spl12_42
| ~ spl12_44
| ~ spl12_3
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f423,f186,f175,f158,f154,f75,f438,f429]) ).
fof(f457,plain,
( ~ program(sK0)
| ~ spl12_29
| spl12_40 ),
inference(resolution,[],[f393,f198]) ).
fof(f458,plain,
( $false
| ~ spl12_27
| ~ spl12_29
| spl12_40 ),
inference(forward_subsumption_resolution,[],[f457,f188]) ).
fof(f459,plain,
( ~ spl12_27
| ~ spl12_29
| spl12_40 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f473,plain,
( ~ program(sK0)
| ~ spl12_21
| spl12_42 ),
inference(resolution,[],[f431,f163]) ).
fof(f474,plain,
( $false
| ~ spl12_21
| ~ spl12_27
| spl12_42 ),
inference(forward_subsumption_resolution,[],[f473,f188]) ).
fof(f475,plain,
( ~ spl12_21
| ~ spl12_27
| spl12_42 ),
inference(avatar_contradiction_clause,[],[f474]) ).
fof(f478,plain,
( ~ program(sK9(sK0))
| ~ spl12_21
| spl12_44 ),
inference(resolution,[],[f440,f163]) ).
fof(f479,plain,
( ~ program(sK0)
| ~ spl12_21
| ~ spl12_28
| spl12_44 ),
inference(resolution,[],[f478,f193]) ).
fof(f480,plain,
( $false
| ~ spl12_21
| ~ spl12_27
| ~ spl12_28
| spl12_44 ),
inference(forward_subsumption_resolution,[],[f479,f188]) ).
fof(f481,plain,
( ~ spl12_21
| ~ spl12_27
| ~ spl12_28
| spl12_44 ),
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f508,plain,
( ~ program(sK5)
| ~ program(sK5)
| ~ spl12_10
| ~ spl12_12
| ~ spl12_16 ),
inference(resolution,[],[f111,f225]) ).
fof(f509,plain,
( ~ program(sK5)
| ~ spl12_10
| ~ spl12_12
| ~ spl12_16 ),
inference(duplicate_literal_removal,[],[f508]) ).
fof(f511,plain,
( $false
| ~ spl12_10
| ~ spl12_12
| ~ spl12_16
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f509,f146]) ).
fof(f512,plain,
( ~ spl12_10
| ~ spl12_12
| ~ spl12_16
| ~ spl12_17 ),
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f516,plain,
( $false
| ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f318,f364]) ).
fof(f517,plain,
( ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_36 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f519,plain,
( ~ spl12_32
| ~ spl12_33
| ~ spl12_3
| ~ spl12_9
| ~ spl12_17 ),
inference(avatar_split_clause,[],[f326,f144,f106,f75,f332,f328]) ).
fof(f523,plain,
( ! [X0] :
( program(sK9(X0))
| ~ program(X0) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f84,f58]) ).
fof(f525,plain,
( spl12_28
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f523,f83,f192]) ).
fof(f527,plain,
( ~ spl12_40
| spl12_41
| ~ spl12_14
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f389,f186,f175,f170,f165,f126,f395,f391]) ).
fof(f565,plain,
( halts2(sK6(sK0),sK6(sK0))
| ~ spl12_41 ),
inference(resolution,[],[f397,f45]) ).
fof(f581,plain,
( ~ program(sK6(sK0))
| ~ spl12_18
| ~ spl12_41 ),
inference(resolution,[],[f565,f152]) ).
fof(f584,plain,
( $false
| ~ spl12_18
| ~ spl12_40
| ~ spl12_41 ),
inference(forward_subsumption_resolution,[],[f581,f392]) ).
fof(f585,plain,
( ~ spl12_18
| ~ spl12_40
| ~ spl12_41 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f587,plain,
( $false
| ~ spl12_18
| ~ spl12_21
| ~ spl12_27 ),
inference(resolution,[],[f202,f188]) ).
fof(f594,plain,
( ~ spl12_18
| ~ spl12_21
| ~ spl12_27 ),
inference(avatar_contradiction_clause,[],[f587]) ).
cnf(s2,plain,
( spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s4,plain,
( spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f86]) ).
cnf(s6,plain,
( spl12_4
| spl12_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s7,plain,
( spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f96]) ).
cnf(s8,plain,
( spl12_6
| spl12_8 ),
inference(sat_conversion,[],[f100]) ).
cnf(s9,plain,
( spl12_3
| spl12_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s10,plain,
( spl12_3
| spl12_7 ),
inference(sat_conversion,[],[f103]) ).
cnf(s13,plain,
( spl12_9
| spl12_10
| spl12_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s14,plain,
( spl12_12
| spl12_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s15,plain,
( spl12_9
| spl12_10
| spl12_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s16,plain,
( spl12_12
| spl12_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s19,plain,
( spl12_2
| spl12_13
| spl12_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s20,plain,
( spl12_13
| spl12_16 ),
inference(sat_conversion,[],[f140]) ).
cnf(s21,plain,
( spl12_2
| spl12_14
| spl12_15 ),
inference(sat_conversion,[],[f141]) ).
cnf(s22,plain,
( spl12_14
| spl12_16 ),
inference(sat_conversion,[],[f142]) ).
cnf(s23,plain,
( spl12_14
| spl12_17 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl12_18
| spl12_19 ),
inference(sat_conversion,[],[f156]) ).
cnf(s26,plain,
( spl12_18
| spl12_20 ),
inference(sat_conversion,[],[f160]) ).
cnf(s27,plain,
( spl12_21
| spl12_22 ),
inference(sat_conversion,[],[f167]) ).
cnf(s28,plain,
( spl12_21
| spl12_23 ),
inference(sat_conversion,[],[f172]) ).
cnf(s29,plain,
( spl12_24
| spl12_25 ),
inference(sat_conversion,[],[f180]) ).
cnf(s30,plain,
( spl12_24
| spl12_26 ),
inference(sat_conversion,[],[f184]) ).
cnf(s31,plain,
( spl12_26
| spl12_27 ),
inference(sat_conversion,[],[f189]) ).
cnf(s32,plain,
( spl12_25
| spl12_27 ),
inference(sat_conversion,[],[f190]) ).
cnf(s33,plain,
( spl12_8
| spl12_28 ),
inference(sat_conversion,[],[f194]) ).
cnf(s34,plain,
( spl12_7
| spl12_28 ),
inference(sat_conversion,[],[f195]) ).
cnf(s35,plain,
( spl12_17
| spl12_29 ),
inference(sat_conversion,[],[f199]) ).
cnf(s36,plain,
( ~ spl12_13
| spl12_29 ),
inference(sat_conversion,[],[f203]) ).
cnf(s44,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(sat_conversion,[],[f239]) ).
cnf(s45,plain,
( ~ spl12_25
| ~ spl12_26 ),
inference(sat_conversion,[],[f246]) ).
cnf(s47,plain,
( ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28 ),
inference(sat_conversion,[],[f325]) ).
cnf(s50,plain,
( ~ spl12_12
| ~ spl12_16
| ~ spl12_17
| ~ spl12_28
| spl12_32 ),
inference(sat_conversion,[],[f359]) ).
cnf(s52,plain,
( ~ spl12_2
| spl12_33
| ~ spl12_36 ),
inference(sat_conversion,[],[f371]) ).
cnf(s53,plain,
( ~ spl12_17
| ~ spl12_28
| spl12_36 ),
inference(sat_conversion,[],[f377]) ).
cnf(s54,plain,
( ~ spl12_14
| ~ spl12_19
| ~ spl12_20
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27
| ~ spl12_29 ),
inference(sat_conversion,[],[f380]) ).
cnf(s63,plain,
( ~ spl12_3
| ~ spl12_19
| ~ spl12_20
| ~ spl12_24
| ~ spl12_27
| ~ spl12_42
| ~ spl12_44 ),
inference(sat_conversion,[],[f441]) ).
cnf(s65,plain,
( ~ spl12_27
| ~ spl12_29
| spl12_40 ),
inference(sat_conversion,[],[f459]) ).
cnf(s69,plain,
( ~ spl12_21
| ~ spl12_27
| spl12_42 ),
inference(sat_conversion,[],[f475]) ).
cnf(s70,plain,
( ~ spl12_21
| ~ spl12_27
| ~ spl12_28
| spl12_44 ),
inference(sat_conversion,[],[f481]) ).
cnf(s77,plain,
( ~ spl12_10
| ~ spl12_12
| ~ spl12_16
| ~ spl12_17 ),
inference(sat_conversion,[],[f512]) ).
cnf(s79,plain,
( ~ spl12_6
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17
| ~ spl12_36 ),
inference(sat_conversion,[],[f517]) ).
cnf(s80,plain,
( ~ spl12_3
| ~ spl12_9
| ~ spl12_17
| ~ spl12_32
| ~ spl12_33 ),
inference(sat_conversion,[],[f519]) ).
cnf(s82,plain,
( ~ spl12_5
| spl12_28 ),
inference(sat_conversion,[],[f525]) ).
cnf(s84,plain,
( ~ spl12_14
| ~ spl12_22
| ~ spl12_23
| ~ spl12_24
| ~ spl12_27
| ~ spl12_40
| spl12_41 ),
inference(sat_conversion,[],[f527]) ).
cnf(s91,plain,
( ~ spl12_18
| ~ spl12_40
| ~ spl12_41 ),
inference(sat_conversion,[],[f585]) ).
cnf(s94,plain,
( ~ spl12_18
| ~ spl12_21
| ~ spl12_27 ),
inference(sat_conversion,[],[f594]) ).
cnf(s95,plain,
spl12_24,
inference(rat,[],[s45,s29,s30]) ).
cnf(s96,plain,
spl12_27,
inference(rat,[],[s45,s31,s32]) ).
cnf(s97,plain,
( spl12_21
| spl12_18
| ~ spl12_29
| ~ spl12_14 ),
inference(rat,[],[s54,s27,s28,s26,s25,s95,s96]) ).
cnf(s98,plain,
( spl12_18
| ~ spl12_29
| ~ spl12_14
| ~ spl12_28
| ~ spl12_3 ),
inference(rat,[],[s63,s69,s70,s97,s25,s26,s95,s96]) ).
cnf(s99,plain,
( spl12_10
| spl12_9
| ~ spl12_28
| ~ spl12_3 ),
inference(rat,[],[s84,s27,s28,s91,s94,s98,s65,s36,s15,s13,s96,s95]) ).
cnf(s100,plain,
( ~ spl12_14
| ~ spl12_29
| ~ spl12_28
| ~ spl12_3 ),
inference(rat,[],[s84,s27,s28,s91,s94,s98,s65,s96,s95]) ).
cnf(s101,plain,
( spl12_14
| ~ spl12_10 ),
inference(rat,[],[s77,s16,s22,s23]) ).
cnf(s102,plain,
( ~ spl12_10
| ~ spl12_28
| ~ spl12_3 ),
inference(rat,[],[s77,s14,s20,s35,s36,s100,s101]) ).
cnf(s103,plain,
( spl12_14
| ~ spl12_9
| ~ spl12_28
| ~ spl12_6
| spl12_2 ),
inference(rat,[],[s79,s53,s21,s16,s22,s23]) ).
cnf(s105,plain,
spl12_28,
inference(rat,[],[s44,s4,s33,s34,s82]) ).
cnf(s106,plain,
spl12_3,
inference(rat,[],[s44,s2,s9,s10]) ).
cnf(s107,plain,
~ spl12_10,
inference(rat,[],[s102,s106,s105]) ).
cnf(s108,plain,
spl12_9,
inference(rat,[],[s99,s106,s107,s105]) ).
cnf(s109,plain,
( spl12_14
| ~ spl12_2 ),
inference(rat,[],[s80,s52,s50,s53,s16,s22,s23,s106,s108,s105]) ).
cnf(s110,plain,
~ spl12_2,
inference(rat,[],[s80,s52,s50,s53,s14,s20,s35,s36,s100,s109,s106,s108,s105]) ).
cnf(s112,plain,
spl12_6,
inference(rat,[],[s44,s6,s7,s8]) ).
cnf(s113,plain,
spl12_14,
inference(rat,[],[s103,s110,s105,s108,s112]) ).
cnf(s114,plain,
~ spl12_29,
inference(rat,[],[s100,s105,s106,s113]) ).
cnf(s115,plain,
~ spl12_13,
inference(rat,[],[s36,s114]) ).
cnf(s116,plain,
spl12_17,
inference(rat,[],[s35,s114]) ).
cnf(s117,plain,
spl12_16,
inference(rat,[],[s20,s115]) ).
cnf(s118,plain,
spl12_12,
inference(rat,[],[s14,s115]) ).
cnf(s119,plain,
spl12_15,
inference(rat,[],[s19,s110,s115]) ).
cnf(s123,plain,
$false,
inference(rat,[],[s47,s117,s116,s112,s108,s105,s118,s119]) ).
fof(f595,plain,
$false,
inference(avatar_sat_refutation,[],[s123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 21:45:23 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (805960)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (805969)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2043670642:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (805966)% WARNING: option uhcvi not known.
% 0.21/0.28 % (805969) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-805960-805969"...
% 0.21/0.28 % (805966)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=199593914:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (805965)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2601085805_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (805967)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1430917720:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (805968)dis+10_1_sil=32000:sp=arity:random_seed=1070982757:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (805970)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=912481575:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (805971)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1602944576:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (805969)...printing done.
% 0.21/0.28 % TRYING [1]
% 0.21/0.28 % (805969)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (805969)------------------------------
% 0.21/0.28 % (805969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (805969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (805969)CaDiCaL version: 2.1.3
% 0.21/0.28 % (805969)Termination reason: Refutation
% 0.21/0.28 % (805969)Time elapsed: 0.008 s
% 0.21/0.28 % (805969)Peak memory usage: 12 MB
% 0.21/0.28 % (805969)Instructions burned: 20 (million)
% 0.21/0.28 % (805960)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------