%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.10s 0.24s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 34
% Syntax : Number of formulae : 266 ( 11 unt; 30 def)
% Number of atoms : 1039 ( 0 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 1346 ( 573 ~; 613 |; 105 &)
% ( 28 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 37 ( 36 usr; 29 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 257 ( 0 sgn 224 !; 33 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ( program(X0)
& ! [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) ) ) ) )
=> ? [X3] :
( program(X3)
& ! [X1] :
( ( ( program(X1)
& halts3(X0,X1,X1)
& outputs(X0,good) )
=> ~ halts2(X3,X1) )
& ( ( program(X1)
& halts3(X0,X1,X1)
& outputs(X0,bad) )
=> ( halts2(X3,X1)
& outputs(X3,bad) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,conjecture,
~ ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f5,negated_conjecture,
~ ~ ? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,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(f7,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(f8,plain,
! [X0] :
( ( program(X0)
& ! [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) ) ) ) )
=> ? [X3] :
( program(X3)
& ! [X4] :
( ( ( program(X4)
& halts3(X0,X4,X4)
& outputs(X0,good) )
=> ~ halts2(X3,X4) )
& ( ( program(X4)
& halts3(X0,X4,X4)
& outputs(X0,bad) )
=> ( halts2(X3,X4)
& outputs(X3,bad) ) ) ) ) ),
inference(rectify,[],[f3]) ).
fof(f9,plain,
? [X0] :
( algorithm(X0)
& ! [X1] :
( program(X1)
=> ! [X2] : decides(X0,X1,X2) ) ),
inference(flattening,[],[f5]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f7]) ).
fof(f12,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,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ? [X3] :
( program(X3)
& ! [X4] :
( ( ~ halts2(X3,X4)
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,good) )
& ( ( halts2(X3,X4)
& outputs(X3,bad) )
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,bad) ) ) )
| ~ program(X0)
| ? [X1,X2] :
( ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X2) )
| ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X2) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0] :
( ? [X3] :
( program(X3)
& ! [X4] :
( ( ~ halts2(X3,X4)
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,good) )
& ( ( halts2(X3,X4)
& outputs(X3,bad) )
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,bad) ) ) )
| ~ program(X0)
| ? [X1,X2] :
( ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X2) )
| ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X2) ) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
? [X0] :
( algorithm(X0)
& ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,definition,
! [X2,X1,X0] :
( ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X2) )
| ~ sP0(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f17,definition,
! [X0] :
( ? [X3] :
( program(X3)
& ! [X4] :
( ( ~ halts2(X3,X4)
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,good) )
& ( ( halts2(X3,X4)
& outputs(X3,bad) )
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,bad) ) ) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f18,plain,
! [X0] :
( sP1(X0)
| ~ program(X0)
| ? [X1,X2] :
( ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,good) )
& program(X1)
& halts2(X1,X2) )
| sP0(X2,X1,X0) ) ),
inference(definition_folding,[],[f14,f17,f16]) ).
fof(f19,plain,
( ? [X0] :
( program(X0)
& ! [X1] :
( ! [X2] : decides(X0,X1,X2)
| ~ program(X1) ) )
| ! [X3] :
( ~ algorithm(X3)
| ? [X4] :
( ? [X5] : ~ decides(X3,X4,X5)
& program(X4) ) ) ),
inference(rectify,[],[f10]) ).
fof(f20,plain,
( ( program(sK2)
& ! [X1] :
( ! [X2] : decides(sK2,X1,X2)
| ~ program(X1) ) )
| ! [X3] :
( ~ algorithm(X3)
| ( ~ decides(X3,sK3(X3),sK4(X3))
& program(sK3(X3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X4,sK3(X3)),skolemize(X5,sK4(X3))],[f19]) ).
fof(f21,plain,
! [X0] :
( ! [X1,X2] :
( ( ( halts3(X0,X1,X2)
& outputs(X0,good) )
| ~ program(X1)
| ~ halts2(X1,X2) )
& ( ( halts3(X0,X1,X2)
& outputs(X0,bad) )
| ~ program(X1)
| halts2(X1,X2) ) )
| ~ program(X0)
| ? [X3] :
( ? [X4] : ~ decides(X0,X3,X4)
& program(X3) ) ),
inference(rectify,[],[f12]) ).
fof(f22,plain,
! [X0] :
( ! [X1,X2] :
( ( ( halts3(X0,X1,X2)
& outputs(X0,good) )
| ~ program(X1)
| ~ halts2(X1,X2) )
& ( ( halts3(X0,X1,X2)
& outputs(X0,bad) )
| ~ program(X1)
| halts2(X1,X2) ) )
| ~ program(X0)
| ( ~ decides(X0,sK5(X0),sK6(X0))
& program(sK5(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X3,sK5(X0)),skolemize(X4,sK6(X0))],[f21]) ).
fof(f23,plain,
! [X0] :
( ? [X3] :
( program(X3)
& ! [X4] :
( ( ~ halts2(X3,X4)
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,good) )
& ( ( halts2(X3,X4)
& outputs(X3,bad) )
| ~ program(X4)
| ~ halts3(X0,X4,X4)
| ~ outputs(X0,bad) ) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0] :
( ? [X1] :
( program(X1)
& ! [X2] :
( ( ~ halts2(X1,X2)
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,good) )
& ( ( halts2(X1,X2)
& outputs(X1,bad) )
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,bad) ) ) )
| ~ sP1(X0) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ( program(sK7(X0))
& ! [X2] :
( ( ~ halts2(sK7(X0),X2)
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,good) )
& ( ( halts2(sK7(X0),X2)
& outputs(sK7(X0),bad) )
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,bad) ) ) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f24]) ).
fof(f26,plain,
! [X2,X1,X0] :
( ( ( ~ halts3(X0,X1,X2)
| ~ outputs(X0,bad) )
& program(X1)
& ~ halts2(X1,X2) )
| ~ sP0(X2,X1,X0) ),
inference(nnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ( ~ halts3(X2,X1,X0)
| ~ outputs(X2,bad) )
& program(X1)
& ~ halts2(X1,X0) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0] :
( sP1(X0)
| ~ program(X0)
| ( ( ~ halts3(X0,sK8(X0),sK9(X0))
| ~ outputs(X0,good) )
& program(sK8(X0))
& halts2(sK8(X0),sK9(X0)) )
| sP0(sK9(X0),sK8(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0))],[f18]) ).
fof(f29,plain,
( algorithm(sK10)
& ! [X1] :
( ! [X2] : decides(sK10,X1,X2)
| ~ program(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f15]) ).
fof(f30,plain,
! [X2,X3,X1] :
( decides(sK2,X1,X2)
| ~ program(X1)
| ~ algorithm(X3)
| program(sK3(X3)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X3,X1] :
( decides(sK2,X1,X2)
| ~ program(X1)
| ~ algorithm(X3)
| ~ decides(X3,sK3(X3),sK4(X3)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X3] :
( program(sK2)
| ~ algorithm(X3)
| program(sK3(X3)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X3] :
( program(sK2)
| ~ algorithm(X3)
| ~ decides(X3,sK3(X3),sK4(X3)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X2,X0,X1] :
( outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| program(sK5(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1] :
( outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| program(sK5(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( outputs(X0,good)
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| program(sK5(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1] :
( outputs(X0,good)
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| program(sK5(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1] :
( halts3(X0,X1,X2)
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| ~ decides(X0,sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0] :
( halts2(sK7(X0),X2)
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,bad)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X2,X0] :
( ~ halts2(sK7(X0),X2)
| ~ program(X2)
| ~ halts3(X0,X2,X2)
| ~ outputs(X0,good)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0] :
( program(sK7(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ halts2(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X0,X1] :
( program(X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ halts3(X2,X1,X0)
| ~ outputs(X2,bad)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0] :
( sP1(X0)
| ~ program(X0)
| halts2(sK8(X0),sK9(X0))
| sP0(sK9(X0),sK8(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X0] :
( sP1(X0)
| ~ program(X0)
| program(sK8(X0))
| sP0(sK9(X0),sK8(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0] :
( sP1(X0)
| ~ program(X0)
| ~ halts3(X0,sK8(X0),sK9(X0))
| ~ outputs(X0,good)
| sP0(sK9(X0),sK8(X0),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X1] :
( decides(sK10,X1,X2)
| ~ program(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
algorithm(sK10),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X3] :
( program(sK2)
| ~ algorithm(X3)
| decides(X3,sK3(X3),sK4(X3)) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f55,plain,
! [X2,X3,X1] :
( ~ decides(sK2,X1,X2)
| ~ program(X1)
| ~ algorithm(X3)
| decides(X3,sK3(X3),sK4(X3)) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f56,plain,
! [X2,X3,X1] :
( ~ decides(sK2,X1,X2)
| ~ program(X1)
| ~ algorithm(X3)
| program(sK3(X3)) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f57,plain,
! [X2,X0,X1] :
( decides(X0,sK5(X0),sK6(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f58,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f59,plain,
! [X2,X0,X1] :
( outputs(X0,good)
| ~ program(X1)
| ~ halts2(X1,X2)
| ~ program(X0)
| decides(X0,sK5(X0),sK6(X0)) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f60,plain,
! [X2,X0,X1] :
( decides(X0,sK5(X0),sK6(X0))
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f61,plain,
! [X2,X0,X1] :
( program(sK5(X0))
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| ~ halts3(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f62,plain,
! [X2,X0,X1] :
( outputs(X0,bad)
| ~ program(X1)
| halts2(X1,X2)
| ~ program(X0)
| decides(X0,sK5(X0),sK6(X0)) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f63,plain,
! [X0] :
( program(sK7(X0))
| sP1(X0) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f64,plain,
! [X2,X0] :
( sP1(X0)
| ~ program(X2)
| halts3(X0,X2,X2)
| ~ outputs(X0,good)
| ~ halts2(sK7(X0),X2) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f65,plain,
! [X2,X0] :
( sP1(X0)
| ~ program(X2)
| halts3(X0,X2,X2)
| ~ outputs(X0,bad)
| halts2(sK7(X0),X2) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ outputs(X2,bad)
| halts3(X2,X1,X0) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f68,plain,
! [X0] :
( sP0(sK9(X0),sK8(X0),X0)
| ~ program(X0)
| halts3(X0,sK8(X0),sK9(X0))
| ~ outputs(X0,good)
| ~ sP1(X0) ),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f69,plain,
! [X0] :
( program(sK8(X0))
| ~ program(X0)
| ~ sP1(X0)
| sP0(sK9(X0),sK8(X0),X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f70,plain,
! [X0] :
( halts2(sK8(X0),sK9(X0))
| ~ program(X0)
| ~ sP1(X0)
| sP0(sK9(X0),sK8(X0),X0) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f71,plain,
! [X2,X1] :
( ~ decides(sK10,X1,X2)
| ~ program(X1) ),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f73,definition,
( spl11_1
<=> ! [X2,X1] :
( ~ program(X1)
| halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f74,plain,
( ! [X2,X1] :
( halts2(X1,X2)
| ~ program(X1) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl11_2
<=> ! [X0] :
( outputs(X0,bad)
| program(sK5(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f77,plain,
( ! [X0] :
( program(sK5(X0))
| outputs(X0,bad)
| ~ program(X0) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f34,f76,f73]) ).
fof(f80,definition,
( spl11_3
<=> ! [X0] :
( outputs(X0,bad)
| decides(X0,sK5(X0),sK6(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( outputs(X0,bad)
| decides(X0,sK5(X0),sK6(X0))
| ~ program(X0) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f62,f80,f73]) ).
fof(f84,definition,
( spl11_4
<=> ! [X2,X1] :
( ~ program(X1)
| ~ halts2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f85,plain,
( ! [X2,X1] :
( ~ halts2(X1,X2)
| ~ program(X1) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl11_5
<=> ! [X0] :
( outputs(X0,good)
| program(sK5(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f88,plain,
( ! [X0] :
( program(sK5(X0))
| outputs(X0,good)
| ~ program(X0) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( spl11_4
| spl11_5 ),
inference(avatar_split_clause,[],[f38,f87,f84]) ).
fof(f91,definition,
( spl11_6
<=> ! [X0] :
( outputs(X0,good)
| decides(X0,sK5(X0),sK6(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f92,plain,
( ! [X0] :
( outputs(X0,good)
| decides(X0,sK5(X0),sK6(X0))
| ~ program(X0) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( spl11_4
| spl11_6 ),
inference(avatar_split_clause,[],[f59,f91,f84]) ).
fof(f95,definition,
( spl11_7
<=> ! [X3] :
( ~ algorithm(X3)
| program(sK3(X3)) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f96,plain,
( ! [X3] :
( program(sK3(X3))
| ~ algorithm(X3) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl11_8
<=> ! [X2,X1] :
( ~ decides(sK2,X1,X2)
| ~ program(X1) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f99,plain,
( ! [X2,X1] :
( ~ decides(sK2,X1,X2)
| ~ program(X1) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( spl11_7
| spl11_8 ),
inference(avatar_split_clause,[],[f56,f98,f95]) ).
fof(f102,definition,
( spl11_9
<=> ! [X3] :
( ~ algorithm(X3)
| decides(X3,sK3(X3),sK4(X3)) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f103,plain,
( ! [X3] :
( decides(X3,sK3(X3),sK4(X3))
| ~ algorithm(X3) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( spl11_9
| spl11_8 ),
inference(avatar_split_clause,[],[f55,f98,f102]) ).
fof(f106,definition,
( spl11_10
<=> program(sK2) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
fof(f108,plain,
( program(sK2)
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl11_7
| spl11_10 ),
inference(avatar_split_clause,[],[f32,f106,f95]) ).
fof(f110,plain,
( spl11_9
| spl11_10 ),
inference(avatar_split_clause,[],[f54,f106,f102]) ).
fof(f112,plain,
( ~ algorithm(sK10)
| ~ program(sK3(sK10))
| ~ spl11_9 ),
inference(resolution,[],[f103,f71]) ).
fof(f114,definition,
( spl11_11
<=> program(sK3(sK10)) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f116,plain,
( ~ program(sK3(sK10))
| spl11_11 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl11_12
<=> algorithm(sK10) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f120,plain,
( ~ algorithm(sK10)
| spl11_12 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl11_11
| ~ spl11_12
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f112,f102,f118,f114]) ).
fof(f122,plain,
( $false
| spl11_12 ),
inference(resolution,[],[f120,f53]) ).
fof(f123,plain,
spl11_12,
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f124,plain,
( ~ algorithm(sK10)
| ~ spl11_7
| spl11_11 ),
inference(resolution,[],[f116,f96]) ).
fof(f126,plain,
( ~ spl11_12
| ~ spl11_7
| spl11_11 ),
inference(avatar_split_clause,[],[f124,f114,f95,f118]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ program(X0)
| ~ halts2(X0,X1)
| ~ program(sK2)
| ~ halts3(sK2,X0,X1)
| ~ program(sK5(sK2)) )
| ~ spl11_8 ),
inference(resolution,[],[f57,f99]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ program(X0)
| halts2(X0,X1)
| ~ program(sK2)
| ~ halts3(sK2,X0,X1)
| ~ program(sK5(sK2)) )
| ~ spl11_8 ),
inference(resolution,[],[f60,f99]) ).
fof(f146,definition,
( spl11_15
<=> program(sK5(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
fof(f148,plain,
( ~ program(sK5(sK2))
| spl11_15 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f150,definition,
( spl11_16
<=> ! [X0,X1] :
( ~ program(X0)
| ~ halts3(sK2,X0,X1)
| halts2(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
fof(f151,plain,
( ! [X0,X1] :
( ~ halts3(sK2,X0,X1)
| ~ program(X0)
| halts2(X0,X1) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( ~ spl11_15
| ~ spl11_10
| spl11_16
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f144,f98,f150,f106,f146]) ).
fof(f170,plain,
! [X0] :
( ~ program(X0)
| halts3(X0,sK8(X0),sK9(X0))
| ~ outputs(X0,good)
| ~ sP1(X0)
| ~ outputs(X0,bad)
| halts3(X0,sK8(X0),sK9(X0)) ),
inference(resolution,[],[f68,f67]) ).
fof(f171,plain,
! [X0] :
( halts3(X0,sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ sP1(X0)
| ~ halts2(sK8(X0),sK9(X0)) ),
inference(resolution,[],[f68,f46]) ).
fof(f172,plain,
! [X0] :
( halts3(X0,sK8(X0),sK9(X0))
| ~ program(X0)
| ~ outputs(X0,good)
| ~ sP1(X0)
| ~ outputs(X0,bad) ),
inference(duplicate_literal_removal,[],[f170]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ program(X0)
| halts2(X0,X1)
| ~ program(sK2)
| ~ halts3(sK2,X0,X1) )
| spl11_15 ),
inference(resolution,[],[f148,f61]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ program(X0)
| ~ halts2(X0,X1)
| ~ program(sK2)
| ~ halts3(sK2,X0,X1) )
| spl11_15 ),
inference(resolution,[],[f148,f58]) ).
fof(f178,definition,
( spl11_20
<=> outputs(sK2,bad) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
fof(f179,plain,
( ~ outputs(sK2,bad)
| spl11_20 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f182,plain,
( ~ spl11_10
| spl11_16
| spl11_15 ),
inference(avatar_split_clause,[],[f173,f146,f150,f106]) ).
fof(f183,plain,
( decides(sK2,sK5(sK2),sK6(sK2))
| ~ program(sK2)
| ~ spl11_3
| spl11_20 ),
inference(resolution,[],[f179,f81]) ).
fof(f185,definition,
( spl11_21
<=> decides(sK2,sK5(sK2),sK6(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
fof(f187,plain,
( decides(sK2,sK5(sK2),sK6(sK2))
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f189,plain,
( ! [X0] :
( ~ program(X0)
| ~ program(X0) )
| ~ spl11_1
| ~ spl11_4 ),
inference(resolution,[],[f74,f85]) ).
fof(f190,plain,
( ! [X0] : ~ program(X0)
| ~ spl11_1
| ~ spl11_4 ),
inference(duplicate_literal_removal,[],[f189]) ).
fof(f192,plain,
( $false
| ~ spl11_1
| ~ spl11_4
| ~ spl11_10 ),
inference(resolution,[],[f190,f108]) ).
fof(f194,plain,
( ~ spl11_1
| ~ spl11_4
| ~ spl11_10 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f196,definition,
( spl11_22
<=> ! [X0,X1] :
( ~ program(X0)
| ~ halts3(sK2,X0,X1)
| ~ halts2(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
fof(f197,plain,
( ! [X0,X1] :
( ~ halts3(sK2,X0,X1)
| ~ program(X0)
| ~ halts2(X0,X1) )
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f198,plain,
( ~ spl11_15
| ~ spl11_10
| spl11_22
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f142,f98,f196,f106,f146]) ).
fof(f203,plain,
( ~ spl11_10
| spl11_22
| spl11_15 ),
inference(avatar_split_clause,[],[f174,f146,f196,f106]) ).
fof(f212,plain,
( outputs(sK2,good)
| ~ program(sK2)
| ~ spl11_5
| spl11_15 ),
inference(resolution,[],[f88,f148]) ).
fof(f214,definition,
( spl11_24
<=> outputs(sK2,good) ),
introduced(definition,[new_symbols(definition,[spl11_24])],[avatar_definition]) ).
fof(f215,plain,
( ~ outputs(sK2,good)
| spl11_24 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( ~ spl11_10
| spl11_24
| ~ spl11_5
| spl11_15 ),
inference(avatar_split_clause,[],[f212,f146,f87,f214,f106]) ).
fof(f222,definition,
( spl11_25
<=> halts2(sK8(sK2),sK9(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_25])],[avatar_definition]) ).
fof(f223,plain,
( halts2(sK8(sK2),sK9(sK2))
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ halts2(sK8(sK2),sK9(sK2))
| spl11_25 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl11_26
<=> program(sK8(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_26])],[avatar_definition]) ).
fof(f228,plain,
( ~ program(sK8(sK2))
| spl11_26 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f230,definition,
( spl11_27
<=> sP1(sK2) ),
introduced(definition,[new_symbols(definition,[spl11_27])],[avatar_definition]) ).
fof(f232,plain,
( ~ sP1(sK2)
| spl11_27 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f234,plain,
( ! [X0] :
( ~ program(X0)
| halts3(sK2,X0,X0)
| ~ outputs(sK2,bad)
| halts2(sK7(sK2),X0) )
| spl11_27 ),
inference(resolution,[],[f232,f65]) ).
fof(f235,plain,
( ! [X0] :
( ~ program(X0)
| halts3(sK2,X0,X0)
| ~ outputs(sK2,good)
| ~ halts2(sK7(sK2),X0) )
| spl11_27 ),
inference(resolution,[],[f232,f64]) ).
fof(f237,definition,
( spl11_28
<=> ! [X0] :
( ~ program(X0)
| ~ halts2(sK7(sK2),X0)
| halts3(sK2,X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_28])],[avatar_definition]) ).
fof(f238,plain,
( ! [X0] :
( halts3(sK2,X0,X0)
| ~ halts2(sK7(sK2),X0)
| ~ program(X0) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f239,plain,
( ~ spl11_24
| spl11_28
| spl11_27 ),
inference(avatar_split_clause,[],[f235,f230,f237,f214]) ).
fof(f241,definition,
( spl11_29
<=> ! [X0] :
( ~ program(X0)
| halts2(sK7(sK2),X0)
| halts3(sK2,X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_29])],[avatar_definition]) ).
fof(f242,plain,
( ! [X0] :
( halts2(sK7(sK2),X0)
| ~ program(X0)
| halts3(sK2,X0,X0) )
| ~ spl11_29 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( ~ spl11_20
| spl11_29
| spl11_27 ),
inference(avatar_split_clause,[],[f234,f230,f241,f178]) ).
fof(f244,plain,
( ~ program(sK2)
| ~ sP1(sK2)
| sP0(sK9(sK2),sK8(sK2),sK2)
| spl11_26 ),
inference(resolution,[],[f228,f69]) ).
fof(f247,definition,
( spl11_30
<=> sP0(sK9(sK2),sK8(sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl11_30])],[avatar_definition]) ).
fof(f249,plain,
( sP0(sK9(sK2),sK8(sK2),sK2)
| ~ spl11_30 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,plain,
( spl11_30
| ~ spl11_27
| ~ spl11_10
| spl11_26 ),
inference(avatar_split_clause,[],[f244,f226,f106,f230,f247]) ).
fof(f251,plain,
( ~ program(sK2)
| ~ sP1(sK2)
| sP0(sK9(sK2),sK8(sK2),sK2)
| spl11_25 ),
inference(resolution,[],[f224,f70]) ).
fof(f252,plain,
( ~ program(sK8(sK2))
| ~ spl11_1
| spl11_25 ),
inference(resolution,[],[f224,f74]) ).
fof(f253,plain,
( ~ spl11_26
| ~ spl11_1
| spl11_25 ),
inference(avatar_split_clause,[],[f252,f222,f73,f226]) ).
fof(f254,plain,
( spl11_30
| ~ spl11_27
| ~ spl11_10
| spl11_25 ),
inference(avatar_split_clause,[],[f251,f222,f106,f230,f247]) ).
fof(f256,plain,
( ! [X0,X1] : ~ sP0(X0,sK8(sK2),X1)
| spl11_26 ),
inference(resolution,[],[f228,f47]) ).
fof(f257,plain,
( $false
| spl11_26
| ~ spl11_30 ),
inference(resolution,[],[f249,f256]) ).
fof(f258,plain,
( ~ outputs(sK2,bad)
| halts3(sK2,sK8(sK2),sK9(sK2))
| ~ spl11_30 ),
inference(resolution,[],[f249,f67]) ).
fof(f259,plain,
( ~ halts2(sK8(sK2),sK9(sK2))
| ~ spl11_30 ),
inference(resolution,[],[f249,f46]) ).
fof(f260,plain,
( spl11_26
| ~ spl11_30 ),
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f262,definition,
( spl11_31
<=> halts3(sK2,sK8(sK2),sK9(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_31])],[avatar_definition]) ).
fof(f264,plain,
( halts3(sK2,sK8(sK2),sK9(sK2))
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl11_31
| ~ spl11_20
| ~ spl11_30 ),
inference(avatar_split_clause,[],[f258,f247,f178,f262]) ).
fof(f266,plain,
( ~ spl11_10
| spl11_21
| ~ spl11_3
| spl11_20 ),
inference(avatar_split_clause,[],[f183,f178,f80,f185,f106]) ).
fof(f267,plain,
( ~ spl11_25
| ~ spl11_30 ),
inference(avatar_split_clause,[],[f259,f247,f222]) ).
fof(f270,plain,
( ~ program(sK5(sK2))
| ~ spl11_8
| ~ spl11_21 ),
inference(resolution,[],[f187,f99]) ).
fof(f273,plain,
( outputs(sK2,bad)
| ~ program(sK2)
| ~ spl11_2
| spl11_15 ),
inference(resolution,[],[f77,f148]) ).
fof(f274,plain,
( ~ program(sK8(sK2))
| halts2(sK8(sK2),sK9(sK2))
| ~ spl11_16
| ~ spl11_31 ),
inference(resolution,[],[f151,f264]) ).
fof(f275,plain,
( ~ program(sK8(sK2))
| halts2(sK8(sK2),sK9(sK2))
| ~ program(sK2)
| ~ outputs(sK2,good)
| ~ sP1(sK2)
| ~ outputs(sK2,bad)
| ~ spl11_16 ),
inference(resolution,[],[f151,f172]) ).
fof(f276,plain,
( ~ spl11_20
| ~ spl11_27
| ~ spl11_24
| ~ spl11_10
| spl11_25
| ~ spl11_26
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f275,f150,f226,f222,f106,f214,f230,f178]) ).
fof(f277,plain,
( spl11_25
| ~ spl11_26
| ~ spl11_16
| ~ spl11_31 ),
inference(avatar_split_clause,[],[f274,f262,f150,f226,f222]) ).
fof(f288,plain,
( ~ program(sK2)
| ~ outputs(sK2,good)
| ~ sP1(sK2)
| ~ halts2(sK8(sK2),sK9(sK2))
| ~ program(sK8(sK2))
| ~ halts2(sK8(sK2),sK9(sK2))
| ~ spl11_22 ),
inference(resolution,[],[f171,f197]) ).
fof(f289,plain,
( ~ program(sK2)
| ~ outputs(sK2,good)
| ~ sP1(sK2)
| ~ halts2(sK8(sK2),sK9(sK2))
| ~ program(sK8(sK2))
| ~ spl11_22 ),
inference(duplicate_literal_removal,[],[f288]) ).
fof(f290,plain,
( ~ spl11_26
| ~ spl11_25
| ~ spl11_27
| ~ spl11_24
| ~ spl11_10
| ~ spl11_22 ),
inference(avatar_split_clause,[],[f289,f196,f106,f214,f230,f222,f226]) ).
fof(f295,plain,
( ! [X0] :
( ~ halts2(sK7(sK2),X0)
| ~ program(X0)
| ~ program(X0)
| ~ halts2(X0,X0) )
| ~ spl11_22
| ~ spl11_28 ),
inference(resolution,[],[f238,f197]) ).
fof(f296,plain,
( ! [X0] :
( ~ halts2(sK7(sK2),X0)
| ~ halts2(X0,X0)
| ~ program(X0) )
| ~ spl11_22
| ~ spl11_28 ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f300,plain,
( ~ halts2(sK7(sK2),sK7(sK2))
| ~ program(sK7(sK2))
| ~ spl11_22
| ~ spl11_28 ),
inference(factoring,[],[f296]) ).
fof(f303,definition,
( spl11_32
<=> program(sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_32])],[avatar_definition]) ).
fof(f305,plain,
( ~ program(sK7(sK2))
| spl11_32 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f307,definition,
( spl11_33
<=> halts2(sK7(sK2),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_33])],[avatar_definition]) ).
fof(f308,plain,
( halts2(sK7(sK2),sK7(sK2))
| ~ spl11_33 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f309,plain,
( ~ halts2(sK7(sK2),sK7(sK2))
| spl11_33 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f315,plain,
( sP1(sK2)
| spl11_32 ),
inference(resolution,[],[f305,f63]) ).
fof(f317,plain,
( spl11_27
| spl11_32 ),
inference(avatar_split_clause,[],[f315,f303,f230]) ).
fof(f318,plain,
( ~ program(sK7(sK2))
| ~ spl11_1
| spl11_33 ),
inference(resolution,[],[f309,f74]) ).
fof(f319,plain,
( ~ spl11_32
| ~ spl11_1
| spl11_33 ),
inference(avatar_split_clause,[],[f318,f307,f73,f303]) ).
fof(f321,plain,
( ~ spl11_10
| spl11_20
| ~ spl11_2
| spl11_15 ),
inference(avatar_split_clause,[],[f273,f146,f76,f178,f106]) ).
fof(f326,plain,
( ~ program(sK7(sK2))
| halts3(sK2,sK7(sK2),sK7(sK2))
| ~ spl11_29
| spl11_33 ),
inference(resolution,[],[f242,f309]) ).
fof(f330,definition,
( spl11_35
<=> halts3(sK2,sK7(sK2),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_35])],[avatar_definition]) ).
fof(f332,plain,
( halts3(sK2,sK7(sK2),sK7(sK2))
| ~ spl11_35 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f333,plain,
( spl11_35
| ~ spl11_32
| ~ spl11_29
| spl11_33 ),
inference(avatar_split_clause,[],[f326,f307,f241,f303,f330]) ).
fof(f335,plain,
( ~ program(sK7(sK2))
| halts2(sK7(sK2),sK7(sK2))
| ~ spl11_16
| ~ spl11_35 ),
inference(resolution,[],[f332,f151]) ).
fof(f337,plain,
( spl11_33
| ~ spl11_32
| ~ spl11_16
| ~ spl11_35 ),
inference(avatar_split_clause,[],[f335,f330,f150,f303,f307]) ).
fof(f338,plain,
( decides(sK2,sK5(sK2),sK6(sK2))
| ~ program(sK2)
| ~ spl11_6
| spl11_24 ),
inference(resolution,[],[f215,f92]) ).
fof(f340,plain,
( ~ program(sK8(sK2))
| ~ spl11_4
| ~ spl11_25 ),
inference(resolution,[],[f85,f223]) ).
fof(f341,plain,
( ~ spl11_26
| ~ spl11_4
| ~ spl11_25 ),
inference(avatar_split_clause,[],[f340,f222,f84,f226]) ).
fof(f346,plain,
( ~ program(sK7(sK2))
| ~ spl11_4
| ~ spl11_33 ),
inference(resolution,[],[f308,f85]) ).
fof(f347,plain,
( ~ spl11_32
| ~ spl11_4
| ~ spl11_33 ),
inference(avatar_split_clause,[],[f346,f307,f84,f303]) ).
fof(f348,plain,
( ~ spl11_32
| ~ spl11_33
| ~ spl11_22
| ~ spl11_28 ),
inference(avatar_split_clause,[],[f300,f237,f196,f307,f303]) ).
fof(f349,plain,
( ~ spl11_15
| ~ spl11_8
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f270,f185,f98,f146]) ).
fof(f350,plain,
( ~ spl11_10
| spl11_21
| ~ spl11_6
| spl11_24 ),
inference(avatar_split_clause,[],[f338,f214,f91,f185,f106]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s2,plain,
( spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl11_4
| spl11_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s4,plain,
( spl11_4
| spl11_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( spl11_7
| spl11_8 ),
inference(sat_conversion,[],[f100]) ).
cnf(s6,plain,
( spl11_8
| spl11_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s7,plain,
( spl11_7
| spl11_10 ),
inference(sat_conversion,[],[f109]) ).
cnf(s8,plain,
( spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f110]) ).
cnf(s9,plain,
( ~ spl11_9
| ~ spl11_11
| ~ spl11_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s10,plain,
spl11_12,
inference(sat_conversion,[],[f123]) ).
cnf(s11,plain,
( ~ spl11_7
| spl11_11
| ~ spl11_12 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( ~ spl11_8
| ~ spl11_10
| ~ spl11_15
| spl11_16 ),
inference(sat_conversion,[],[f152]) ).
cnf(s16,plain,
( ~ spl11_10
| spl11_15
| spl11_16 ),
inference(sat_conversion,[],[f182]) ).
cnf(s18,plain,
( ~ spl11_1
| ~ spl11_4
| ~ spl11_10 ),
inference(sat_conversion,[],[f194]) ).
cnf(s19,plain,
( ~ spl11_8
| ~ spl11_10
| ~ spl11_15
| spl11_22 ),
inference(sat_conversion,[],[f198]) ).
cnf(s21,plain,
( ~ spl11_10
| spl11_15
| spl11_22 ),
inference(sat_conversion,[],[f203]) ).
cnf(s22,plain,
( ~ spl11_5
| ~ spl11_10
| spl11_15
| spl11_24 ),
inference(sat_conversion,[],[f217]) ).
cnf(s24,plain,
( ~ spl11_24
| spl11_27
| spl11_28 ),
inference(sat_conversion,[],[f239]) ).
cnf(s25,plain,
( ~ spl11_20
| spl11_27
| spl11_29 ),
inference(sat_conversion,[],[f243]) ).
cnf(s26,plain,
( ~ spl11_10
| spl11_26
| ~ spl11_27
| spl11_30 ),
inference(sat_conversion,[],[f250]) ).
cnf(s27,plain,
( ~ spl11_1
| spl11_25
| ~ spl11_26 ),
inference(sat_conversion,[],[f253]) ).
cnf(s28,plain,
( ~ spl11_10
| spl11_25
| ~ spl11_27
| spl11_30 ),
inference(sat_conversion,[],[f254]) ).
cnf(s29,plain,
( spl11_26
| ~ spl11_30 ),
inference(sat_conversion,[],[f260]) ).
cnf(s30,plain,
( ~ spl11_20
| ~ spl11_30
| spl11_31 ),
inference(sat_conversion,[],[f265]) ).
cnf(s31,plain,
( ~ spl11_3
| ~ spl11_10
| spl11_20
| spl11_21 ),
inference(sat_conversion,[],[f266]) ).
cnf(s32,plain,
( ~ spl11_25
| ~ spl11_30 ),
inference(sat_conversion,[],[f267]) ).
cnf(s34,plain,
( ~ spl11_10
| ~ spl11_16
| ~ spl11_20
| ~ spl11_24
| spl11_25
| ~ spl11_26
| ~ spl11_27 ),
inference(sat_conversion,[],[f276]) ).
cnf(s35,plain,
( ~ spl11_16
| spl11_25
| ~ spl11_26
| ~ spl11_31 ),
inference(sat_conversion,[],[f277]) ).
cnf(s36,plain,
( ~ spl11_10
| ~ spl11_22
| ~ spl11_24
| ~ spl11_25
| ~ spl11_26
| ~ spl11_27 ),
inference(sat_conversion,[],[f290]) ).
cnf(s40,plain,
( spl11_27
| spl11_32 ),
inference(sat_conversion,[],[f317]) ).
cnf(s41,plain,
( ~ spl11_1
| ~ spl11_32
| spl11_33 ),
inference(sat_conversion,[],[f319]) ).
cnf(s43,plain,
( ~ spl11_2
| ~ spl11_10
| spl11_15
| spl11_20 ),
inference(sat_conversion,[],[f321]) ).
cnf(s44,plain,
( ~ spl11_29
| ~ spl11_32
| spl11_33
| spl11_35 ),
inference(sat_conversion,[],[f333]) ).
cnf(s46,plain,
( ~ spl11_16
| ~ spl11_32
| spl11_33
| ~ spl11_35 ),
inference(sat_conversion,[],[f337]) ).
cnf(s47,plain,
( ~ spl11_4
| ~ spl11_25
| ~ spl11_26 ),
inference(sat_conversion,[],[f341]) ).
cnf(s48,plain,
( ~ spl11_4
| ~ spl11_32
| ~ spl11_33 ),
inference(sat_conversion,[],[f347]) ).
cnf(s49,plain,
( ~ spl11_22
| ~ spl11_28
| ~ spl11_32
| ~ spl11_33 ),
inference(sat_conversion,[],[f348]) ).
cnf(s50,plain,
( ~ spl11_8
| ~ spl11_15
| ~ spl11_21 ),
inference(sat_conversion,[],[f349]) ).
cnf(s51,plain,
( ~ spl11_6
| ~ spl11_10
| spl11_21
| spl11_24 ),
inference(sat_conversion,[],[f350]) ).
cnf(s52,plain,
( ~ spl11_9
| ~ spl11_11 ),
inference(rat,[],[s9,s10]) ).
cnf(s53,plain,
( spl11_27
| ~ spl11_24
| ~ spl11_20
| ~ spl11_22
| ~ spl11_16 ),
inference(rat,[],[s44,s46,s49,s24,s25,s40]) ).
cnf(s54,plain,
( spl11_25
| ~ spl11_27
| ~ spl11_24
| ~ spl11_20
| ~ spl11_16
| ~ spl11_10 ),
inference(rat,[],[s29,s34,s28]) ).
cnf(s55,plain,
( spl11_15
| ~ spl11_10
| ~ spl11_5
| ~ spl11_2 ),
inference(rat,[],[s26,s36,s32,s54,s53,s22,s43,s21,s16]) ).
cnf(s56,plain,
( spl11_7
| spl11_4
| spl11_1 ),
inference(rat,[],[s26,s36,s32,s54,s53,s31,s51,s13,s19,s50,s55,s5,s7,s2,s1,s4,s3]) ).
cnf(s57,plain,
( spl11_4
| spl11_1 ),
inference(rat,[],[s26,s36,s32,s54,s53,s31,s51,s13,s19,s50,s55,s6,s8,s52,s11,s56,s3,s4,s2,s1,s10]) ).
cnf(s59,plain,
( spl11_27
| ~ spl11_20
| ~ spl11_16
| ~ spl11_4 ),
inference(rat,[],[s44,s46,s48,s25,s40]) ).
cnf(s60,plain,
( spl11_26
| ~ spl11_27
| ~ spl11_10 ),
inference(rat,[],[s26,s29]) ).
cnf(s63,plain,
( spl11_15
| ~ spl11_10
| spl11_1 ),
inference(rat,[],[s30,s28,s35,s47,s60,s59,s43,s16,s1,s57]) ).
cnf(s64,plain,
( spl11_7
| spl11_1 ),
inference(rat,[],[s30,s28,s35,s47,s60,s59,s31,s13,s50,s63,s5,s7,s2,s57]) ).
cnf(s65,plain,
spl11_1,
inference(rat,[],[s30,s28,s35,s47,s60,s59,s31,s13,s50,s63,s6,s8,s52,s11,s64,s57,s2,s10]) ).
cnf(s67,plain,
( spl11_27
| ~ spl11_24
| ~ spl11_22 ),
inference(rat,[],[s49,s41,s24,s40,s65]) ).
cnf(s68,plain,
( spl11_15
| ~ spl11_10
| ~ spl11_5 ),
inference(rat,[],[s36,s27,s60,s67,s22,s21,s65]) ).
cnf(s69,plain,
( spl11_7
| spl11_4 ),
inference(rat,[],[s36,s27,s60,s67,s51,s19,s50,s68,s5,s7,s4,s3,s65]) ).
cnf(s70,plain,
spl11_4,
inference(rat,[],[s36,s27,s60,s67,s51,s19,s50,s68,s6,s8,s52,s11,s69,s3,s4,s65,s10]) ).
cnf(s71,plain,
~ spl11_10,
inference(rat,[],[s18,s65,s70]) ).
cnf(s72,plain,
spl11_9,
inference(rat,[],[s8,s71]) ).
cnf(s73,plain,
spl11_7,
inference(rat,[],[s7,s71]) ).
cnf(s74,plain,
~ spl11_11,
inference(rat,[],[s52,s72]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s11,s10,s74,s73]) ).
fof(f351,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:48:49 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.24 % (4062992)Will run a generic schedule for satisfiability detection.
% 0.10/0.24 % (4063003)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2162435307:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.24 % (4062998)% WARNING: option uhcvi not known.
% 0.10/0.24 % (4063003) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4062992-4063003"...
% 0.10/0.24 % (4063003)...printing done.
% 0.10/0.24 % (4063003)Refutation found. Thanks to Tanya!
% 0.10/0.24 % SZS status Theorem for theBenchmark
% 0.10/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.24 % (4063003)------------------------------
% 0.10/0.24 % (4063003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.24 % (4063003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.24 % (4063003)CaDiCaL version: 2.1.3
% 0.10/0.24 % (4063003)Termination reason: Refutation
% 0.10/0.24 % (4063003)Time elapsed: 0.005 s
% 0.10/0.24 % (4063003)Peak memory usage: 12 MB
% 0.10/0.24 % (4063003)Instructions burned: 13 (million)
% 0.10/0.24 % (4062992)Success in time 0.03 s
% 0.10/0.24 % Vampire exiting
%------------------------------------------------------------------------------