TSTP Solution File: COM003_1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : COM003_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 15:53:32 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 34
% Syntax : Number of formulae : 108 ( 18 unt; 20 typ; 0 def)
% Number of atoms : 361 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 441 ( 168 ~; 149 |; 89 &)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 180 ( 140 !; 40 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
program: $tType ).
tff(type_def_6,type,
algorithm: $tType ).
tff(type_def_7,type,
input: $tType ).
tff(type_def_8,type,
output: $tType ).
tff(func_def_0,type,
bad: output ).
tff(func_def_1,type,
good: output ).
tff(func_def_2,type,
algorithm_of: program > algorithm ).
tff(func_def_3,type,
as_input: program > input ).
tff(func_def_4,type,
sK2: program > program ).
tff(func_def_5,type,
sK3: program ).
tff(func_def_6,type,
sK4: program ).
tff(func_def_7,type,
sK5: program > program ).
tff(func_def_8,type,
sK6: algorithm ).
tff(func_def_9,type,
sK7: algorithm > input ).
tff(func_def_10,type,
sK8: algorithm > program ).
tff(func_def_11,type,
sK9: program ).
tff(pred_def_1,type,
decides: ( algorithm * program * input ) > $o ).
tff(pred_def_2,type,
halts2: ( program * input ) > $o ).
tff(pred_def_3,type,
halts3: ( program * program * input ) > $o ).
tff(pred_def_4,type,
outputs: ( program * output ) > $o ).
tff(f140,plain,
$false,
inference(subsumption_resolution,[],[f136,f134]) ).
tff(f134,plain,
~ outputs(sK4,bad),
inference(subsumption_resolution,[],[f133,f66]) ).
tff(f66,plain,
sP0,
inference(subsumption_resolution,[],[f65,f46]) ).
tff(f46,plain,
! [X1: program] :
( ~ halts2(sK3,as_input(X1))
| ~ halts2(X1,as_input(X1))
| sP0 ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,plain,
( ! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
| ~ halts2(sK3,as_input(X1)) )
& ( ( halts2(sK3,as_input(X1))
& outputs(sK3,bad) )
| halts2(X1,as_input(X1)) ) )
| sP0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).
tff(f25,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
| ~ halts2(X0,as_input(X1)) )
& ( ( halts2(X0,as_input(X1))
& outputs(X0,bad) )
| halts2(X1,as_input(X1)) ) )
=> ! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
| ~ halts2(sK3,as_input(X1)) )
& ( ( halts2(sK3,as_input(X1))
& outputs(sK3,bad) )
| halts2(X1,as_input(X1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f24,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
| ~ halts2(X0,as_input(X1)) )
& ( ( halts2(X0,as_input(X1))
& outputs(X0,bad) )
| halts2(X1,as_input(X1)) ) )
| sP0 ),
inference(rectify,[],[f18]) ).
tff(f18,plain,
( ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
| ~ halts2(X2,as_input(X3)) )
& ( ( halts2(X2,as_input(X3))
& outputs(X2,bad) )
| halts2(X3,as_input(X3)) ) )
| sP0 ),
inference(definition_folding,[],[f16,f17]) ).
tff(f17,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ halts2(X0,as_input(X1))
| ~ outputs(X0,bad) ) ) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f16,plain,
( ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
| ~ halts2(X2,as_input(X3)) )
& ( ( halts2(X2,as_input(X3))
& outputs(X2,bad) )
| halts2(X3,as_input(X3)) ) )
| ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ halts2(X0,as_input(X1))
| ~ outputs(X0,bad) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( halts2(X0,as_input(X1))
& outputs(X0,bad) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( halts2(X2,as_input(X3))
& outputs(X2,bad) ) )
& ( halts2(X3,as_input(X3))
=> ~ halts2(X2,as_input(X3)) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
( ? [X4: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ( outputs(X4,good)
& halts2(X4,as_input(X1)) ) )
& ( ~ halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,bad) ) ) )
=> ? [X5: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ~ halts2(X5,as_input(X1)) )
& ( ~ halts2(X1,as_input(X1))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
tff(f65,plain,
( sP0
| halts2(sK3,as_input(sK3)) ),
inference(factoring,[],[f45]) ).
tff(f45,plain,
! [X1: program] :
( halts2(X1,as_input(X1))
| halts2(sK3,as_input(X1))
| sP0 ),
inference(cnf_transformation,[],[f26]) ).
tff(f133,plain,
( ~ outputs(sK4,bad)
| ~ sP0 ),
inference(subsumption_resolution,[],[f131,f109]) ).
tff(f109,plain,
! [X0: program] : halts2(sK4,as_input(X0)),
inference(resolution,[],[f105,f63]) ).
tff(f63,plain,
! [X1: program] :
( ~ sP1
| halts2(sK4,as_input(X1)) ),
inference(subsumption_resolution,[],[f48,f50]) ).
tff(f50,plain,
! [X1: program] :
( ~ sP1
| halts2(sK4,as_input(X1))
| halts2(X1,as_input(X1)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
( ! [X1: program] :
( ( ( halts2(sK4,as_input(X1))
& outputs(sK4,bad) )
| halts2(X1,as_input(X1)) )
& ( ( halts2(sK4,as_input(X1))
& outputs(sK4,good) )
| ~ halts2(X1,as_input(X1)) ) )
| ~ sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f28,f29]) ).
tff(f29,plain,
( ? [X0: program] :
! [X1: program] :
( ( ( halts2(X0,as_input(X1))
& outputs(X0,bad) )
| halts2(X1,as_input(X1)) )
& ( ( halts2(X0,as_input(X1))
& outputs(X0,good) )
| ~ halts2(X1,as_input(X1)) ) )
=> ! [X1: program] :
( ( ( halts2(sK4,as_input(X1))
& outputs(sK4,bad) )
| halts2(X1,as_input(X1)) )
& ( ( halts2(sK4,as_input(X1))
& outputs(sK4,good) )
| ~ halts2(X1,as_input(X1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
( ? [X0: program] :
! [X1: program] :
( ( ( halts2(X0,as_input(X1))
& outputs(X0,bad) )
| halts2(X1,as_input(X1)) )
& ( ( halts2(X0,as_input(X1))
& outputs(X0,good) )
| ~ halts2(X1,as_input(X1)) ) )
| ~ sP1 ),
inference(rectify,[],[f27]) ).
tff(f27,plain,
( ? [X2: program] :
! [X3: program] :
( ( ( halts2(X2,as_input(X3))
& outputs(X2,bad) )
| halts2(X3,as_input(X3)) )
& ( ( halts2(X2,as_input(X3))
& outputs(X2,good) )
| ~ halts2(X3,as_input(X3)) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f19]) ).
tff(f19,plain,
( ? [X2: program] :
! [X3: program] :
( ( ( halts2(X2,as_input(X3))
& outputs(X2,bad) )
| halts2(X3,as_input(X3)) )
& ( ( halts2(X2,as_input(X3))
& outputs(X2,good) )
| ~ halts2(X3,as_input(X3)) ) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f48,plain,
! [X1: program] :
( ~ halts2(X1,as_input(X1))
| ~ sP1
| halts2(sK4,as_input(X1)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f105,plain,
sP1,
inference(subsumption_resolution,[],[f104,f74]) ).
tff(f74,plain,
! [X0: program,X1: input] : halts3(sK9,X0,X1),
inference(resolution,[],[f73,f64]) ).
tff(f64,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| halts3(X2,X3,X4) ),
inference(subsumption_resolution,[],[f59,f57]) ).
tff(f57,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| halts2(X3,X4)
| halts3(X2,X3,X4) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: input,X1: program,X2: program] :
( ~ decides(algorithm_of(X2),X1,X0)
| ! [X3: program,X4: input] :
( ( ( outputs(X2,good)
& halts3(X2,X3,X4) )
| ~ halts2(X3,X4) )
& ( ( outputs(X2,bad)
& halts3(X2,X3,X4) )
| halts2(X3,X4) ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,plain,
! [X2: input,X1: program,X0: program] :
( ~ decides(algorithm_of(X0),X1,X2)
| ! [X4: program,X3: input] :
( ( ( outputs(X0,good)
& halts3(X0,X4,X3) )
| ~ halts2(X4,X3) )
& ( ( outputs(X0,bad)
& halts3(X0,X4,X3) )
| halts2(X4,X3) ) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,plain,
! [X2: input,X1: program,X0: program] :
( decides(algorithm_of(X0),X1,X2)
=> ! [X4: program,X3: input] :
( ( ~ halts2(X4,X3)
=> ( outputs(X0,bad)
& halts3(X0,X4,X3) ) )
& ( halts2(X4,X3)
=> ( outputs(X0,good)
& halts3(X0,X4,X3) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X3: program,X1: program,X2: input] :
( decides(algorithm_of(X3),X1,X2)
=> ! [X2: input,X1: program] :
( ( ~ halts2(X1,X2)
=> ( halts3(X3,X1,X2)
& outputs(X3,bad) ) )
& ( halts2(X1,X2)
=> ( outputs(X3,good)
& halts3(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f59,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( halts3(X2,X3,X4)
| ~ halts2(X3,X4)
| ~ decides(algorithm_of(X2),X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
tff(f73,plain,
! [X0: program,X1: input] : decides(algorithm_of(sK9),X0,X1),
inference(resolution,[],[f56,f55]) ).
tff(f55,plain,
! [X2: program,X1: input] : decides(sK6,X2,X1),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X1: input,X2: program] : decides(sK6,X2,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f33,f34]) ).
tff(f34,plain,
( ? [X0: algorithm] :
! [X1: input,X2: program] : decides(X0,X2,X1)
=> ! [X2: program,X1: input] : decides(sK6,X2,X1) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
? [X0: algorithm] :
! [X1: input,X2: program] : decides(X0,X2,X1),
inference(rectify,[],[f10]) ).
tff(f10,plain,
? [X0: algorithm] :
! [X2: input,X1: program] : decides(X0,X1,X2),
inference(flattening,[],[f9]) ).
tff(f9,plain,
~ ~ ? [X0: algorithm] :
! [X2: input,X1: program] : decides(X0,X1,X2),
inference(rectify,[],[f6]) ).
tff(f6,negated_conjecture,
~ ~ ? [X6: algorithm] :
! [X7: program,X8: input] : decides(X6,X7,X8),
inference(negated_conjecture,[],[f5]) ).
tff(f5,conjecture,
~ ? [X6: algorithm] :
! [X7: program,X8: input] : decides(X6,X7,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(f56,plain,
! [X0: algorithm,X4: input,X5: program] :
( ~ decides(X0,sK8(X0),sK7(X0))
| decides(algorithm_of(sK9),X5,X4) ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
( ! [X0: algorithm] : ~ decides(X0,sK8(X0),sK7(X0))
| ! [X4: input,X5: program] : decides(algorithm_of(sK9),X5,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f14,f37,f36]) ).
tff(f36,plain,
! [X0: algorithm] :
( ? [X1: input,X2: program] : ~ decides(X0,X2,X1)
=> ~ decides(X0,sK8(X0),sK7(X0)) ),
introduced(choice_axiom,[]) ).
tff(f37,plain,
( ? [X3: program] :
! [X4: input,X5: program] : decides(algorithm_of(X3),X5,X4)
=> ! [X5: program,X4: input] : decides(algorithm_of(sK9),X5,X4) ),
introduced(choice_axiom,[]) ).
tff(f14,plain,
( ! [X0: algorithm] :
? [X1: input,X2: program] : ~ decides(X0,X2,X1)
| ? [X3: program] :
! [X4: input,X5: program] : decides(algorithm_of(X3),X5,X4) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
( ? [X0: algorithm] :
! [X2: program,X1: input] : decides(X0,X2,X1)
=> ? [X3: program] :
! [X4: input,X5: program] : decides(algorithm_of(X3),X5,X4) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( ? [X0: algorithm] :
! [X2: input,X1: program] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X2: input,X1: program] : decides(algorithm_of(X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f104,plain,
( sP1
| ~ halts3(sK9,sK5(sK9),as_input(sK5(sK9))) ),
inference(subsumption_resolution,[],[f103,f94]) ).
tff(f94,plain,
outputs(sK9,bad),
inference(subsumption_resolution,[],[f93,f76]) ).
tff(f76,plain,
! [X0: program,X1: input] :
( halts2(X0,X1)
| outputs(sK9,bad) ),
inference(resolution,[],[f58,f73]) ).
tff(f58,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| outputs(X2,bad)
| halts2(X3,X4) ),
inference(cnf_transformation,[],[f39]) ).
tff(f93,plain,
( outputs(sK9,bad)
| ~ halts2(sK9,as_input(sK2(sK9))) ),
inference(subsumption_resolution,[],[f92,f76]) ).
tff(f92,plain,
( outputs(sK9,bad)
| ~ halts2(sK2(sK9),as_input(sK2(sK9)))
| ~ halts2(sK9,as_input(sK2(sK9))) ),
inference(resolution,[],[f88,f83]) ).
tff(f83,plain,
( outputs(sK9,good)
| outputs(sK9,bad) ),
inference(resolution,[],[f77,f76]) ).
tff(f77,plain,
! [X0: program,X1: input] :
( ~ halts2(X0,X1)
| outputs(sK9,good) ),
inference(resolution,[],[f60,f73]) ).
tff(f60,plain,
! [X2: program,X3: program,X0: input,X1: program,X4: input] :
( ~ decides(algorithm_of(X2),X1,X0)
| ~ halts2(X3,X4)
| outputs(X2,good) ),
inference(cnf_transformation,[],[f39]) ).
tff(f88,plain,
! [X0: program] :
( ~ outputs(X0,good)
| ~ halts2(sK2(X0),as_input(sK2(X0)))
| ~ halts2(X0,as_input(sK2(X0))) ),
inference(resolution,[],[f43,f66]) ).
tff(f43,plain,
! [X0: program] :
( ~ sP0
| ~ halts2(X0,as_input(sK2(X0)))
| ~ outputs(X0,good)
| ~ halts2(sK2(X0),as_input(sK2(X0))) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
( ! [X0: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK2(X0))) )
& halts2(sK2(X0),as_input(sK2(X0))) )
| ( ~ halts2(sK2(X0),as_input(sK2(X0)))
& ( ~ halts2(X0,as_input(sK2(X0)))
| ~ outputs(X0,bad) ) ) )
| ~ sP0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f21,f22]) ).
tff(f22,plain,
! [X0: program] :
( ? [X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ halts2(X0,as_input(X1))
| ~ outputs(X0,bad) ) ) )
=> ( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK2(X0))) )
& halts2(sK2(X0),as_input(sK2(X0))) )
| ( ~ halts2(sK2(X0),as_input(sK2(X0)))
& ( ~ halts2(X0,as_input(sK2(X0)))
| ~ outputs(X0,bad) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f21,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ( ~ halts2(X1,as_input(X1))
& ( ~ halts2(X0,as_input(X1))
| ~ outputs(X0,bad) ) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f17]) ).
tff(f103,plain,
( ~ outputs(sK9,bad)
| sP1
| ~ halts3(sK9,sK5(sK9),as_input(sK5(sK9))) ),
inference(duplicate_literal_removal,[],[f100]) ).
tff(f100,plain,
( sP1
| ~ halts3(sK9,sK5(sK9),as_input(sK5(sK9)))
| sP1
| ~ outputs(sK9,bad) ),
inference(resolution,[],[f97,f61]) ).
tff(f61,plain,
! [X0: program] :
( ~ outputs(X0,good)
| ~ outputs(X0,bad)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| sP1 ),
inference(duplicate_literal_removal,[],[f53]) ).
tff(f53,plain,
! [X0: program] :
( sP1
| ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| ~ outputs(X0,bad)
| ~ outputs(X0,good)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
( ! [X0: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) )
& ~ halts2(sK5(X0),as_input(sK5(X0))) )
| ( halts2(sK5(X0),as_input(sK5(X0)))
& ( ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| ~ outputs(X0,good) ) ) )
| sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f20,f31]) ).
tff(f31,plain,
! [X0: program] :
( ? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| ( halts2(X1,as_input(X1))
& ( ~ halts3(X0,X1,as_input(X1))
| ~ outputs(X0,good) ) ) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK5(X0),as_input(sK5(X0))) )
& ~ halts2(sK5(X0),as_input(sK5(X0))) )
| ( halts2(sK5(X0),as_input(sK5(X0)))
& ( ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| ~ outputs(X0,good) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f20,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| ( halts2(X1,as_input(X1))
& ( ~ halts3(X0,X1,as_input(X1))
| ~ outputs(X0,good) ) ) )
| sP1 ),
inference(definition_folding,[],[f15,f19]) ).
tff(f15,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| ( halts2(X1,as_input(X1))
& ( ~ halts3(X0,X1,as_input(X1))
| ~ outputs(X0,good) ) ) )
| ? [X2: program] :
! [X3: program] :
( ( ( halts2(X2,as_input(X3))
& outputs(X2,bad) )
| halts2(X3,as_input(X3)) )
& ( ( halts2(X2,as_input(X3))
& outputs(X2,good) )
| ~ halts2(X3,as_input(X3)) ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts3(X0,X1,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( halts3(X0,X1,as_input(X1))
& outputs(X0,good) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( halts2(X3,as_input(X3))
=> ( halts2(X2,as_input(X3))
& outputs(X2,good) ) )
& ( ~ halts2(X3,as_input(X3))
=> ( halts2(X2,as_input(X3))
& outputs(X2,bad) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
( ? [X3: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( halts3(X3,X1,as_input(X1))
& outputs(X3,bad) ) )
& ( halts2(X1,as_input(X1))
=> ( halts3(X3,X1,as_input(X1))
& outputs(X3,good) ) ) )
=> ? [X4: program] :
! [X1: program] :
( ( halts2(X1,as_input(X1))
=> ( halts2(X4,as_input(X1))
& outputs(X4,good) ) )
& ( ~ halts2(X1,as_input(X1))
=> ( outputs(X4,bad)
& halts2(X4,as_input(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(f97,plain,
( outputs(sK9,good)
| sP1 ),
inference(resolution,[],[f96,f77]) ).
tff(f96,plain,
( halts2(sK5(sK9),as_input(sK5(sK9)))
| sP1 ),
inference(subsumption_resolution,[],[f95,f94]) ).
tff(f95,plain,
( ~ outputs(sK9,bad)
| sP1
| halts2(sK5(sK9),as_input(sK5(sK9))) ),
inference(resolution,[],[f54,f74]) ).
tff(f54,plain,
! [X0: program] :
( ~ halts3(X0,sK5(X0),as_input(sK5(X0)))
| halts2(sK5(X0),as_input(sK5(X0)))
| sP1
| ~ outputs(X0,bad) ),
inference(cnf_transformation,[],[f32]) ).
tff(f131,plain,
( ~ halts2(sK4,as_input(sK2(sK4)))
| ~ outputs(sK4,bad)
| ~ sP0 ),
inference(resolution,[],[f124,f62]) ).
tff(f62,plain,
! [X0: program] :
( ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK2(X0)))
| ~ outputs(X0,bad)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f42]) ).
tff(f42,plain,
! [X0: program] :
( ~ halts2(X0,as_input(sK2(X0)))
| ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK2(X0)))
| ~ sP0
| ~ outputs(X0,bad) ),
inference(cnf_transformation,[],[f23]) ).
tff(f124,plain,
outputs(sK4,good),
inference(resolution,[],[f108,f109]) ).
tff(f108,plain,
! [X0: program] :
( ~ halts2(X0,as_input(X0))
| outputs(sK4,good) ),
inference(resolution,[],[f105,f47]) ).
tff(f47,plain,
! [X1: program] :
( ~ sP1
| ~ halts2(X1,as_input(X1))
| outputs(sK4,good) ),
inference(cnf_transformation,[],[f30]) ).
tff(f136,plain,
outputs(sK4,bad),
inference(resolution,[],[f132,f107]) ).
tff(f107,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| outputs(sK4,bad) ),
inference(resolution,[],[f105,f49]) ).
tff(f49,plain,
! [X1: program] :
( ~ sP1
| outputs(sK4,bad)
| halts2(X1,as_input(X1)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f132,plain,
~ halts2(sK2(sK4),as_input(sK2(sK4))),
inference(subsumption_resolution,[],[f128,f109]) ).
tff(f128,plain,
( ~ halts2(sK4,as_input(sK2(sK4)))
| ~ halts2(sK2(sK4),as_input(sK2(sK4))) ),
inference(resolution,[],[f124,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COM003_1 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 17:01:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.52 % (4635)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.52 % (4620)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.53 % (4643)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.53 TRYING [2]
% 0.19/0.53 % (4641)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 % (4635)First to succeed.
% 0.19/0.53 TRYING [3]
% 0.19/0.53 % (4635)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (4635)------------------------------
% 0.19/0.53 % (4635)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (4635)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (4635)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (4635)Memory used [KB]: 895
% 0.19/0.53 % (4635)Time elapsed: 0.126 s
% 0.19/0.53 % (4635)Instructions burned: 3 (million)
% 0.19/0.53 % (4635)------------------------------
% 0.19/0.53 % (4635)------------------------------
% 0.19/0.53 % (4619)Success in time 0.177 s
%------------------------------------------------------------------------------