TSTP Solution File: COM003_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : Mon May 20 19:11:09 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 48
% Syntax : Number of formulae : 152 ( 17 unt; 27 typ; 0 def)
% Number of atoms : 430 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 481 ( 176 ~; 190 |; 80 &)
% ( 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 : 32 ( 17 >; 15 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 258 ( 216 !; 42 ?; 258 :)
% 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,
sK9: algorithm ).
tff(func_def_5,type,
sK10: program > program ).
tff(func_def_6,type,
sK11: program ).
tff(func_def_7,type,
sK12: program > program ).
tff(func_def_8,type,
sK13: program ).
tff(func_def_9,type,
sK14: program ).
tff(func_def_10,type,
sK15: algorithm > program ).
tff(func_def_11,type,
sK16: algorithm > input ).
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(pred_def_5,type,
sP0: ( program * program ) > $o ).
tff(pred_def_6,type,
sP1: ( program * program ) > $o ).
tff(pred_def_8,type,
sP3: ( program * program ) > $o ).
tff(pred_def_9,type,
sP4: ( program * program ) > $o ).
tff(pred_def_10,type,
sP5: ( program * program ) > $o ).
tff(pred_def_12,type,
sP7: ( program * input * program ) > $o ).
tff(pred_def_13,type,
sP8: ( program * input * program ) > $o ).
tff(f172,plain,
$false,
inference(subsumption_resolution,[],[f170,f167]) ).
tff(f167,plain,
outputs(sK14,good),
inference(resolution,[],[f164,f124]) ).
tff(f124,plain,
! [X0: program,X1: input] :
( ~ halts2(X0,X1)
| outputs(sK14,good) ),
inference(resolution,[],[f121,f82]) ).
tff(f82,plain,
! [X2: program,X0: program,X1: input] :
( ~ sP7(X0,X1,X2)
| ~ halts2(X2,X1)
| outputs(X0,good) ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: program,X1: input,X2: program] :
( ( outputs(X0,good)
& halts3(X0,X2,X1) )
| ~ halts2(X2,X1)
| ~ sP7(X0,X1,X2) ),
inference(rectify,[],[f57]) ).
tff(f57,plain,
! [X0: program,X4: input,X3: program] :
( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ sP7(X0,X4,X3) ),
inference(nnf_transformation,[],[f26]) ).
tff(f26,plain,
! [X0: program,X4: input,X3: program] :
( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4)
| ~ sP7(X0,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f121,plain,
! [X0: input,X1: program] : sP7(sK14,X0,X1),
inference(resolution,[],[f119,f83]) ).
tff(f83,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| sP7(X0,X4,X3) ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,plain,
! [X0: program,X1: program,X2: input] :
( ! [X3: program,X4: input] :
( sP8(X0,X4,X3)
& sP7(X0,X4,X3) )
| ~ decides(algorithm_of(X0),X1,X2) ),
inference(definition_folding,[],[f16,f27,f26]) ).
tff(f27,plain,
! [X0: program,X4: input,X3: program] :
( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ sP8(X0,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f16,plain,
! [X0: program,X1: program,X2: input] :
( ! [X3: program,X4: input] :
( ( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4) )
& ( ( outputs(X0,good)
& halts3(X0,X3,X4) )
| ~ halts2(X3,X4) ) )
| ~ decides(algorithm_of(X0),X1,X2) ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,plain,
! [X0: program,X1: program,X2: input] :
( decides(algorithm_of(X0),X1,X2)
=> ! [X3: program,X4: input] :
( ( ~ halts2(X3,X4)
=> ( outputs(X0,bad)
& halts3(X0,X3,X4) ) )
& ( halts2(X3,X4)
=> ( outputs(X0,good)
& halts3(X0,X3,X4) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X3: program,X1: program,X2: input] :
( decides(algorithm_of(X3),X1,X2)
=> ! [X1: program,X2: input] :
( ( ~ halts2(X1,X2)
=> ( outputs(X3,bad)
& halts3(X3,X1,X2) ) )
& ( halts2(X1,X2)
=> ( outputs(X3,good)
& halts3(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
tff(f119,plain,
! [X0: program,X1: input] : decides(algorithm_of(sK14),X0,X1),
inference(resolution,[],[f78,f59]) ).
tff(f59,plain,
! [X2: input,X1: program] : decides(sK9,X1,X2),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X1: program,X2: input] : decides(sK9,X1,X2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f8,f29]) ).
tff(f29,plain,
( ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2)
=> ! [X2: input,X1: program] : decides(sK9,X1,X2) ),
introduced(choice_axiom,[]) ).
tff(f8,plain,
? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2),
inference(flattening,[],[f7]) ).
tff(f7,plain,
~ ~ ? [X0: algorithm] :
! [X1: program,X2: input] : 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/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(f78,plain,
! [X2: input,X3: algorithm,X1: program] :
( ~ decides(X3,sK15(X3),sK16(X3))
| decides(algorithm_of(sK14),X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
( ! [X1: program,X2: input] : decides(algorithm_of(sK14),X1,X2)
| ! [X3: algorithm] : ~ decides(X3,sK15(X3),sK16(X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f51,f53,f52]) ).
tff(f52,plain,
( ? [X0: program] :
! [X1: program,X2: input] : decides(algorithm_of(X0),X1,X2)
=> ! [X2: input,X1: program] : decides(algorithm_of(sK14),X1,X2) ),
introduced(choice_axiom,[]) ).
tff(f53,plain,
! [X3: algorithm] :
( ? [X4: program,X5: input] : ~ decides(X3,X4,X5)
=> ~ decides(X3,sK15(X3),sK16(X3)) ),
introduced(choice_axiom,[]) ).
tff(f51,plain,
( ? [X0: program] :
! [X1: program,X2: input] : decides(algorithm_of(X0),X1,X2)
| ! [X3: algorithm] :
? [X4: program,X5: input] : ~ decides(X3,X4,X5) ),
inference(rectify,[],[f15]) ).
tff(f15,plain,
( ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5)
| ! [X0: algorithm] :
? [X1: program,X2: input] : ~ decides(X0,X1,X2) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,plain,
( ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X4: program,X5: input] : decides(algorithm_of(X3),X4,X5) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( ? [X0: algorithm] :
! [X1: program,X2: input] : decides(X0,X1,X2)
=> ? [X3: program] :
! [X1: program,X2: input] : decides(algorithm_of(X3),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f164,plain,
halts2(sK12(sK14),as_input(sK12(sK14))),
inference(subsumption_resolution,[],[f163,f123]) ).
tff(f123,plain,
! [X0: program,X1: input] :
( outputs(sK14,bad)
| halts2(X0,X1) ),
inference(resolution,[],[f120,f80]) ).
tff(f80,plain,
! [X2: program,X0: program,X1: input] :
( ~ sP8(X0,X1,X2)
| halts2(X2,X1)
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: program,X1: input,X2: program] :
( ( outputs(X0,bad)
& halts3(X0,X2,X1) )
| halts2(X2,X1)
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f55]) ).
tff(f55,plain,
! [X0: program,X4: input,X3: program] :
( ( outputs(X0,bad)
& halts3(X0,X3,X4) )
| halts2(X3,X4)
| ~ sP8(X0,X4,X3) ),
inference(nnf_transformation,[],[f27]) ).
tff(f120,plain,
! [X0: input,X1: program] : sP8(sK14,X0,X1),
inference(resolution,[],[f119,f84]) ).
tff(f84,plain,
! [X2: input,X3: program,X0: program,X1: program,X4: input] :
( ~ decides(algorithm_of(X0),X1,X2)
| sP8(X0,X4,X3) ),
inference(cnf_transformation,[],[f28]) ).
tff(f163,plain,
( ~ outputs(sK14,bad)
| halts2(sK12(sK14),as_input(sK12(sK14))) ),
inference(subsumption_resolution,[],[f162,f74]) ).
tff(f74,plain,
! [X0: program,X1: program] :
( ~ sP3(X0,X1)
| halts2(X1,as_input(X1)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: program,X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0: program,X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f162,plain,
( ~ outputs(sK14,bad)
| sP3(sK14,sK12(sK14))
| halts2(sK12(sK14),as_input(sK12(sK14))) ),
inference(resolution,[],[f160,f132]) ).
tff(f132,plain,
! [X0: program,X1: input] :
( halts3(sK14,X0,X1)
| halts2(X0,X1) ),
inference(resolution,[],[f79,f120]) ).
tff(f79,plain,
! [X2: program,X0: program,X1: input] :
( ~ sP8(X0,X1,X2)
| halts2(X2,X1)
| halts3(X0,X2,X1) ),
inference(cnf_transformation,[],[f56]) ).
tff(f160,plain,
! [X0: program] :
( ~ halts3(X0,sK12(X0),as_input(sK12(X0)))
| ~ outputs(X0,bad)
| sP3(X0,sK12(X0)) ),
inference(subsumption_resolution,[],[f69,f159]) ).
tff(f159,plain,
sP6,
inference(subsumption_resolution,[],[f158,f116]) ).
tff(f116,plain,
! [X0: program] :
( halts2(sK13,as_input(X0))
| sP6 ),
inference(subsumption_resolution,[],[f115,f100]) ).
tff(f100,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| halts2(sK13,as_input(X0))
| sP6 ),
inference(resolution,[],[f70,f77]) ).
tff(f77,plain,
! [X1: program] :
( sP5(sK13,X1)
| sP6 ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
( ! [X1: program] :
( sP5(sK13,X1)
& sP4(sK13,X1) )
| sP6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f48,f49]) ).
tff(f49,plain,
( ? [X0: program] :
! [X1: program] :
( sP5(X0,X1)
& sP4(X0,X1) )
=> ! [X1: program] :
( sP5(sK13,X1)
& sP4(sK13,X1) ) ),
introduced(choice_axiom,[]) ).
tff(f48,plain,
( ? [X0: program] :
! [X1: program] :
( sP5(X0,X1)
& sP4(X0,X1) )
| sP6 ),
inference(rectify,[],[f25]) ).
tff(f25,plain,
( ? [X2: program] :
! [X3: program] :
( sP5(X2,X3)
& sP4(X2,X3) )
| sP6 ),
inference(definition_folding,[],[f14,f24,f23,f22,f21]) ).
tff(f22,plain,
! [X2: program,X3: program] :
( ( outputs(X2,good)
& halts2(X2,as_input(X3)) )
| ~ halts2(X3,as_input(X3))
| ~ sP4(X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f23,plain,
! [X2: program,X3: program] :
( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3))
| ~ sP5(X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f24,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP3(X0,X1) )
| ~ sP6 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f14,plain,
( ? [X2: program] :
! [X3: program] :
( ( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3)) )
& ( ( outputs(X2,good)
& halts2(X2,as_input(X3)) )
| ~ halts2(X3,as_input(X3)) ) )
| ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| ( ( ~ outputs(X0,good)
| ~ halts3(X0,X1,as_input(X1)) )
& halts2(X1,as_input(X1)) ) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts3(X0,X1,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts3(X0,X1,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( halts2(X3,as_input(X3))
=> ( outputs(X2,good)
& halts2(X2,as_input(X3)) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
( ? [X3: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X3,bad)
& halts3(X3,X1,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X3,good)
& halts3(X3,X1,as_input(X1)) ) ) )
=> ? [X4: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X4,bad)
& halts2(X4,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X4,good)
& halts2(X4,as_input(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
tff(f70,plain,
! [X0: program,X1: program] :
( ~ sP5(X0,X1)
| halts2(X1,as_input(X1))
| halts2(X0,as_input(X1)) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: program,X1: program] :
( ( outputs(X0,bad)
& halts2(X0,as_input(X1)) )
| halts2(X1,as_input(X1))
| ~ sP5(X0,X1) ),
inference(rectify,[],[f43]) ).
tff(f43,plain,
! [X2: program,X3: program] :
( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3))
| ~ sP5(X2,X3) ),
inference(nnf_transformation,[],[f23]) ).
tff(f115,plain,
! [X0: program] :
( ~ halts2(X0,as_input(X0))
| halts2(sK13,as_input(X0))
| sP6 ),
inference(resolution,[],[f72,f76]) ).
tff(f76,plain,
! [X1: program] :
( sP4(sK13,X1)
| sP6 ),
inference(cnf_transformation,[],[f50]) ).
tff(f72,plain,
! [X0: program,X1: program] :
( ~ sP4(X0,X1)
| ~ halts2(X1,as_input(X1))
| halts2(X0,as_input(X1)) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: program,X1: program] :
( ( outputs(X0,good)
& halts2(X0,as_input(X1)) )
| ~ halts2(X1,as_input(X1))
| ~ sP4(X0,X1) ),
inference(rectify,[],[f45]) ).
tff(f45,plain,
! [X2: program,X3: program] :
( ( outputs(X2,good)
& halts2(X2,as_input(X3)) )
| ~ halts2(X3,as_input(X3))
| ~ sP4(X2,X3) ),
inference(nnf_transformation,[],[f22]) ).
tff(f158,plain,
( ~ halts2(sK13,as_input(sK10(sK13)))
| sP6 ),
inference(duplicate_literal_removal,[],[f155]) ).
tff(f155,plain,
( ~ halts2(sK13,as_input(sK10(sK13)))
| sP6
| sP6 ),
inference(resolution,[],[f153,f110]) ).
tff(f110,plain,
( outputs(sK13,good)
| sP6 ),
inference(subsumption_resolution,[],[f107,f87]) ).
tff(f87,plain,
! [X0: program] :
( ~ halts2(X0,as_input(X0))
| outputs(sK13,good)
| sP6 ),
inference(resolution,[],[f73,f76]) ).
tff(f73,plain,
! [X0: program,X1: program] :
( ~ sP4(X0,X1)
| ~ halts2(X1,as_input(X1))
| outputs(X0,good) ),
inference(cnf_transformation,[],[f46]) ).
tff(f107,plain,
( halts2(sK13,as_input(sK13))
| sP6
| outputs(sK13,good) ),
inference(duplicate_literal_removal,[],[f105]) ).
tff(f105,plain,
( halts2(sK13,as_input(sK13))
| sP6
| outputs(sK13,good)
| sP6 ),
inference(resolution,[],[f100,f87]) ).
tff(f153,plain,
! [X0: program] :
( ~ outputs(X0,good)
| ~ halts2(X0,as_input(sK10(X0)))
| sP6 ),
inference(resolution,[],[f152,f65]) ).
tff(f65,plain,
! [X0: program,X1: program] :
( ~ sP0(X0,X1)
| ~ halts2(X0,as_input(X1))
| ~ outputs(X0,good) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: program,X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f17]) ).
tff(f17,plain,
! [X0: program,X1: program] :
( ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f152,plain,
! [X0: program] :
( sP0(X0,sK10(X0))
| sP6 ),
inference(subsumption_resolution,[],[f148,f98]) ).
tff(f98,plain,
sP2,
inference(subsumption_resolution,[],[f94,f66]) ).
tff(f66,plain,
! [X1: program] :
( ~ halts2(sK11,as_input(X1))
| ~ halts2(X1,as_input(X1))
| sP2 ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
( ! [X1: program] :
( sP1(sK11,X1)
& ( ~ halts2(sK11,as_input(X1))
| ~ halts2(X1,as_input(X1)) ) )
| sP2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f37,f38]) ).
tff(f38,plain,
( ? [X0: program] :
! [X1: program] :
( sP1(X0,X1)
& ( ~ halts2(X0,as_input(X1))
| ~ halts2(X1,as_input(X1)) ) )
=> ! [X1: program] :
( sP1(sK11,X1)
& ( ~ halts2(sK11,as_input(X1))
| ~ halts2(X1,as_input(X1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f37,plain,
( ? [X0: program] :
! [X1: program] :
( sP1(X0,X1)
& ( ~ halts2(X0,as_input(X1))
| ~ halts2(X1,as_input(X1)) ) )
| sP2 ),
inference(rectify,[],[f20]) ).
tff(f20,plain,
( ? [X2: program] :
! [X3: program] :
( sP1(X2,X3)
& ( ~ halts2(X2,as_input(X3))
| ~ halts2(X3,as_input(X3)) ) )
| sP2 ),
inference(definition_folding,[],[f13,f19,f18,f17]) ).
tff(f18,plain,
! [X2: program,X3: program] :
( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3))
| ~ sP1(X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f19,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP0(X0,X1) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f13,plain,
( ? [X2: program] :
! [X3: program] :
( ( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3)) )
& ( ~ halts2(X2,as_input(X3))
| ~ halts2(X3,as_input(X3)) ) )
| ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| ( ( ~ outputs(X0,good)
| ~ halts2(X0,as_input(X1)) )
& halts2(X1,as_input(X1)) ) ) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
( ? [X0: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X0,bad)
& halts2(X0,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X0,good)
& halts2(X0,as_input(X1)) ) ) )
=> ? [X2: program] :
! [X3: program] :
( ( ~ halts2(X3,as_input(X3))
=> ( outputs(X2,bad)
& halts2(X2,as_input(X3)) ) )
& ( 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,bad)
& halts2(X4,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ( outputs(X4,good)
& halts2(X4,as_input(X1)) ) ) )
=> ? [X5: program] :
! [X1: program] :
( ( ~ halts2(X1,as_input(X1))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X1)) ) )
& ( halts2(X1,as_input(X1))
=> ~ halts2(X5,as_input(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(f94,plain,
( halts2(sK11,as_input(sK11))
| sP2 ),
inference(factoring,[],[f88]) ).
tff(f88,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| halts2(sK11,as_input(X0))
| sP2 ),
inference(resolution,[],[f62,f67]) ).
tff(f67,plain,
! [X1: program] :
( sP1(sK11,X1)
| sP2 ),
inference(cnf_transformation,[],[f39]) ).
tff(f62,plain,
! [X0: program,X1: program] :
( ~ sP1(X0,X1)
| halts2(X1,as_input(X1))
| halts2(X0,as_input(X1)) ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: program,X1: program] :
( ( outputs(X0,bad)
& halts2(X0,as_input(X1)) )
| halts2(X1,as_input(X1))
| ~ sP1(X0,X1) ),
inference(rectify,[],[f34]) ).
tff(f34,plain,
! [X2: program,X3: program] :
( ( outputs(X2,bad)
& halts2(X2,as_input(X3)) )
| halts2(X3,as_input(X3))
| ~ sP1(X2,X3) ),
inference(nnf_transformation,[],[f18]) ).
tff(f148,plain,
! [X0: program] :
( sP6
| sP0(X0,sK10(X0))
| ~ sP2 ),
inference(resolution,[],[f145,f60]) ).
tff(f60,plain,
! [X0: program] :
( ~ halts2(sK10(X0),as_input(sK10(X0)))
| sP0(X0,sK10(X0))
| ~ sP2 ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
( ! [X0: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK10(X0))) )
& ~ halts2(sK10(X0),as_input(sK10(X0))) )
| sP0(X0,sK10(X0)) )
| ~ sP2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f31,f32]) ).
tff(f32,plain,
! [X0: program] :
( ? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP0(X0,X1) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK10(X0))) )
& ~ halts2(sK10(X0),as_input(sK10(X0))) )
| sP0(X0,sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP0(X0,X1) )
| ~ sP2 ),
inference(nnf_transformation,[],[f19]) ).
tff(f145,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| sP6 ),
inference(subsumption_resolution,[],[f144,f110]) ).
tff(f144,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| sP6
| ~ outputs(sK13,good) ),
inference(subsumption_resolution,[],[f142,f116]) ).
tff(f142,plain,
! [X0: program] :
( halts2(X0,as_input(X0))
| sP6
| ~ halts2(sK13,as_input(sK10(sK13)))
| ~ outputs(sK13,good) ),
inference(resolution,[],[f141,f65]) ).
tff(f141,plain,
! [X0: program] :
( sP0(sK13,sK10(sK13))
| halts2(X0,as_input(X0))
| sP6 ),
inference(subsumption_resolution,[],[f139,f109]) ).
tff(f109,plain,
! [X0: program] :
( sP0(X0,sK10(X0))
| sP6
| halts2(sK13,as_input(sK10(X0))) ),
inference(subsumption_resolution,[],[f103,f98]) ).
tff(f103,plain,
! [X0: program] :
( halts2(sK13,as_input(sK10(X0)))
| sP6
| sP0(X0,sK10(X0))
| ~ sP2 ),
inference(resolution,[],[f100,f60]) ).
tff(f139,plain,
! [X0: program] :
( ~ halts2(sK13,as_input(sK10(sK13)))
| sP0(sK13,sK10(sK13))
| halts2(X0,as_input(X0))
| sP6 ),
inference(resolution,[],[f137,f86]) ).
tff(f86,plain,
! [X0: program] :
( outputs(sK13,bad)
| halts2(X0,as_input(X0))
| sP6 ),
inference(resolution,[],[f71,f77]) ).
tff(f71,plain,
! [X0: program,X1: program] :
( ~ sP5(X0,X1)
| halts2(X1,as_input(X1))
| outputs(X0,bad) ),
inference(cnf_transformation,[],[f44]) ).
tff(f137,plain,
! [X0: program] :
( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK10(X0)))
| sP0(X0,sK10(X0)) ),
inference(subsumption_resolution,[],[f61,f98]) ).
tff(f61,plain,
! [X0: program] :
( ~ outputs(X0,bad)
| ~ halts2(X0,as_input(sK10(X0)))
| sP0(X0,sK10(X0))
| ~ sP2 ),
inference(cnf_transformation,[],[f33]) ).
tff(f69,plain,
! [X0: program] :
( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),as_input(sK12(X0)))
| sP3(X0,sK12(X0))
| ~ sP6 ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
( ! [X0: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),as_input(sK12(X0))) )
& ~ halts2(sK12(X0),as_input(sK12(X0))) )
| sP3(X0,sK12(X0)) )
| ~ sP6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f40,f41]) ).
tff(f41,plain,
! [X0: program] :
( ? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP3(X0,X1) )
=> ( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,sK12(X0),as_input(sK12(X0))) )
& ~ halts2(sK12(X0),as_input(sK12(X0))) )
| sP3(X0,sK12(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f40,plain,
( ! [X0: program] :
? [X1: program] :
( ( ( ~ outputs(X0,bad)
| ~ halts3(X0,X1,as_input(X1)) )
& ~ halts2(X1,as_input(X1)) )
| sP3(X0,X1) )
| ~ sP6 ),
inference(nnf_transformation,[],[f24]) ).
tff(f170,plain,
~ outputs(sK14,good),
inference(resolution,[],[f168,f136]) ).
tff(f136,plain,
! [X0: program] :
( ~ sP3(sK14,X0)
| ~ outputs(sK14,good) ),
inference(resolution,[],[f135,f75]) ).
tff(f75,plain,
! [X0: program,X1: program] :
( ~ halts3(X0,X1,as_input(X1))
| ~ outputs(X0,good)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f135,plain,
! [X0: program,X1: input] : halts3(sK14,X0,X1),
inference(subsumption_resolution,[],[f134,f132]) ).
tff(f134,plain,
! [X0: program,X1: input] :
( ~ halts2(X0,X1)
| halts3(sK14,X0,X1) ),
inference(resolution,[],[f81,f121]) ).
tff(f81,plain,
! [X2: program,X0: program,X1: input] :
( ~ sP7(X0,X1,X2)
| ~ halts2(X2,X1)
| halts3(X0,X2,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f168,plain,
sP3(sK14,sK12(sK14)),
inference(subsumption_resolution,[],[f165,f159]) ).
tff(f165,plain,
( sP3(sK14,sK12(sK14))
| ~ sP6 ),
inference(resolution,[],[f164,f68]) ).
tff(f68,plain,
! [X0: program] :
( ~ halts2(sK12(X0),as_input(sK12(X0)))
| sP3(X0,sK12(X0))
| ~ sP6 ),
inference(cnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 10:36:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (24447)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (24452)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38 % (24449)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (24451)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38 % (24450)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.22/0.38 % (24448)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38 % (24453)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38 % (24454)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38 % (24452)First to succeed.
% 0.22/0.38 Detected minimum model sizes of [1,1,1,1]
% 0.22/0.38 Detected maximum model sizes of [2,max,max,max]
% 0.22/0.38 Detected minimum model sizes of [1,1,1,1]
% 0.22/0.38 TRYING [1,1,1,1]
% 0.22/0.38 Detected maximum model sizes of [2,max,max,max]
% 0.22/0.38 TRYING [1,1,1,1]
% 0.22/0.38 TRYING [2,1,1,1]
% 0.22/0.38 % (24453)Also succeeded, but the first one will report.
% 0.22/0.38 TRYING [2,1,1,1]
% 0.22/0.38 Detected minimum model sizes of [1,1,1,1,1,1]
% 0.22/0.38 Detected maximum model sizes of [2,max,max,max,max,max]
% 0.22/0.38 TRYING [1,2,1,1]
% 0.22/0.38 Detected minimum model sizes of [1,1,1,1,1,1]
% 0.22/0.38 Detected maximum model sizes of [2,max,max,max,max,max]
% 0.22/0.38 TRYING [1,1,1,1,1,1]
% 0.22/0.38 TRYING [1,1,1,1,1,1]
% 0.22/0.38 TRYING [1,2,1,1]
% 0.22/0.38 TRYING [1,1,2,1]
% 0.22/0.38 TRYING [2,1,1,1,1,1]
% 0.22/0.39 TRYING [1,1,2,1]
% 0.22/0.39 TRYING [2,1,1,1,1,1]
% 0.22/0.39 % (24452)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24447"
% 0.22/0.39 TRYING [1,2,1,1,1,1]
% 0.22/0.39 % (24452)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (24452)------------------------------
% 0.22/0.39 % (24452)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39 % (24452)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (24452)Memory used [KB]: 831
% 0.22/0.39 % (24452)Time elapsed: 0.007 s
% 0.22/0.39 % (24452)Instructions burned: 9 (million)
% 0.22/0.39 % (24447)Success in time 0.011 s
%------------------------------------------------------------------------------