TSTP Solution File: NUM482+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 : Tue Apr 30 20:34:52 EDT 2024
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 151 ( 56 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 179 ( 60 ~; 54 |; 55 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
( ( ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xk = sdtasdt0(W0,W1) )
| doDivides0(W0,xk) ) )
=> ( W0 = sz10
| W0 = xk ) )
& isPrime0(xk) )
=> ? [W0] :
( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xk = sdtasdt0(W0,W1) )
| doDivides0(W0,xk) )
& ( ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& W0 = sdtasdt0(W1,W2) )
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) )
| isPrime0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ( ( ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xk = sdtasdt0(W0,W1) )
| doDivides0(W0,xk) ) )
=> ( W0 = sz10
| W0 = xk ) )
& isPrime0(xk) )
=> ? [W0] :
( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xk = sdtasdt0(W0,W1) )
| doDivides0(W0,xk) )
& ( ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& W0 = sdtasdt0(W1,W2) )
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) )
| isPrime0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f64,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f65,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f156,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f170,plain,
( ! [W0] :
( ~ aNaturalNumber0(W0)
| ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) )
| W0 = sz10
| W0 = xk )
& isPrime0(xk)
& ! [W0] :
( ~ aNaturalNumber0(W0)
| ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) )
| ( ( W0 = sz00
| W0 = sz10
| ? [W1] :
( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& W0 = sdtasdt0(W1,W2) )
& doDivides0(W1,W0)
& W1 != sz10
& W1 != W0 ) )
& ~ isPrime0(W0) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f171,plain,
! [W0] :
( pd0_0(W0)
=> ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) ) ),
introduced(predicate_definition,[f170]) ).
fof(f172,plain,
( ! [W0] :
( ~ aNaturalNumber0(W0)
| ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) )
| W0 = sz10
| W0 = xk )
& isPrime0(xk)
& ! [W0] :
( ~ aNaturalNumber0(W0)
| pd0_0(W0)
| ( ( W0 = sz00
| W0 = sz10
| ? [W1] :
( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& W0 = sdtasdt0(W1,W2) )
& doDivides0(W1,W0)
& W1 != sz10
& W1 != W0 ) )
& ~ isPrime0(W0) ) ) ),
inference(formula_renaming,[status(thm)],[f170,f171]) ).
fof(f173,plain,
( ! [W0] :
( ~ aNaturalNumber0(W0)
| ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) )
| W0 = sz10
| W0 = xk )
& isPrime0(xk)
& ! [W0] :
( ~ aNaturalNumber0(W0)
| pd0_0(W0)
| ( ( W0 = sz00
| W0 = sz10
| ( aNaturalNumber0(sk0_5(W0))
& aNaturalNumber0(sk0_6(W0))
& W0 = sdtasdt0(sk0_5(W0),sk0_6(W0))
& doDivides0(sk0_5(W0),W0)
& sk0_5(W0) != sz10
& sk0_5(W0) != W0 ) )
& ~ isPrime0(W0) ) ) ),
inference(skolemization,[status(esa)],[f172]) ).
fof(f176,plain,
isPrime0(xk),
inference(cnf_transformation,[status(esa)],[f173]) ).
fof(f183,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| pd0_0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[status(esa)],[f173]) ).
fof(f184,plain,
! [W0] :
( ~ pd0_0(W0)
| ( ! [W1] :
( ~ aNaturalNumber0(W1)
| xk != sdtasdt0(W0,W1) )
& ~ doDivides0(W0,xk) ) ),
inference(pre_NNF_transformation,[status(esa)],[f171]) ).
fof(f185,plain,
! [X0,X1] :
( ~ pd0_0(X0)
| ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f184]) ).
fof(f218,plain,
( spl0_4
<=> pd0_0(xk) ),
introduced(split_symbol_definition) ).
fof(f219,plain,
( pd0_0(xk)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( spl0_5
<=> isPrime0(xk) ),
introduced(split_symbol_definition) ).
fof(f223,plain,
( ~ isPrime0(xk)
| spl0_5 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( pd0_0(xk)
| ~ isPrime0(xk) ),
inference(resolution,[status(thm)],[f156,f183]) ).
fof(f225,plain,
( spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f224,f218,f221]) ).
fof(f226,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f176]) ).
fof(f227,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f230,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[f65,f156]) ).
fof(f268,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xk != sdtasdt0(xk,X0)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f219,f185]) ).
fof(f271,plain,
( xk != sdtasdt0(xk,sz10)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f268,f47]) ).
fof(f272,plain,
( xk != xk
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f230,f271]) ).
fof(f273,plain,
( $false
| ~ spl0_4 ),
inference(trivial_equality_resolution,[status(esa)],[f272]) ).
fof(f274,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f275,plain,
$false,
inference(sat_refutation,[status(thm)],[f225,f227,f274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n026.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:55:48 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 0.07/0.27 % Refutation found
% 0.07/0.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28 % Elapsed time: 0.014924 seconds
% 0.07/0.28 % CPU time: 0.025323 seconds
% 0.07/0.28 % Total memory used: 11.803 MB
% 0.07/0.28 % Net memory used: 11.787 MB
%------------------------------------------------------------------------------