%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:45 PM UTC 2026
% Result : Theorem 0.15s 0.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 88 ( 20 unt; 13 def)
% Number of atoms : 276 ( 77 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 300 ( 112 ~; 125 |; 42 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 41 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [W0] :
( ( W0 != sz10
& W0 != sz00
& aNaturalNumber0(W0) )
=> ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f58,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f137,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f138,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f153,plain,
! [W0] :
( ( isPrime0(W0)
<=> ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 ) )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f154,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [W0] :
( ( ( ( sK2_skl(W0) != W0
& sK2_skl(W0) != sz10
& doDivides0(sK2_skl(W0),W0)
& aNaturalNumber0(sK2_skl(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f154]) ).
fof(f156,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f163,plain,
! [W0] :
( ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f164,plain,
! [W0] :
( ( isPrime0(sK3_skl(W0))
& doDivides0(sK3_skl(W0),W0)
& aNaturalNumber0(sK3_skl(W0)) )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W1,sK3_skl(W0))],[f163]) ).
fof(f165,plain,
! [X0] :
( aNaturalNumber0(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0] :
( doDivides0(sK3_skl(X0),X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0] :
( isPrime0(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f168,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f169,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f170,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f174,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f181,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f182,plain,
( xk != sz10
& xk != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f183,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
xk != sz10,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f187,plain,
! [W0] :
( ~ isPrime0(W0)
| ~ doDivides0(W0,xk)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f188,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f199,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f203,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(destructive_equality_resolution,[status(thm)],[f156]) ).
fof(f204,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[status(thm)],[f203,f53]) ).
fof(f211,definition,
( sQ1_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ isPrime0(sK3_skl(xk))
| ~ aNaturalNumber0(sK3_skl(xk))
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f166,f188]) ).
fof(f310,definition,
( sQ15_spl
<=> xk = sz00 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ15_spl
| xk = sz00 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,definition,
( sQ16_spl
<=> xk = sz10 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( ~ sQ16_spl
| xk = sz10 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,definition,
( sQ17_spl
<=> aNaturalNumber0(sK3_skl(xk)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ17_spl
| ~ aNaturalNumber0(sK3_skl(xk)) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
( sQ18_spl
<=> isPrime0(sK3_skl(xk)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ18_spl
| ~ isPrime0(sK3_skl(xk)) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f309,f211,f310,f313,f316,f319]) ).
fof(f386,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f181,f199]) ).
fof(f387,definition,
( sQ32_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ32_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ33_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ33_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,definition,
( sQ34_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ34_spl
| xp = sz00 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f399,definition,
( sQ36_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ36_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f406,definition,
( sQ38_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( sQ38_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ39_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ39_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f416,plain,
( sQ1_spl
| ~ sQ39_spl
| sQ34_spl
| ~ sQ38_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f386,f387,f406,f393,f409,f211]) ).
fof(f418,plain,
( ~ sQ34_spl
| isPrime0(sz00) ),
inference(backward_demodulation,[status(thm)],[f394,f173]) ).
fof(f428,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f204]) ).
fof(f429,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f430,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f389]) ).
fof(f431,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f432,plain,
( sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f174]) ).
fof(f433,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f434,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f184]) ).
fof(f435,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f183]) ).
fof(f437,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f461,plain,
( sQ38_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f408,f59]) ).
fof(f462,plain,
( sQ38_spl
| ~ sQ33_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f461,f399,f390,f406]) ).
fof(f463,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f168]) ).
fof(f464,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f465,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f169]) ).
fof(f466,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f574,plain,
( sQ17_spl
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f318,f165]) ).
fof(f575,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f574,f211,f310,f313,f316]) ).
fof(f578,plain,
( sQ18_spl
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f321,f167]) ).
fof(f582,plain,
( sQ18_spl
| sQ16_spl
| sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f578,f211,f310,f313,f319]) ).
fof(f604,plain,
$false,
inference(sat_refutation,[status(thm)],[f322,f416,f429,f431,f433,f435,f437,f462,f464,f466,f575,f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:37:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 0.15/0.49 % Refutation found
% 0.15/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.122157 seconds
% 0.15/0.51 % CPU time: 0.714005 seconds
% 0.15/0.51 % Total memory used: 110.357 MB
% 0.15/0.51 % Net memory used: 109.720 MB
%------------------------------------------------------------------------------