%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM496+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 01:40:44 PM UTC 2026
% Result : Theorem 16.44s 2.56s
% Output : CNFRefutation 16.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 14 unt; 2 def)
% Number of atoms : 308 ( 125 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 350 ( 110 ~; 153 |; 78 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 37 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [W0] :
( ( W0 != sz10
& W0 != sz00
& aNaturalNumber0(W0) )
=> ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( ( doDivides0(xp,xm)
& ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) )
| ( doDivides0(xp,xr)
& ? [W0] :
( xr = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
| doDivides0(xp,xn)
| ? [W0] :
( xn = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
| doDivides0(xp,xn)
| ? [W0] :
( xn = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f144,plain,
! [W0,W1,W2] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f145,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f152,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(f153,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)],[f152]) ).
fof(f154,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))],[f153]) ).
fof(f156,plain,
! [X0] :
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f162,plain,
! [W0] :
( ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f163,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))],[f162]) ).
fof(f164,plain,
! [X0] :
( aNaturalNumber0(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0] :
( doDivides0(sK3_skl(X0),X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f166,plain,
! [X0] :
( isPrime0(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f169,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f181,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f182,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK5_skl)
& aNaturalNumber0(sK5_skl)
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W0,sK5_skl)],[f181]) ).
fof(f183,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
xp != sz10,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f186,plain,
! [X0] :
( X0 = xp
| X0 = sz10
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f195,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f196,plain,
sdtpldt0(xp,xr) = xn,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f207,definition,
( sP2_prd
<=> ( doDivides0(xp,xr)
& ? [W0] :
( xr = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f208,plain,
( ( doDivides0(xp,xm)
& ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) )
| sP2_prd ),
inference(formula_renaming,[status(thm)],[f46,f207]) ).
fof(f209,plain,
( ( doDivides0(xp,xm)
& xm = sdtasdt0(xp,sK9_skl)
& aNaturalNumber0(sK9_skl) )
| sP2_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(W0,sK9_skl)],[f208]) ).
fof(f212,plain,
( doDivides0(xp,xm)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f213,plain,
( ~ doDivides0(xp,xm)
& ! [W0] :
( xm != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) )
& ~ doDivides0(xp,xn)
& ! [W0] :
( xn != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f215,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f217,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f238,plain,
( ( ~ doDivides0(xp,xr)
| ! [W0] :
( xr != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) )
| sP2_prd )
& ( ( doDivides0(xp,xr)
& ? [W0] :
( xr = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f239,plain,
( ( ~ doDivides0(xp,xr)
| ! [W0] :
( xr != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) )
| sP2_prd )
& ( ( doDivides0(xp,xr)
& xr = sdtasdt0(xp,sK13_skl)
& aNaturalNumber0(sK13_skl) )
| ~ sP2_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(W0,sK13_skl)],[f238]) ).
fof(f242,plain,
( doDivides0(xp,xr)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f255,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(destructive_equality_resolution,[status(thm)],[f156]) ).
fof(f495,plain,
~ isPrime0(sz10),
inference(forward_subsumption_resolution,[status(thm)],[f255,f53]) ).
fof(f504,plain,
! [X0] :
( doDivides0(X0,xn)
| ~ doDivides0(X0,xr)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f196,f145]) ).
fof(f508,plain,
! [X0] :
( doDivides0(X0,xn)
| ~ doDivides0(X0,xr)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f169]) ).
fof(f518,plain,
sP2_prd,
inference(forward_subsumption_resolution,[status(thm)],[f212,f217]) ).
fof(f687,plain,
doDivides0(xp,xr),
inference(forward_subsumption_resolution,[status(thm)],[f242,f518]) ).
fof(f857,plain,
! [X0] :
( doDivides0(X0,xn)
| ~ doDivides0(X0,xr)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f195]) ).
fof(f858,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f857,f687]) ).
fof(f886,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f858,f169]) ).
fof(f1083,plain,
~ doDivides0(xp,xp),
inference(forward_subsumption_resolution,[status(thm)],[f886,f215]) ).
fof(f1311,plain,
( sK3_skl(xp) = xp
| sK3_skl(xp) = sz10
| ~ aNaturalNumber0(sK3_skl(xp))
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f165,f186]) ).
fof(f1318,plain,
( sK3_skl(xp) = xp
| sK3_skl(xp) = sz10
| ~ aNaturalNumber0(sK3_skl(xp))
| xp = sz10
| xp = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f1311,f169]) ).
fof(f3556,plain,
( sK3_skl(xp) = xp
| sK3_skl(xp) = sz10
| ~ aNaturalNumber0(sK3_skl(xp))
| xp = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f1318,f183]) ).
fof(f3557,plain,
( xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp)
| sK3_skl(xp) = xp
| sK3_skl(xp) = sz10
| xp = sz10 ),
inference(resolution,[status(thm)],[f3556,f164]) ).
fof(f3558,plain,
( xp = sz00
| ~ aNaturalNumber0(xp)
| sK3_skl(xp) = xp
| sK3_skl(xp) = sz10
| xp = sz10 ),
inference(duplicate_literals_removal,[status(thm)],[f3557]) ).
fof(f3559,plain,
( xp = sz00
| ~ aNaturalNumber0(xp)
| sK3_skl(xp) = xp
| sK3_skl(xp) = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f3558,f184]) ).
fof(f3560,plain,
( xp = sz00
| sK3_skl(xp) = xp
| sK3_skl(xp) = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f3559,f169]) ).
fof(f3563,plain,
( xp = sz00
| sK3_skl(xp) = xp
| isPrime0(sz10)
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f3560,f166]) ).
fof(f3569,plain,
( sK3_skl(xp) = xp
| isPrime0(sz10)
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literals_removal,[status(thm)],[f3563]) ).
fof(f3570,plain,
( sK3_skl(xp) = xp
| isPrime0(sz10)
| xp = sz10
| xp = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f3569,f169]) ).
fof(f3572,plain,
( sK3_skl(xp) = xp
| isPrime0(sz10)
| xp = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f3570,f183]) ).
fof(f3576,plain,
( isPrime0(sz10)
| xp = sz10
| doDivides0(xp,xp)
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f3572,f165]) ).
fof(f3582,plain,
( isPrime0(sz10)
| doDivides0(xp,xp)
| xp = sz10
| xp = sz00
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literals_removal,[status(thm)],[f3576]) ).
fof(f3583,plain,
( isPrime0(sz10)
| doDivides0(xp,xp)
| xp = sz10
| xp = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f3582,f169]) ).
fof(f3585,plain,
( isPrime0(sz10)
| doDivides0(xp,xp)
| xp = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f3583,f183]) ).
fof(f3586,plain,
( isPrime0(sz10)
| xp = sz10 ),
inference(resolution,[status(thm)],[f3585,f1083]) ).
fof(f3604,plain,
isPrime0(sz10),
inference(forward_subsumption_resolution,[status(thm)],[f3586,f184]) ).
fof(f3610,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3604,f495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM496+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:39:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 16.44/2.56 % Refutation found
% 16.44/2.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.44/2.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.59/2.62 % Elapsed time: 2.241909 seconds
% 0.59/2.62 % CPU time: 17.077956 seconds
% 0.59/2.62 % Total memory used: 175.441 MB
% 0.59/2.62 % Net memory used: 167.054 MB
%------------------------------------------------------------------------------