%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:40:45 PM UTC 2026
% Result : Theorem 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 6 unt; 1 def)
% Number of atoms : 164 ( 72 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 192 ( 62 ~; 70 |; 56 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 26 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(f45,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
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)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
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(f207,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f210,plain,
( xk != sz10
& xk != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f211,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
xk != sz10,
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f215,plain,
! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f216,definition,
! [W0] :
( sP2_prd(W0)
<=> ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f217,plain,
! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| sP2_prd(W0)
| ~ aNaturalNumber0(W0) ),
inference(formula_renaming,[status(thm)],[f215,f216]) ).
fof(f218,plain,
! [W0] :
( ( ~ isPrime0(W0)
& ( ( sK8_skl(W0) != W0
& sK8_skl(W0) != sz10
& doDivides0(sK8_skl(W0),W0)
& W0 = sdtasdt0(sK8_skl(W0),sK9_skl(W0))
& aNaturalNumber0(sK9_skl(W0))
& aNaturalNumber0(sK8_skl(W0)) )
| W0 = sz10
| W0 = sz00 ) )
| sP2_prd(W0)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0))],[f217]) ).
fof(f225,plain,
! [X0] :
( ~ isPrime0(X0)
| sP2_prd(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f246,plain,
! [W0] :
( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) )
| sP2_prd(W0) )
& ( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP2_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f216]) ).
fof(f247,plain,
( ! [W0] :
( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) )
| sP2_prd(W0) )
& ! [W0] :
( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP2_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f246]) ).
fof(f248,plain,
( ! [W0] :
( doDivides0(W0,xk)
| ( xk = sdtasdt0(W0,sK13_skl(W0))
& aNaturalNumber0(sK13_skl(W0)) )
| sP2_prd(W0) )
& ! [W0] :
( ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ sP2_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(W1,sK13_skl(W0))],[f247]) ).
fof(f250,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f447,plain,
! [X0] :
( sP2_prd(sK3_skl(X0))
| ~ aNaturalNumber0(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f167,f225]) ).
fof(f448,plain,
! [X0] :
( sP2_prd(sK3_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f165]) ).
fof(f569,plain,
( ~ sP2_prd(sK3_skl(xk))
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f166,f250]) ).
fof(f574,plain,
( ~ sP2_prd(sK3_skl(xk))
| xk = sz10
| xk = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f207]) ).
fof(f581,plain,
( ~ sP2_prd(sK3_skl(xk))
| xk = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f211]) ).
fof(f582,plain,
( xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk)
| xk = sz10 ),
inference(resolution,[status(thm)],[f581,f448]) ).
fof(f584,plain,
( xk = sz00
| ~ aNaturalNumber0(xk)
| xk = sz10 ),
inference(duplicate_literals_removal,[status(thm)],[f582]) ).
fof(f585,plain,
( xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f212]) ).
fof(f607,plain,
sz00 != sz00,
inference(backward_demodulation,[status(thm)],[f611,f211]) ).
fof(f611,plain,
xk = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f585,f207]) ).
fof(f619,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 02:40:08 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.41 % Drodi V4.1.1
% 0.11/0.47 % Refutation found
% 0.11/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.51 % Elapsed time: 0.097861 seconds
% 0.11/0.51 % CPU time: 0.491831 seconds
% 0.11/0.51 % Total memory used: 113.069 MB
% 0.11/0.51 % Net memory used: 112.270 MB
%------------------------------------------------------------------------------