%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM491+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 : n003.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 01:40:43 PM UTC 2026
% Result : Theorem 0.10s 0.61s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 8 unt; 3 def)
% Number of atoms : 74 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 80 ( 33 ~; 31 |; 10 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
doDivides0(xp,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f48]) ).
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(f131,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f132,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f132]) ).
fof(f136,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f169,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f170,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f182,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f136]) ).
fof(f202,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ1_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ1_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f59]) ).
fof(f219,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f218,f182]) ).
fof(f221,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f219,f205,f202]) ).
fof(f226,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f170]) ).
fof(f227,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f169]) ).
fof(f229,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
$false,
inference(sat_refutation,[status(thm)],[f221,f227,f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM491+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n003.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Mon Sep 21 02:36:04 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 0.10/0.61 % Refutation found
% 0.10/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.65 % Elapsed time: 0.051226 seconds
% 0.13/0.65 % CPU time: 0.149429 seconds
% 0.13/0.65 % Total memory used: 97.725 MB
% 0.13/0.65 % Net memory used: 97.663 MB
%------------------------------------------------------------------------------