%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM514+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 : n014.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 01:40:48 PM UTC 2026
% Result : Theorem 0.12s 0.59s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 8 unt; 3 def)
% Number of atoms : 94 ( 17 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 100 ( 37 ~; 34 |; 21 &)
% ( 4 <=>; 4 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 24 !; 5 ?)
% 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(f55,hypothesis,
( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,conjecture,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f66,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f139,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(f140,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)],[f139]) ).
fof(f141,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))],[f140]) ).
fof(f144,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f178,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f271,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f275,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f276,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ! [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f280,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f346,plain,
! [X0,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f144]) ).
fof(f347,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f67]) ).
fof(f373,plain,
~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
inference(forward_demodulation,[status(thm)],[f275,f280]) ).
fof(f616,definition,
( sQ45_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ45_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f631,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f618,f178]) ).
fof(f632,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f633,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f347,f373]) ).
fof(f634,definition,
( sQ49_spl
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ49_spl
| ~ aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,plain,
( ~ sQ49_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f633,f616,f634]) ).
fof(f638,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f271]) ).
fof(f639,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f640,plain,
$false,
inference(sat_refutation,[status(thm)],[f632,f637,f639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM514+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.53 % Computer : n014.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Mon Sep 21 02:37:06 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.55 % Drodi V4.1.1
% 0.12/0.59 % Refutation found
% 0.12/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.63 % Elapsed time: 0.082799 seconds
% 0.12/0.63 % CPU time: 0.257129 seconds
% 0.12/0.63 % Total memory used: 109.469 MB
% 0.12/0.63 % Net memory used: 109.219 MB
%------------------------------------------------------------------------------