%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM492+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 : n010.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 0.14s 0.94s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 137 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 159 ( 63 ~; 51 |; 41 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 31 ( 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,sdtpldt0(W1,W2))
& doDivides0(W0,W1) )
=> doDivides0(W0,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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( doDivides0(xp,sdtasdt0(xp,xm))
& ? [W0] :
( sdtasdt0(xp,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
( doDivides0(xp,sdtasdt0(xr,xm))
| ? [W0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xr,xm))
| ? [W0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f59,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f148,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f149,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f170,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f171,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f183,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(f184,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)],[f183]) ).
fof(f191,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK5_skl),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f192,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f197,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f206,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f209,plain,
( doDivides0(xp,sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) = sdtasdt0(xp,sK9_skl)
& aNaturalNumber0(sK9_skl)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK8_skl)
& aNaturalNumber0(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(W0,sK8_skl),skolemize(W0,sK9_skl)],[f48]) ).
fof(f212,plain,
aNaturalNumber0(sK9_skl),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f213,plain,
sdtasdt0(xp,xm) = sdtasdt0(xp,sK9_skl),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f214,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f215,plain,
( ~ doDivides0(xp,sdtasdt0(xr,xm))
& ! [W0] :
( sdtasdt0(xr,xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f217,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f300,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(xr,xm))
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f206,f149]) ).
fof(f476,plain,
doDivides0(xp,sdtasdt0(xp,sK5_skl)),
inference(backward_demodulation,[status(thm)],[f191,f192]) ).
fof(f539,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK9_skl)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f213,f60]) ).
fof(f549,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK9_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f171]) ).
fof(f652,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[f549,f212]) ).
fof(f1585,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(xr,xm))
| ~ doDivides0(X0,sdtasdt0(xp,sK5_skl))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f191,f300]) ).
fof(f1586,plain,
! [X0] :
( doDivides0(X0,sdtasdt0(xr,xm))
| ~ doDivides0(X0,sdtasdt0(xp,sK5_skl))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1585,f652]) ).
fof(f1603,plain,
( ~ doDivides0(xp,sdtasdt0(xp,sK5_skl))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1586,f217]) ).
fof(f1641,plain,
( ~ doDivides0(xp,sdtasdt0(xp,sK5_skl))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1603,f171]) ).
fof(f1719,plain,
( ~ doDivides0(xp,sdtasdt0(xp,sK5_skl))
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1641,f214]) ).
fof(f1720,plain,
~ aNaturalNumber0(sdtasdt0(xr,xm)),
inference(resolution,[status(thm)],[f1719,f476]) ).
fof(f1732,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1720,f60]) ).
fof(f1733,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[status(thm)],[f1732,f197]) ).
fof(f1734,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1733,f170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM492+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:35:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.40 % Drodi V4.1.1
% 0.14/0.94 % Refutation found
% 0.14/0.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.47/0.98 % Elapsed time: 0.599402 seconds
% 2.47/0.98 % CPU time: 4.281995 seconds
% 2.47/0.98 % Total memory used: 136.774 MB
% 2.47/0.98 % Net memory used: 133.493 MB
%------------------------------------------------------------------------------