%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM490+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 : n018.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 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 50 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 56 ( 20 ~; 12 |; 23 &)
% ( 0 <=>; 1 =>; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 5 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(f46,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
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(f189,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK5_skl),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f204,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f205,plain,
( sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f206,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f247,plain,
sdtasdt0(xp,sK5_skl) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(forward_demodulation,[status(thm)],[f189,f204]) ).
fof(f248,plain,
sdtasdt0(xp,sK5_skl) != sdtasdt0(xn,xm),
inference(forward_demodulation,[status(thm)],[f247,f206]) ).
fof(f249,plain,
sdtasdt0(xp,sK5_skl) != sdtasdt0(xp,sK5_skl),
inference(forward_demodulation,[status(thm)],[f189,f248]) ).
fof(f250,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM490+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:36:29 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.62 % Elapsed time: 0.145233 seconds
% 0.23/0.62 % CPU time: 0.186540 seconds
% 0.23/0.62 % Total memory used: 27.611 MB
% 0.23/0.62 % Net memory used: 27.503 MB
%------------------------------------------------------------------------------