%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM501+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 59.40s 8.49s
% Output : CNFRefutation 59.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 19 unt; 1 def)
% Number of atoms : 213 ( 59 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 254 ( 98 ~; 81 |; 66 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 65 ( 54 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& ! [W0] :
( ( ( doDivides0(W0,xr)
| ? [W1] :
( xr = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xr
| W0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
( doDivides0(xr,sdtasdt0(xn,xm))
| ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,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(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f68,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f132,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(f133,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)],[f132]) ).
fof(f134,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))],[f133]) ).
fof(f137,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f144,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W1,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
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(f190,plain,
aNaturalNumber0(sK5_skl),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f191,plain,
sdtasdt0(xp,sK5_skl) = sdtasdt0(xn,xm),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f208,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f209,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f216,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f217,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK8_skl)
& aNaturalNumber0(sK8_skl)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W0,sK8_skl)],[f216]) ).
fof(f218,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f221,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f227,plain,
( ~ doDivides0(xr,sdtasdt0(xn,xm))
& ! [W0] :
( sdtasdt0(xn,xm) != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f229,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f257,plain,
~ doDivides0(xr,sdtasdt0(xp,sK5_skl)),
inference(forward_demodulation,[status(thm)],[f191,f229]) ).
fof(f264,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,sK5_skl),
inference(forward_demodulation,[status(thm)],[f191,f209]) ).
fof(f274,plain,
! [X0,X2] :
( ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f276,plain,
! [X0,X1] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f60]) ).
fof(f303,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
inference(resolution,[status(thm)],[f69,f171]) ).
fof(f309,plain,
! [X0] :
( sdtasdt0(X0,xk) = sdtasdt0(xk,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f69,f208]) ).
fof(f318,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(resolution,[status(thm)],[f309,f171]) ).
fof(f330,plain,
sdtasdt0(xp,sK5_skl) = sdtasdt0(xk,xp),
inference(forward_demodulation,[status(thm)],[f264,f318]) ).
fof(f403,plain,
( doDivides0(xk,sdtasdt0(xp,sK5_skl))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(paramodulation,[status(thm)],[f330,f276]) ).
fof(f404,plain,
( aNaturalNumber0(sdtasdt0(xp,sK5_skl))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f330,f60]) ).
fof(f405,plain,
( doDivides0(xk,sdtasdt0(xp,sK5_skl))
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f208]) ).
fof(f406,plain,
( aNaturalNumber0(sdtasdt0(xp,sK5_skl))
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f171]) ).
fof(f407,plain,
aNaturalNumber0(sdtasdt0(xp,sK5_skl)),
inference(resolution,[status(thm)],[f406,f208]) ).
fof(f421,plain,
sdtasdt0(sK5_skl,xp) = sdtasdt0(xp,sK5_skl),
inference(resolution,[status(thm)],[f303,f190]) ).
fof(f431,plain,
aNaturalNumber0(sdtasdt0(sK5_skl,xp)),
inference(backward_demodulation,[status(thm)],[f421,f407]) ).
fof(f436,plain,
~ doDivides0(xr,sdtasdt0(sK5_skl,xp)),
inference(backward_demodulation,[status(thm)],[f421,f257]) ).
fof(f445,plain,
( doDivides0(xk,sdtasdt0(sK5_skl,xp))
| ~ aNaturalNumber0(xp) ),
inference(backward_demodulation,[status(thm)],[f421,f405]) ).
fof(f455,plain,
doDivides0(xk,sdtasdt0(sK5_skl,xp)),
inference(forward_subsumption_resolution,[status(thm)],[f445,f171]) ).
fof(f628,plain,
! [X0] :
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sK5_skl,xp))
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtasdt0(sK5_skl,xp)) ),
inference(resolution,[status(thm)],[f145,f436]) ).
fof(f633,plain,
! [X0] :
( ~ doDivides0(X0,sdtasdt0(sK5_skl,xp))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f431]) ).
fof(f640,plain,
! [X0] :
( ~ doDivides0(xr,X0)
| ~ doDivides0(X0,sdtasdt0(sK5_skl,xp))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f633,f218]) ).
fof(f642,plain,
( ~ doDivides0(xk,sdtasdt0(sK5_skl,xp))
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[f640,f221]) ).
fof(f646,plain,
~ doDivides0(xk,sdtasdt0(sK5_skl,xp)),
inference(forward_subsumption_resolution,[status(thm)],[f642,f208]) ).
fof(f647,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f455,f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM501+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n026.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 02:38:08 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.14/0.58 % Drodi V4.1.1
% 59.40/8.49 % Refutation found
% 59.40/8.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 59.40/8.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 62.11/8.56 % Elapsed time: 7.973199 seconds
% 62.11/8.56 % CPU time: 62.717519 seconds
% 62.11/8.56 % Total memory used: 266.318 MB
% 62.11/8.56 % Net memory used: 249.452 MB
%------------------------------------------------------------------------------