%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM492+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 0.15s 6.38s
% Output : CNFRefutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 18 unt; 1 def)
% Number of atoms : 127 ( 17 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 156 ( 73 ~; 61 |; 15 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
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))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
xr = sdtmndt0(xn,xp),
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))
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
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(f98,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f99,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [W0,W1] :
( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ! [W2] :
( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
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(f169,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f170,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f171,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f176,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f177,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f181,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f184,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f185,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f187,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f101]) ).
fof(f290,plain,
! [X0] :
( ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f149,f185]) ).
fof(f291,plain,
! [X0] :
( ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f171]) ).
fof(f358,plain,
! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f291,f60]) ).
fof(f359,plain,
! [X0] :
( ~ aNaturalNumber0(xr)
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f170]) ).
fof(f1165,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f187,f176]) ).
fof(f1169,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[status(thm)],[f177,f1165]) ).
fof(f1170,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f1169,f171]) ).
fof(f1174,plain,
! [X0] :
( ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm)))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f359,f1177]) ).
fof(f1177,plain,
aNaturalNumber0(xr),
inference(forward_subsumption_resolution,[status(thm)],[f1170,f169]) ).
fof(f1256,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(paramodulation,[status(thm)],[f181,f1174]) ).
fof(f1260,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1256,f184]) ).
fof(f2050,plain,
~ aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[f1260,f175]) ).
fof(f2051,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f2050,f60]) ).
fof(f2052,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[status(thm)],[f2051,f171]) ).
fof(f2055,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2052,f170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM492+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n003.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 02:36:21 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.15/5.40 % Drodi V4.1.1
% 0.15/6.38 % Refutation found
% 0.15/6.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/6.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.16/6.43 % Elapsed time: 1.025113 seconds
% 7.16/6.43 % CPU time: 7.593242 seconds
% 7.16/6.43 % Total memory used: 149.790 MB
% 7.16/6.43 % Net memory used: 143.730 MB
%------------------------------------------------------------------------------