%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:40:44 PM UTC 2026
% Result : Theorem 4.71s 1.10s
% Output : CNFRefutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 16 unt; 2 def)
% Number of atoms : 190 ( 36 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 227 ( 97 ~; 95 |; 24 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 61 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/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/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(f33,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,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(f42,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f57,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f96,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(f97,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)],[f96]) ).
fof(f98,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)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) = X1
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,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))],[f131]) ).
fof(f135,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f144,plain,
! [W0,W1,W2] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f145,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f167,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f169,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f175,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f179,plain,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f180,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f181,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f184,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f185,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f135]) ).
fof(f195,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f58]) ).
fof(f335,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[f71,f169]) ).
fof(f395,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f335,f195]) ).
fof(f399,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(xp,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f169]) ).
fof(f631,plain,
doDivides0(xp,xp),
inference(forward_subsumption_resolution,[status(thm)],[f399,f53]) ).
fof(f796,plain,
doDivides0(xp,xr),
inference(forward_subsumption_resolution,[status(thm)],[f179,f182]) ).
fof(f798,plain,
! [X0] :
( doDivides0(xp,sdtpldt0(X0,xr))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f796,f145]) ).
fof(f801,plain,
! [X0] :
( doDivides0(xp,sdtpldt0(X0,xr))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f798,f169]) ).
fof(f1383,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f184,f174]) ).
fof(f1387,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[status(thm)],[f175,f1383]) ).
fof(f1388,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f1387,f169]) ).
fof(f1392,plain,
( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f185,f174]) ).
fof(f1396,plain,
( sdtpldt0(xp,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[status(thm)],[f175,f1392]) ).
fof(f1397,plain,
( sdtpldt0(xp,xr) = xn
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f1396,f169]) ).
fof(f1401,plain,
! [X0] :
( doDivides0(xp,sdtpldt0(X0,xr))
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f801,f1404]) ).
fof(f1404,plain,
aNaturalNumber0(xr),
inference(forward_subsumption_resolution,[status(thm)],[f1388,f167]) ).
fof(f3132,plain,
sdtpldt0(xp,xr) = xn,
inference(forward_subsumption_resolution,[status(thm)],[f1397,f167]) ).
fof(f3138,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f3132,f1401]) ).
fof(f3148,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f3138,f169]) ).
fof(f3264,plain,
doDivides0(xp,xn),
inference(forward_subsumption_resolution,[status(thm)],[f3148,f631]) ).
fof(f3265,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f181,f3264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:40:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 4.71/1.10 % Refutation found
% 4.71/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.71/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.48/1.13 % Elapsed time: 0.766503 seconds
% 5.48/1.13 % CPU time: 5.726396 seconds
% 5.48/1.13 % Total memory used: 145.501 MB
% 5.48/1.13 % Net memory used: 140.045 MB
%------------------------------------------------------------------------------