%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM475+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 : n016.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 01:40:39 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 24 unt; 2 def)
% Number of atoms : 209 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 250 ( 108 ~; 107 |; 23 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
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(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f50,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f74,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f75,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f91,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(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f131,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f132,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f141,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f142,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f143,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f144,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f145,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f146,plain,
xl != sz00,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f147,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f148,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f149,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f150,plain,
xr = sdtmndt0(xq,xp),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f151,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f152,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f154,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f160,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f173,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f150,f154]) ).
fof(f174,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f149]) ).
fof(f188,plain,
( sdtasdt0(xl,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(resolution,[status(thm)],[f75,f151]) ).
fof(f197,plain,
( sdtasdt0(xl,xr) = xn
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f143]) ).
fof(f212,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f152]) ).
fof(f213,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(resolution,[status(thm)],[f212,f53]) ).
fof(f214,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f141]) ).
fof(f215,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f214,f53]) ).
fof(f216,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f141]) ).
fof(f217,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(backward_subsumption_resolution,[status(thm)],[f174,f216]) ).
fof(f292,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| xl = sz00
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f148,f160]) ).
fof(f293,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| xl = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f147,f160]) ).
fof(f294,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| xl = sz00
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f141]) ).
fof(f295,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| xl = sz00
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f141]) ).
fof(f296,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f146]) ).
fof(f297,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[f296,f145]) ).
fof(f298,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[f297,f51]) ).
fof(f299,plain,
( ~ aNaturalNumber0(xn)
| aNaturalNumber0(xq) ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f142]) ).
fof(f300,plain,
~ aNaturalNumber0(xp),
inference(backward_subsumption_resolution,[status(thm)],[f217,f301]) ).
fof(f301,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[status(thm)],[f299,f143]) ).
fof(f302,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| xl = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f142]) ).
fof(f303,plain,
( aNaturalNumber0(xp)
| xl = sz00 ),
inference(resolution,[status(thm)],[f302,f144]) ).
fof(f304,plain,
aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[status(thm)],[f303,f146]) ).
fof(f305,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f304,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:38:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.069533 seconds
% 0.09/0.44 % CPU time: 0.228753 seconds
% 0.09/0.44 % Total memory used: 105.383 MB
% 0.09/0.44 % Net memory used: 105.131 MB
%------------------------------------------------------------------------------