%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM489+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 : n011.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 01:40:42 PM UTC 2026
% Result : Theorem 0.15s 5.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 14 unt; 5 def)
% Number of atoms : 88 ( 23 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 89 ( 36 ~; 36 |; 9 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f45,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f94,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(f95,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)],[f94]) ).
fof(f96,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)],[f95]) ).
fof(f98,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) = X1
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f165,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f167,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f172,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f173,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f176,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f179,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f98]) ).
fof(f275,definition,
( sQ10_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ10_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ11_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ11_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,definition,
( sQ12_spl
<=> sdtlseqdt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ12_spl
| ~ sdtlseqdt0(xp,xn) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f288,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f172]) ).
fof(f289,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f165]) ).
fof(f291,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f292,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f167]) ).
fof(f293,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f439,plain,
( sdtpldt0(xp,xr) = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f173,f179]) ).
fof(f441,definition,
( sQ31_spl
<=> sdtpldt0(xp,xr) = xn ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ31_spl
| sdtpldt0(xp,xr) = xn ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f439,f275,f278,f281,f441]) ).
fof(f446,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f176]) ).
fof(f447,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f446]) ).
fof(f448,plain,
$false,
inference(sat_refutation,[status(thm)],[f289,f291,f293,f444,f447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.41 % Computer : n011.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Mon Sep 21 02:34:45 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.43 % Drodi V4.1.1
% 0.15/5.48 % Refutation found
% 0.15/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.50 % Elapsed time: 0.071509 seconds
% 0.20/5.50 % CPU time: 0.290953 seconds
% 0.20/5.50 % Total memory used: 80.115 MB
% 0.20/5.50 % Net memory used: 79.854 MB
%------------------------------------------------------------------------------