%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 01:40:36 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 7 unt; 2 def)
% Number of atoms : 42 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 14 ~; 12 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
( sdtlseqdt0(xm,xm)
| ? [W0] :
( sdtpldt0(xm,W0) = xm
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ( sdtlseqdt0(xm,xm)
| ? [W0] :
( sdtpldt0(xm,W0) = xm
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f26,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f76,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f77,plain,
( ~ sdtlseqdt0(xm,xm)
& ! [W0] :
( sdtpldt0(xm,W0) != xm
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
! [X0] :
( sdtpldt0(xm,X0) != xm
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f105,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f38,f78]) ).
fof(f108,definition,
( sQ2_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ2_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ3_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ3_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f105,f108,f111]) ).
fof(f120,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f26]) ).
fof(f121,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f76]) ).
fof(f123,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f122]) ).
fof(f124,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f121,f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:32:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.055974 seconds
% 0.13/0.43 % CPU time: 0.151627 seconds
% 0.13/0.43 % Total memory used: 80.755 MB
% 0.13/0.43 % Net memory used: 80.495 MB
%------------------------------------------------------------------------------