%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM458+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 : n026.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 12 unt; 4 def)
% Number of atoms : 82 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 83 ( 34 ~; 33 |; 9 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
sdtlseqdt0(xm,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ sdtlseqdt0(xm,xm),
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(f64,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sK0_skl(W1,W0)) = W1
& aNaturalNumber0(sK0_skl(W1,W0)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f65]) ).
fof(f69,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f76,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f77,plain,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f84,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[f38,f76]) ).
fof(f85,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(xm,sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f84,f78]) ).
fof(f86,definition,
( sQ0_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ0_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,definition,
( sQ1_spl
<=> sdtlseqdt0(xm,sdtpldt0(xm,sz00)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ1_spl
| sdtlseqdt0(xm,sdtpldt0(xm,sz00)) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
( sQ2_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ2_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f86,f89,f92]) ).
fof(f96,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f26]) ).
fof(f97,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f76]) ).
fof(f99,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f100,plain,
( ~ sQ1_spl
| sdtlseqdt0(xm,xm) ),
inference(forward_demodulation,[status(thm)],[f84,f90]) ).
fof(f101,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f77]) ).
fof(f102,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f103,plain,
$false,
inference(sat_refutation,[status(thm)],[f95,f97,f99,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.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 02:34:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.050460 seconds
% 0.09/0.42 % CPU time: 0.144136 seconds
% 0.09/0.42 % Total memory used: 80.651 MB
% 0.09/0.42 % Net memory used: 80.378 MB
%------------------------------------------------------------------------------