%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM472+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 01:40:39 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 11 unt; 4 def)
% Number of atoms : 83 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 33 |; 10 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
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(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f82,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(f83,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)],[f82]) ).
fof(f84,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))],[f83]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f139,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f140,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f146,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f87]) ).
fof(f161,definition,
( sQ1_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ1_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f179,definition,
( sQ5_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ5_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f183,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f139]) ).
fof(f184,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f140]) ).
fof(f186,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f214,definition,
( sQ8_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ8_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f223,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f44]) ).
fof(f224,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f226,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f48]) ).
fof(f227,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f226,f146]) ).
fof(f229,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f227,f161,f179]) ).
fof(f232,plain,
$false,
inference(sat_refutation,[status(thm)],[f184,f186,f224,f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM472+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n011.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 02:32:55 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.50 % Refutation found
% 0.16/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.51 % Elapsed time: 0.072575 seconds
% 0.16/0.51 % CPU time: 0.166195 seconds
% 0.16/0.51 % Total memory used: 68.190 MB
% 0.16/0.51 % Net memory used: 68.138 MB
%------------------------------------------------------------------------------