%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM523+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 : n014.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 01:40:50 PM UTC 2026
% Result : Theorem 4.69s 1.05s
% Output : CNFRefutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 14 unt; 9 def)
% Number of atoms : 161 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 71 ~; 70 |; 18 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f54,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f127,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f128,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f128]) ).
fof(f132,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f164,plain,
! [W0,W1,W2] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ doDivides0(W2,sdtasdt0(W0,W1))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f165,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f168,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f170,plain,
xm != sz00,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f174,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f175,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f176,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f177,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f178,definition,
( sQ0_spl
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ0_spl
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
( sQ1_spl
<=> doDivides0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f177,f178,f181]) ).
fof(f191,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f132]) ).
fof(f200,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f55]) ).
fof(f205,definition,
( sQ2_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ2_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f223,definition,
( sQ6_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ6_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f227,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f168]) ).
fof(f228,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f166]) ).
fof(f230,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f2118,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f174,f200]) ).
fof(f2135,definition,
( sQ209_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( sQ209_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f2135]) ).
fof(f2138,definition,
( sQ210_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2139,plain,
( ~ sQ210_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f2138]) ).
fof(f2144,definition,
( sQ212_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2146,plain,
( sQ212_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f2144]) ).
fof(f2155,definition,
( sQ215_spl
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2157,plain,
( sQ215_spl
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(component_clause,[status(thm)],[f2155]) ).
fof(f2207,plain,
( ~ sQ215_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f2118,f205,f178,f2155]) ).
fof(f2260,plain,
( sQ209_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2137,f167]) ).
fof(f2261,plain,
sQ209_spl,
inference(contradiction_clause,[status(thm)],[f2260]) ).
fof(f2263,plain,
( sQ212_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2146,f175]) ).
fof(f2264,plain,
sQ212_spl,
inference(contradiction_clause,[status(thm)],[f2263]) ).
fof(f2265,plain,
( ~ sQ210_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2139,f170]) ).
fof(f2266,plain,
~ sQ210_spl,
inference(contradiction_clause,[status(thm)],[f2265]) ).
fof(f2475,plain,
( sQ215_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2157,f55]) ).
fof(f2476,plain,
( sQ215_spl
| ~ sQ209_spl ),
inference(split_clause,[status(thm)],[f2475,f2135,f2155]) ).
fof(f2493,plain,
( ~ sQ0_spl
| doDivides0(xp,xn)
| doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f179,f165]) ).
fof(f2502,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ212_spl
| ~ sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2493,f223,f205,f2144,f181,f178]) ).
fof(f2522,plain,
$false,
inference(sat_refutation,[status(thm)],[f184,f228,f230,f2207,f2261,f2264,f2266,f2476,f2502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:37:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 4.69/1.05 % Refutation found
% 4.69/1.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.69/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.69/1.07 % Elapsed time: 0.698497 seconds
% 4.69/1.07 % CPU time: 5.131603 seconds
% 4.69/1.07 % Total memory used: 140.389 MB
% 4.69/1.07 % Net memory used: 136.463 MB
%------------------------------------------------------------------------------