%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM508+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 01:40:47 PM UTC 2026
% Result : Theorem 41.36s 5.72s
% Output : CNFRefutation 33.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 29
% Syntax : Number of formulae : 109 ( 20 unt; 18 def)
% Number of atoms : 350 ( 24 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 423 ( 182 ~; 186 |; 26 &)
% ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 68 ( 65 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f58,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f60,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f75,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f76,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f133,plain,
! [W0,W1] :
( iLess0(W0,W1)
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f134,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,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(f136,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)],[f135]) ).
fof(f137,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))],[f136]) ).
fof(f140,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f147,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W1,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f148,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
! [W0,W1,W2] :
( doDivides0(W2,W1)
| doDivides0(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(W2,sdtasdt0(W0,W1))
| ~ isPrime0(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f176,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f191,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f193,plain,
isPrime0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f195,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f198,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f199,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f200,plain,
( ~ doDivides0(xr,xm)
& ~ doDivides0(xr,xn) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f201,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f207,plain,
! [X0] :
( ~ doDivides0(X0,xm)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f148,f202]) ).
fof(f208,plain,
! [X0] :
( ~ doDivides0(X0,xn)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f148,f201]) ).
fof(f211,definition,
( sQ0_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ0_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X0] :
( sQ1_spl
<=> ( ~ doDivides0(X0,xm)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0] :
( ~ sQ1_spl
| ~ doDivides0(X0,xm)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
( sQ2_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( sQ2_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f207,f211,f214,f217]) ).
fof(f221,definition,
! [X0] :
( sQ3_spl
<=> ( ~ doDivides0(X0,xn)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f222,plain,
! [X0] :
( ~ sQ3_spl
| ~ doDivides0(X0,xn)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ4_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ4_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f208,f211,f221,f224]) ).
fof(f245,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f213]) ).
fof(f246,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f261,definition,
( sQ7_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ7_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f291,plain,
! [X0] :
( ~ aNaturalNumber0(sz10)
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f76,f140]) ).
fof(f293,definition,
! [X0] :
( sQ12_spl
<=> ( doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f294,plain,
! [X0] :
( ~ sQ12_spl
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ13_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ13_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f291,f293,f296]) ).
fof(f300,plain,
! [X0] :
( ~ sQ12_spl
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f294]) ).
fof(f346,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f58]) ).
fof(f347,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f388,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f173]) ).
fof(f389,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f472,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f300,f222]) ).
fof(f473,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ doDivides0(xr,xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f300,f215]) ).
fof(f476,definition,
( sQ39_spl
<=> doDivides0(xr,xn) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ39_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f472,f211,f476,f293,f221]) ).
fof(f480,definition,
( sQ40_spl
<=> doDivides0(xr,xm) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ40_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f473,f211,f480,f293,f214]) ).
fof(f523,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f172]) ).
fof(f524,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f892,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f174]) ).
fof(f893,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f892]) ).
fof(f912,definition,
( sQ95_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f914,plain,
( sQ95_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f915,definition,
( sQ96_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f917,plain,
( sQ96_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f921,definition,
( sQ98_spl
<=> sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f922,plain,
( ~ sQ98_spl
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(component_clause,[status(thm)],[f921]) ).
fof(f951,plain,
( ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f922,f198]) ).
fof(f952,plain,
~ sQ98_spl,
inference(contradiction_clause,[status(thm)],[f951]) ).
fof(f2242,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(X0,X1),X2))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f176,f134]) ).
fof(f2243,definition,
! [X0,X1,X2] :
( sQ218_spl
<=> ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(X0,X1),X2))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2244,plain,
! [X0,X1,X2] :
( ~ sQ218_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(X0,X1),X2))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f2243]) ).
fof(f2246,plain,
( ~ sQ95_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2242,f2243,f912]) ).
fof(f2585,plain,
( sQ95_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f61,f914]) ).
fof(f2586,definition,
( sQ265_spl
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2588,plain,
( sQ265_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f2586]) ).
fof(f2589,plain,
( sQ95_spl
| ~ sQ7_spl
| ~ sQ265_spl ),
inference(split_clause,[status(thm)],[f2585,f2586,f261,f912]) ).
fof(f3201,definition,
( sQ343_spl
<=> isPrime0(xr) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f3203,plain,
( sQ343_spl
| ~ isPrime0(xr) ),
inference(component_clause,[status(thm)],[f3201]) ).
fof(f3232,plain,
( sQ343_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3203,f193]) ).
fof(f3233,plain,
sQ343_spl,
inference(contradiction_clause,[status(thm)],[f3232]) ).
fof(f5963,plain,
( sQ265_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2588,f61]) ).
fof(f5965,plain,
( sQ265_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5963,f224,f217,f2586]) ).
fof(f11736,plain,
( sQ96_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f917,f61]) ).
fof(f11738,plain,
( sQ96_spl
| ~ sQ0_spl
| ~ sQ265_spl ),
inference(split_clause,[status(thm)],[f11736,f2586,f211,f915]) ).
fof(f13029,plain,
( ~ sQ218_spl
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ isPrime0(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f2244,f199]) ).
fof(f13040,definition,
( sQ1309_spl
<=> doDivides0(xr,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ1309_spl])],[split_symbol_definition]) ).
fof(f13042,plain,
( sQ1309_spl
| ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f13040]) ).
fof(f13043,plain,
( ~ sQ218_spl
| sQ98_spl
| ~ sQ96_spl
| sQ40_spl
| sQ39_spl
| ~ sQ1309_spl
| ~ sQ343_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f13029,f224,f217,f211,f3201,f13040,f476,f480,f915,f921,f2243]) ).
fof(f13098,plain,
( sQ1309_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13042,f195]) ).
fof(f13099,plain,
sQ1309_spl,
inference(contradiction_clause,[status(thm)],[f13098]) ).
fof(f13100,plain,
$false,
inference(sat_refutation,[status(thm)],[f220,f227,f246,f299,f347,f389,f479,f483,f524,f893,f952,f2246,f2589,f3233,f5965,f11738,f13043,f13099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM508+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:35:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 41.36/5.72 % Refutation found
% 41.36/5.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 41.36/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 33.11/5.75 % Elapsed time: 5.379963 seconds
% 33.11/5.75 % CPU time: 42.405891 seconds
% 33.11/5.75 % Total memory used: 281.281 MB
% 33.11/5.75 % Net memory used: 260.325 MB
%------------------------------------------------------------------------------