%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM498+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 01:40:45 PM UTC 2026
% Result : Theorem 10.25s 1.83s
% Output : CNFRefutation 8.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 167 ( 24 unt; 28 def)
% Number of atoms : 516 ( 137 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 601 ( 252 ~; 257 |; 48 &)
% ( 31 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 26 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 80 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
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(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
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(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f52,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f56,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f65,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f70,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0] :
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f73,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f87,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f88,plain,
! [X0,X1] :
( X1 = sz00
| X0 = sz00
| sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f129,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(f130,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)],[f129]) ).
fof(f131,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))],[f130]) ).
fof(f134,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f136,plain,
! [W0,W1] :
( ! [W2] :
( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [W0,W1] :
( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| W2 = sdtsldt0(W1,W0) )
& ! [W2] :
( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0,X1,X2] :
( X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f151,plain,
! [W0] :
( ( isPrime0(W0)
<=> ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 ) )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f152,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [W0] :
( ( ( ( sK2_skl(W0) != W0
& sK2_skl(W0) != sz10
& doDivides0(sK2_skl(W0),W0)
& aNaturalNumber0(sK2_skl(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f152]) ).
fof(f154,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [X0] :
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f156,plain,
! [X0,X1] :
( X1 = X0
| X1 = sz10
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f171,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f172,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f175,plain,
xn != xp,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,plain,
xm != xp,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f179,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f180,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn)
& ( xk = sz10
| xk = sz00 ) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f181,plain,
( xk = sz10
| xk = sz00 ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f183,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f184,definition,
( sQ0_spl
<=> xk = sz00 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ0_spl
| xk = sz00 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
( sQ1_spl
<=> xk = sz10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ1_spl
| xk = sz10 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f181,f184,f187]) ).
fof(f196,definition,
( sQ2_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ2_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f235,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f52]) ).
fof(f236,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f245,definition,
( sQ9_spl
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ9_spl
| ~ aNaturalNumber0(sz00) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f255,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f51]) ).
fof(f256,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f154,f171]) ).
fof(f258,definition,
( sQ11_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ11_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ12_spl
<=> xp = sz00 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f257,f258,f261]) ).
fof(f265,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f168]) ).
fof(f266,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f269,plain,
( ~ sQ0_spl
| sz00 = sdtsldt0(sdtasdt0(xn,xm),xp) ),
inference(forward_demodulation,[status(thm)],[f185,f179]) ).
fof(f271,definition,
( sQ13_spl
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ13_spl
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
( sQ14_spl
<=> sdtasdt0(xn,xm) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ14_spl
| sdtasdt0(xn,xm) = sz00 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f285,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X1,X0))
| ~ aNaturalNumber0(sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f134,f66]) ).
fof(f289,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f134,f73]) ).
fof(f294,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[f134]) ).
fof(f306,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X1,X0))
| ~ aNaturalNumber0(sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f285]) ).
fof(f307,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f57]) ).
fof(f316,definition,
! [X0] :
( sQ19_spl
<=> ( ~ aNaturalNumber0(X0)
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f317,plain,
! [X0] :
( ~ sQ19_spl
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( ~ sQ9_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f289,f316,f245]) ).
fof(f328,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f57]) ).
fof(f331,plain,
! [X0] :
( ~ sQ19_spl
| doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f317]) ).
fof(f347,definition,
( sQ23_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ23_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f354,definition,
( sQ25_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ25_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f418,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f167]) ).
fof(f419,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f436,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f166]) ).
fof(f437,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f480,plain,
( sQ13_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f273,f57]) ).
fof(f481,plain,
( sQ13_spl
| ~ sQ23_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f480,f354,f347,f271]) ).
fof(f484,plain,
( ~ sQ14_spl
| xm = sz00
| xn = sz00
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f275,f88]) ).
fof(f496,definition,
( sQ42_spl
<=> xn = sz00 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( ~ sQ42_spl
| xn = sz00 ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,definition,
( sQ43_spl
<=> xm = sz00 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ43_spl
| xm = sz00 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ14_spl
| sQ43_spl
| sQ42_spl
| ~ sQ23_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f484,f354,f347,f496,f499,f274]) ).
fof(f542,plain,
( ~ sQ43_spl
| ~ doDivides0(xp,sz00) ),
inference(backward_demodulation,[status(thm)],[f500,f183]) ).
fof(f552,plain,
( ~ sQ19_spl
| ~ sQ43_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f542,f331]) ).
fof(f554,plain,
( ~ sQ19_spl
| ~ sQ43_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f552,f258,f499,f316]) ).
fof(f563,plain,
( ~ sQ42_spl
| ~ doDivides0(xp,sz00) ),
inference(backward_demodulation,[status(thm)],[f497,f182]) ).
fof(f678,definition,
( sQ60_spl
<=> xp = xn ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( ~ sQ60_spl
| xp = xn ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f685,definition,
( sQ62_spl
<=> xp = xm ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( ~ sQ62_spl
| xp = xm ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f719,plain,
( xp != sz10
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f155,f171]) ).
fof(f720,definition,
( sQ67_spl
<=> xp = sz10 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( ~ sQ67_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f719,f258,f720]) ).
fof(f818,definition,
( sQ83_spl
<=> sdtasdt0(xn,xm) = xp ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( ~ sQ83_spl
| sdtasdt0(xn,xm) = xp ),
inference(component_clause,[status(thm)],[f818]) ).
fof(f1684,definition,
( sQ195_spl
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1686,plain,
( sQ195_spl
| ~ doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f1684]) ).
fof(f1692,plain,
( sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1686,f172]) ).
fof(f1693,plain,
sQ195_spl,
inference(contradiction_clause,[status(thm)],[f1692]) ).
fof(f1788,plain,
( ~ sQ0_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f139,f269]) ).
fof(f1798,definition,
( sQ204_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1799,plain,
( ~ sQ204_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz00) ),
inference(component_clause,[status(thm)],[f1798]) ).
fof(f1801,plain,
( ~ sQ0_spl
| sQ204_spl
| ~ sQ195_spl
| sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1788,f258,f271,f261,f1684,f1798,f184]) ).
fof(f1826,plain,
( ~ sQ1_spl
| sz10 = sdtsldt0(sdtasdt0(xn,xm),xp) ),
inference(forward_demodulation,[status(thm)],[f188,f179]) ).
fof(f1827,plain,
( ~ sQ1_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f1826,f139]) ).
fof(f1833,definition,
( sQ206_spl
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,sz10) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1834,plain,
( ~ sQ206_spl
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz10) ),
inference(component_clause,[status(thm)],[f1833]) ).
fof(f1836,plain,
( ~ sQ1_spl
| sQ206_spl
| ~ sQ195_spl
| sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1827,f258,f271,f261,f1684,f1833,f187]) ).
fof(f1919,plain,
( ~ sQ206_spl
| sdtasdt0(xn,xm) = xp
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f1834,f70]) ).
fof(f1968,plain,
( ~ sQ206_spl
| sQ83_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1919,f258,f818,f1833]) ).
fof(f2125,plain,
( ~ sQ83_spl
| ~ aNaturalNumber0(xm)
| doDivides0(xn,xp)
| ~ aNaturalNumber0(xn) ),
inference(paramodulation,[status(thm)],[f819,f328]) ).
fof(f2130,plain,
( ~ sQ83_spl
| ~ aNaturalNumber0(xn)
| doDivides0(xm,xp)
| ~ aNaturalNumber0(xm) ),
inference(paramodulation,[status(thm)],[f819,f307]) ).
fof(f2146,definition,
( sQ249_spl
<=> doDivides0(xn,xp) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2147,plain,
( ~ sQ249_spl
| doDivides0(xn,xp) ),
inference(component_clause,[status(thm)],[f2146]) ).
fof(f2193,plain,
( ~ sQ83_spl
| ~ sQ23_spl
| sQ249_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f2125,f354,f2146,f347,f818]) ).
fof(f2210,definition,
( sQ265_spl
<=> doDivides0(xm,xp) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2211,plain,
( ~ sQ265_spl
| doDivides0(xm,xp) ),
inference(component_clause,[status(thm)],[f2210]) ).
fof(f2213,plain,
( ~ sQ83_spl
| ~ sQ25_spl
| sQ265_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2130,f347,f2210,f354,f818]) ).
fof(f2343,plain,
( ~ sQ19_spl
| ~ sQ42_spl
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f563,f331]) ).
fof(f2346,plain,
( ~ sQ19_spl
| ~ sQ42_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2343,f258,f496,f316]) ).
fof(f2395,definition,
( sQ286_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2397,plain,
( sQ286_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f2395]) ).
fof(f2424,plain,
( sQ286_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2397,f171]) ).
fof(f2425,plain,
sQ286_spl,
inference(contradiction_clause,[status(thm)],[f2424]) ).
fof(f2485,plain,
( ~ sQ249_spl
| xn = xp
| xn = sz10
| ~ aNaturalNumber0(xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f2147,f156]) ).
fof(f2491,definition,
( sQ297_spl
<=> xn = sz10 ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2492,plain,
( ~ sQ297_spl
| xn = sz10 ),
inference(component_clause,[status(thm)],[f2491]) ).
fof(f2494,plain,
( ~ sQ249_spl
| sQ60_spl
| sQ297_spl
| ~ sQ25_spl
| ~ sQ286_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2485,f258,f2395,f354,f2491,f678,f2146]) ).
fof(f2512,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f175]) ).
fof(f2513,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f2512]) ).
fof(f2516,plain,
( ~ sQ83_spl
| ~ sQ297_spl
| sdtasdt0(sz10,xm) = xp ),
inference(backward_demodulation,[status(thm)],[f2492,f819]) ).
fof(f2539,plain,
( ~ sQ265_spl
| xm = xp
| xm = sz10
| ~ aNaturalNumber0(xm)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f2211,f156]) ).
fof(f2545,definition,
( sQ304_spl
<=> xm = sz10 ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f2546,plain,
( ~ sQ304_spl
| xm = sz10 ),
inference(component_clause,[status(thm)],[f2545]) ).
fof(f2548,plain,
( ~ sQ265_spl
| sQ62_spl
| sQ304_spl
| ~ sQ23_spl
| ~ sQ286_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2539,f258,f2395,f347,f2545,f685,f2210]) ).
fof(f2566,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f686,f177]) ).
fof(f2567,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f2566]) ).
fof(f3292,plain,
( ~ sQ83_spl
| ~ sQ297_spl
| ~ sQ304_spl
| sdtasdt0(sz10,sz10) = xp ),
inference(forward_demodulation,[status(thm)],[f2546,f2516]) ).
fof(f3294,plain,
( ~ sQ83_spl
| ~ sQ297_spl
| ~ sQ304_spl
| sz10 = xp
| ~ aNaturalNumber0(sz10) ),
inference(paramodulation,[status(thm)],[f3292,f71]) ).
fof(f3329,plain,
( ~ sQ83_spl
| ~ sQ297_spl
| ~ sQ304_spl
| sQ67_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3294,f196,f720,f2545,f2491,f818]) ).
fof(f4901,plain,
( ~ sQ204_spl
| sdtasdt0(xn,xm) = sz00
| ~ aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f1799,f73]) ).
fof(f4950,plain,
( ~ sQ204_spl
| sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4901,f258,f274,f1798]) ).
fof(f5071,plain,
$false,
inference(sat_refutation,[status(thm)],[f190,f236,f256,f264,f266,f319,f419,f437,f481,f502,f554,f723,f1693,f1801,f1836,f1968,f2193,f2213,f2346,f2425,f2494,f2513,f2548,f2567,f3329,f4950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n013.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:34:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 10.25/1.83 % Refutation found
% 10.25/1.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.25/1.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.77/1.86 % Elapsed time: 1.494902 seconds
% 8.77/1.86 % CPU time: 11.341494 seconds
% 8.77/1.86 % Total memory used: 163.578 MB
% 8.77/1.86 % Net memory used: 156.920 MB
%------------------------------------------------------------------------------