%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM495+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 : n007.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 01:40:44 PM UTC 2026
% Result : Theorem 42.37s 5.78s
% Output : CNFRefutation 42.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 124 ( 24 unt; 21 def)
% Number of atoms : 406 ( 39 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 494 ( 212 ~; 216 |; 31 &)
% ( 23 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 81 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
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(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(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(f32,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f55,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f96,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f97,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [W0,W1] :
( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ! [W2] :
( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f128,plain,
! [W0,W1] :
( iLess0(W0,W1)
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f129,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,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))],[f131]) ).
fof(f135,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f142,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(f143,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f167,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f169,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f170,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(f171,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)],[f170]) ).
fof(f172,plain,
isPrime0(xp),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f174,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f175,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f178,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f179,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f180,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xr) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f182,plain,
~ doDivides0(xp,xr),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f183,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f188,plain,
! [X0] :
( ~ doDivides0(X0,xm)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f143,f183]) ).
fof(f189,plain,
! [X0] :
( ~ doDivides0(X0,xr)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f143,f182]) ).
fof(f192,definition,
( sQ0_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ0_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
! [X0] :
( sQ1_spl
<=> ( ~ doDivides0(X0,xm)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f196,plain,
! [X0] :
( ~ sQ1_spl
| ~ doDivides0(X0,xm)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ2_spl
<=> aNaturalNumber0(xm) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ2_spl
| ~ aNaturalNumber0(xm) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f188,f192,f195,f198]) ).
fof(f202,definition,
! [X0] :
( sQ3_spl
<=> ( ~ doDivides0(X0,xr)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ3_spl
| ~ doDivides0(X0,xr)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ4_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f189,f192,f202,f205]) ).
fof(f210,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f169]) ).
fof(f211,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f217,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f168]) ).
fof(f218,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f327,plain,
! [X0] :
( ~ aNaturalNumber0(sz10)
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f71,f135]) ).
fof(f329,definition,
! [X0] :
( sQ22_spl
<=> ( doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f330,plain,
! [X0] :
( ~ sQ22_spl
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ23_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ23_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( ~ sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f327,f329,f332]) ).
fof(f336,plain,
! [X0] :
( ~ sQ22_spl
| doDivides0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f330]) ).
fof(f338,definition,
( sQ24_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ24_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f342,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f167]) ).
fof(f343,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f365,plain,
( ~ sQ1_spl
| ~ sQ22_spl
| ~ doDivides0(xp,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f336,f196]) ).
fof(f370,definition,
( sQ29_spl
<=> doDivides0(xp,xm) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ29_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f365,f192,f370,f329,f195]) ).
fof(f440,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f53]) ).
fof(f441,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f440]) ).
fof(f761,definition,
( sQ71_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( sQ71_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f764,definition,
( sQ72_spl
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( sQ72_spl
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f770,definition,
( sQ74_spl
<=> sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f771,plain,
( ~ sQ74_spl
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f774,plain,
( ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f771,f179]) ).
fof(f775,plain,
~ sQ74_spl,
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f928,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f203,f336]) ).
fof(f943,definition,
( sQ97_spl
<=> doDivides0(xp,xr) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ97_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f928,f192,f943,f202,f329]) ).
fof(f960,definition,
( sQ98_spl
<=> sdtlseqdt0(xp,xn) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( sQ98_spl
| ~ sdtlseqdt0(xp,xn) ),
inference(component_clause,[status(thm)],[f960]) ).
fof(f1020,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[f175,f99]) ).
fof(f1028,plain,
( sQ4_spl
| ~ sQ98_spl
| ~ sQ24_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1020,f192,f338,f960,f205]) ).
fof(f1038,plain,
( sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f962,f174]) ).
fof(f1039,plain,
sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1038]) ).
fof(f1427,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)],[f171,f129]) ).
fof(f1428,definition,
! [X0,X1,X2] :
( sQ140_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,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1429,plain,
! [X0,X1,X2] :
( ~ sQ140_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)],[f1428]) ).
fof(f1431,plain,
( ~ sQ71_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1427,f1428,f761]) ).
fof(f3293,definition,
( sQ328_spl
<=> isPrime0(xp) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3295,plain,
( sQ328_spl
| ~ isPrime0(xp) ),
inference(component_clause,[status(thm)],[f3293]) ).
fof(f3491,plain,
( sQ328_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3295,f172]) ).
fof(f3492,plain,
sQ328_spl,
inference(contradiction_clause,[status(thm)],[f3491]) ).
fof(f6754,definition,
( sQ674_spl
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f6756,plain,
( sQ674_spl
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(component_clause,[status(thm)],[f6754]) ).
fof(f6757,definition,
( sQ675_spl
<=> aNaturalNumber0(sdtpldt0(xr,xm)) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f6759,plain,
( sQ675_spl
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(component_clause,[status(thm)],[f6757]) ).
fof(f7956,plain,
( sQ71_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f763,f56]) ).
fof(f7958,plain,
( sQ71_spl
| ~ sQ0_spl
| ~ sQ674_spl ),
inference(split_clause,[status(thm)],[f7956,f6754,f192,f761]) ).
fof(f10573,plain,
( sQ674_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f6756,f56]) ).
fof(f10575,plain,
( sQ674_spl
| ~ sQ2_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f10573,f338,f198,f6754]) ).
fof(f10634,plain,
( sQ72_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(resolution,[status(thm)],[f766,f56]) ).
fof(f10636,plain,
( sQ72_spl
| ~ sQ0_spl
| ~ sQ675_spl ),
inference(split_clause,[status(thm)],[f10634,f6757,f192,f764]) ).
fof(f10793,plain,
( sQ675_spl
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f6759,f56]) ).
fof(f10795,plain,
( sQ675_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f10793,f205,f198,f6757]) ).
fof(f16525,plain,
( ~ sQ140_spl
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| doDivides0(xp,xm)
| doDivides0(xp,xr)
| ~ doDivides0(xp,sdtasdt0(xr,xm))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f1429,f180]) ).
fof(f16533,definition,
( sQ1679_spl
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
introduced(definition,[new_symbols(definition,[sQ1679_spl])],[split_symbol_definition]) ).
fof(f16535,plain,
( sQ1679_spl
| ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(component_clause,[status(thm)],[f16533]) ).
fof(f16536,plain,
( ~ sQ140_spl
| sQ74_spl
| ~ sQ72_spl
| sQ29_spl
| sQ97_spl
| ~ sQ1679_spl
| ~ sQ328_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f16525,f205,f198,f192,f3293,f16533,f943,f370,f764,f770,f1428]) ).
fof(f16577,plain,
( sQ1679_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16535,f178]) ).
fof(f16578,plain,
sQ1679_spl,
inference(contradiction_clause,[status(thm)],[f16577]) ).
fof(f16579,plain,
$false,
inference(sat_refutation,[status(thm)],[f201,f208,f211,f218,f335,f343,f373,f441,f775,f946,f1028,f1039,f1431,f3492,f7958,f10575,f10636,f10795,f16536,f16578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM495+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:33:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 42.37/5.78 % Refutation found
% 42.37/5.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 42.37/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.83/5.86 % Elapsed time: 5.487017 seconds
% 2.83/5.86 % CPU time: 42.914572 seconds
% 2.83/5.86 % Total memory used: 281.949 MB
% 2.83/5.86 % Net memory used: 256.974 MB
%------------------------------------------------------------------------------