%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM508+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 46.82s 6.41s
% Output : CNFRefutation 32.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 81 ( 15 unt; 2 def)
% Number of atoms : 468 ( 152 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 597 ( 210 ~; 252 |; 125 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 110 ( 82 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
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(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))
| ? [W3] :
( sdtasdt0(W0,W1) = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
& ( isPrime0(W2)
| ( ! [W3] :
( ( doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
=> ( W3 = W2
| W3 = sz10 ) )
& W2 != sz10
& W2 != sz00 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(W2,W1)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( isPrime0(xr)
& ! [W0] :
( ( ( doDivides0(W0,xr)
| ? [W1] :
( xr = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xr
| W0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& ? [W0] :
( sdtpldt0(xr,W0) = xk
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [W0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(W0) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
( doDivides0(xr,xm)
| ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
| doDivides0(xr,xn)
| ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xm)
| ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
| doDivides0(xr,xn)
| ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
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(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(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)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f176,definition,
! [W2] :
( sP0_prd(W2)
<=> ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f177,definition,
! [W0,W2] :
( sP1_prd(W2,W0)
<=> ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f178,plain,
! [W0,W1,W2] :
( ( doDivides0(W2,W1)
& ? [W3] :
( W1 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| sP1_prd(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| sP0_prd(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(formula_renaming,[status(thm)],[f175,f177,f176]) ).
fof(f179,plain,
! [W0,W1,W2] :
( ( doDivides0(W2,W1)
& W1 = sdtasdt0(W2,sK4_skl(W2,W1,W0))
& aNaturalNumber0(sK4_skl(W2,W1,W0)) )
| sP1_prd(W2,W0)
| ~ iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ~ doDivides0(W2,sdtasdt0(W0,W1))
& ! [W3] :
( sdtasdt0(W0,W1) != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) ) )
| sP0_prd(W2)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W3,sK4_skl(W2,W1,W0))],[f178]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( aNaturalNumber0(sK4_skl(X2,X1,X0))
| sP1_prd(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3)
| sP0_prd(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( X1 = sdtasdt0(X2,sK4_skl(X2,X1,X0))
| sP1_prd(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,X1) != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3)
| sP0_prd(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f219,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [W0] :
( xk = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) )
& aNaturalNumber0(xr) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f220,plain,
( isPrime0(xr)
& ! [W0] :
( W0 = xr
| W0 = sz10
| ( ~ doDivides0(W0,xr)
& ! [W1] :
( xr != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK8_skl)
& aNaturalNumber0(sK8_skl)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W0,sK8_skl)],[f219]) ).
fof(f221,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f225,plain,
xr != sz00,
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f226,plain,
xr != sz10,
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f228,plain,
! [X0] :
( X0 = xr
| X0 = sz10
| ~ doDivides0(X0,xr)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f230,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK10_skl)
& aNaturalNumber0(sK10_skl)
& sdtpldt0(xr,sK9_skl) = xk
& aNaturalNumber0(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(W0,sK9_skl),skolemize(W0,sK10_skl)],[f49]) ).
fof(f233,plain,
aNaturalNumber0(sK10_skl),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK10_skl),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f241,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),sK12_skl) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(sK12_skl)
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(W0,sK12_skl)],[f51]) ).
fof(f242,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f245,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f246,plain,
( ~ doDivides0(xr,xm)
& ! [W0] :
( xm != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) )
& ~ doDivides0(xr,xn)
& ! [W0] :
( xn != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f248,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f249,plain,
! [X0] :
( xm != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f251,plain,
! [W2] :
( ( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ( ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(NNF_transformation,[status(thm)],[f176]) ).
fof(f252,plain,
( ! [W2] :
( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ! [W2] :
( ( ~ isPrime0(W2)
& ( ? [W3] :
( W3 != W2
& W3 != sz10
& doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(miniscoping,[status(thm)],[f251]) ).
fof(f253,plain,
( ! [W2] :
( isPrime0(W2)
| ( ! [W3] :
( W3 = W2
| W3 = sz10
| ~ doDivides0(W3,W2)
| ! [W4] :
( W2 != sdtasdt0(W3,W4)
| ~ aNaturalNumber0(W4) )
| ~ aNaturalNumber0(W3) )
& W2 != sz10
& W2 != sz00 )
| sP0_prd(W2) )
& ! [W2] :
( ( ~ isPrime0(W2)
& ( ( sK13_skl(W2) != W2
& sK13_skl(W2) != sz10
& doDivides0(sK13_skl(W2),W2)
& W2 = sdtasdt0(sK13_skl(W2),sK14_skl(W2))
& aNaturalNumber0(sK14_skl(W2))
& aNaturalNumber0(sK13_skl(W2)) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(W3,sK13_skl(W2)),skolemize(W4,sK14_skl(W2))],[f252]) ).
fof(f254,plain,
! [X0] :
( aNaturalNumber0(sK13_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f257,plain,
! [X0] :
( doDivides0(sK13_skl(X0),X0)
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f258,plain,
! [X0] :
( sK13_skl(X0) != sz10
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f259,plain,
! [X0] :
( sK13_skl(X0) != X0
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f264,plain,
! [W0,W2] :
( ( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ( ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ sP1_prd(W2,W0) ) ),
inference(NNF_transformation,[status(thm)],[f177]) ).
fof(f265,plain,
( ! [W0,W2] :
( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( doDivides0(W2,W0)
& ? [W3] :
( W0 = sdtasdt0(W2,W3)
& aNaturalNumber0(W3) ) )
| ~ sP1_prd(W2,W0) ) ),
inference(miniscoping,[status(thm)],[f264]) ).
fof(f266,plain,
( ! [W0,W2] :
( ~ doDivides0(W2,W0)
| ! [W3] :
( W0 != sdtasdt0(W2,W3)
| ~ aNaturalNumber0(W3) )
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( doDivides0(W2,W0)
& W0 = sdtasdt0(W2,sK15_skl(W2,W0))
& aNaturalNumber0(sK15_skl(W2,W0)) )
| ~ sP1_prd(W2,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W3,sK15_skl(W2,W0))],[f265]) ).
fof(f269,plain,
! [X0,X1] :
( doDivides0(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f333,plain,
( sK13_skl(xr) = xr
| sK13_skl(xr) = sz10
| ~ aNaturalNumber0(sK13_skl(xr))
| xr = sz10
| xr = sz00
| ~ sP0_prd(xr) ),
inference(resolution,[status(thm)],[f257,f228]) ).
fof(f336,plain,
( sK13_skl(xr) = xr
| sK13_skl(xr) = sz10
| ~ aNaturalNumber0(sK13_skl(xr))
| xr = sz10
| ~ sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f225]) ).
fof(f450,plain,
! [X0,X1] :
( sP1_prd(xr,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK4_skl(xr,xm,X0)) ),
inference(resolution,[status(thm)],[f249,f181]) ).
fof(f452,plain,
! [X0,X1] :
( sP1_prd(xr,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtasdt0(X0,xm) != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f180]) ).
fof(f530,plain,
( xr = sz10
| xr = sz00
| ~ sP0_prd(xr)
| sK13_skl(xr) = xr
| sK13_skl(xr) = sz10
| xr = sz10
| ~ sP0_prd(xr) ),
inference(resolution,[status(thm)],[f336,f254]) ).
fof(f531,plain,
( xr = sz00
| sK13_skl(xr) = xr
| sK13_skl(xr) = sz10
| xr = sz10
| ~ sP0_prd(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f530]) ).
fof(f532,plain,
( xr = sz00
| sK13_skl(xr) = xr
| sK13_skl(xr) = sz10
| ~ sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f226]) ).
fof(f632,plain,
( xr = sz10
| xr = sz00
| ~ sP0_prd(xr)
| xr = sz00
| sK13_skl(xr) = sz10
| ~ sP0_prd(xr) ),
inference(resolution,[status(thm)],[f532,f259]) ).
fof(f634,plain,
( xr = sz10
| xr = sz00
| sK13_skl(xr) = sz10
| ~ sP0_prd(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f632]) ).
fof(f635,plain,
( xr = sz10
| xr = sz00
| ~ sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f258]) ).
fof(f1640,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolution,[status(thm)],[f245,f134]) ).
fof(f1641,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1640,f242]) ).
fof(f2151,plain,
( sP1_prd(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[f234,f452]) ).
fof(f2268,plain,
( sP1_prd(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f2151,f172]) ).
fof(f2766,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f2268,f1641]) ).
fof(f2770,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f2766,f173]) ).
fof(f2774,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f2770,f61]) ).
fof(f2775,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f2774]) ).
fof(f2776,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f2775,f221]) ).
fof(f2777,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f2776,f61]) ).
fof(f2778,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1_prd(xr,xn)
| ~ aNaturalNumber0(sK10_skl)
| sP0_prd(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f2777]) ).
fof(f2779,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1_prd(xr,xn)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f2778,f233]) ).
fof(f2780,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sP1_prd(xr,xn)
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f2779,f61]) ).
fof(f2781,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sP1_prd(xr,xn)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f2780,f174]) ).
fof(f2810,plain,
( doDivides0(xr,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f2781,f269]) ).
fof(f2811,plain,
( doDivides0(xr,xn)
| ~ aNaturalNumber0(xm)
| sP0_prd(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[f2810,f172]) ).
fof(f2812,plain,
( ~ aNaturalNumber0(xm)
| sP0_prd(xr) ),
inference(resolution,[status(thm)],[f2811,f248]) ).
fof(f2818,plain,
( xr = sz10
| xr = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[f635,f2819]) ).
fof(f2819,plain,
sP0_prd(xr),
inference(forward_subsumption_resolution,[status(thm)],[f2812,f173]) ).
fof(f2835,plain,
sz10 != sz10,
inference(backward_demodulation,[status(thm)],[f2936,f226]) ).
fof(f2936,plain,
xr = sz10,
inference(forward_subsumption_resolution,[status(thm)],[f2818,f225]) ).
fof(f3012,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM508+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n010.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 02:36:26 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 46.82/6.41 % Refutation found
% 46.82/6.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.82/6.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.94/6.46 % Elapsed time: 6.096041 seconds
% 32.94/6.46 % CPU time: 47.996102 seconds
% 32.94/6.46 % Total memory used: 297.882 MB
% 32.94/6.46 % Net memory used: 276.500 MB
%------------------------------------------------------------------------------