%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM495+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 34.43s 4.78s
% Output : CNFRefutation 34.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 18 unt; 2 def)
% Number of atoms : 592 ( 197 equ)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 772 ( 276 ~; 344 |; 137 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 133 ( 105 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
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(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))
| ? [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/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( sdtlseqdt0(xr,xn)
& ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) )
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( doDivides0(xp,sdtasdt0(xr,xm))
& ? [W0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [W0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),W0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(W0) )
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
| doDivides0(xp,xr)
| ? [W0] :
( xr = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [W0] :
( xm = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
| doDivides0(xp,xr)
| ? [W0] :
( xr = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
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(f79,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f81,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f111,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
| ~ aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f115,plain,
! [X0,X1,X2] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
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(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)
& ? [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(f171,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(f172,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(f173,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)],[f170,f172,f171]) ).
fof(f174,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))],[f173]) ).
fof(f180,plain,
! [X0,X1,X2] :
( doDivides0(X2,X1)
| sP1_prd(X2,X0)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| sP0_prd(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f181,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f182,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK5_skl)
& aNaturalNumber0(sK5_skl)
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W0,sK5_skl)],[f181]) ).
fof(f183,plain,
xp != sz00,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
xp != sz10,
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f186,plain,
! [X0] :
( X0 = xp
| X0 = sz10
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f195,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f198,plain,
( sdtlseqdt0(xr,xn)
& sdtpldt0(xr,sK7_skl) = xn
& aNaturalNumber0(sK7_skl)
& xr != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(W0,sK7_skl)],[f44]) ).
fof(f199,plain,
xr != xn,
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f202,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f203,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
& sdtasdt0(xr,xm) = sdtasdt0(xp,sK8_skl)
& aNaturalNumber0(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W0,sK8_skl)],[f45]) ).
fof(f205,plain,
sdtasdt0(xr,xm) = sdtasdt0(xp,sK8_skl),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f206,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f207,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),sK9_skl) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(sK9_skl)
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(W0,sK9_skl)],[f46]) ).
fof(f208,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f212,plain,
( ~ doDivides0(xp,xm)
& ! [W0] :
( xm != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) )
& ~ doDivides0(xp,xr)
& ! [W0] :
( xr != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f213,plain,
! [X0] :
( xr != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f216,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f217,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)],[f171]) ).
fof(f218,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)],[f217]) ).
fof(f219,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)
& ( ( sK10_skl(W2) != W2
& sK10_skl(W2) != sz10
& doDivides0(sK10_skl(W2),W2)
& W2 = sdtasdt0(sK10_skl(W2),sK11_skl(W2))
& aNaturalNumber0(sK11_skl(W2))
& aNaturalNumber0(sK10_skl(W2)) )
| W2 = sz10
| W2 = sz00 ) )
| ~ sP0_prd(W2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(W3,sK10_skl(W2)),skolemize(W4,sK11_skl(W2))],[f218]) ).
fof(f220,plain,
! [X0] :
( aNaturalNumber0(sK10_skl(X0))
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f223,plain,
! [X0] :
( doDivides0(sK10_skl(X0),X0)
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f224,plain,
! [X0] :
( sK10_skl(X0) != sz10
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f225,plain,
! [X0] :
( sK10_skl(X0) != X0
| X0 = sz10
| X0 = sz00
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f230,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)],[f172]) ).
fof(f231,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)],[f230]) ).
fof(f232,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,sK12_skl(W2,W0))
& aNaturalNumber0(sK12_skl(W2,W0)) )
| ~ sP1_prd(W2,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(W3,sK12_skl(W2,W0))],[f231]) ).
fof(f233,plain,
! [X0,X1] :
( aNaturalNumber0(sK12_skl(X0,X1))
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f234,plain,
! [X0,X1] :
( X1 = sdtasdt0(X0,sK12_skl(X0,X1))
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f255,plain,
doDivides0(xp,sdtasdt0(xp,sK8_skl)),
inference(forward_demodulation,[status(thm)],[f205,f206]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X2)
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X2,X1))
| sdtpldt0(X0,X1) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f129,f115]) ).
fof(f284,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X0)
| X2 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X2,X1),sdtpldt0(X0,X1))
| sdtpldt0(X2,X1) = sdtpldt0(X0,X1)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f56]) ).
fof(f296,plain,
( sK10_skl(xp) = xp
| sK10_skl(xp) = sz10
| ~ aNaturalNumber0(sK10_skl(xp))
| xp = sz10
| xp = sz00
| ~ sP0_prd(xp) ),
inference(resolution,[status(thm)],[f223,f186]) ).
fof(f298,plain,
( sK10_skl(xp) = xp
| sK10_skl(xp) = sz10
| ~ aNaturalNumber0(sK10_skl(xp))
| xp = sz10
| ~ sP0_prd(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f183]) ).
fof(f396,plain,
! [X0,X1] :
( doDivides0(xp,X1)
| sP1_prd(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| sP0_prd(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| sdtpldt0(sdtpldt0(X0,X1),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[f284,f180]) ).
fof(f399,plain,
! [X0,X1] :
( doDivides0(xp,X1)
| sP1_prd(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| sP0_prd(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| sdtpldt0(sdtpldt0(X0,X1),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(duplicate_literals_removal,[status(thm)],[f396]) ).
fof(f400,plain,
! [X0,X1] :
( doDivides0(xp,X1)
| sP1_prd(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| sP0_prd(xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| sdtpldt0(sdtpldt0(X0,X1),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f56]) ).
fof(f510,plain,
( xp = sz10
| xp = sz00
| ~ sP0_prd(xp)
| sK10_skl(xp) = xp
| sK10_skl(xp) = sz10
| xp = sz10
| ~ sP0_prd(xp) ),
inference(resolution,[status(thm)],[f298,f220]) ).
fof(f511,plain,
( xp = sz00
| sK10_skl(xp) = xp
| sK10_skl(xp) = sz10
| xp = sz10
| ~ sP0_prd(xp) ),
inference(duplicate_literals_removal,[status(thm)],[f510]) ).
fof(f512,plain,
( xp = sz00
| sK10_skl(xp) = xp
| sK10_skl(xp) = sz10
| ~ sP0_prd(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f184]) ).
fof(f624,plain,
( xp = sz10
| xp = sz00
| ~ sP0_prd(xp)
| xp = sz00
| sK10_skl(xp) = sz10
| ~ sP0_prd(xp) ),
inference(resolution,[status(thm)],[f512,f225]) ).
fof(f626,plain,
( xp = sz10
| xp = sz00
| sK10_skl(xp) = sz10
| ~ sP0_prd(xp) ),
inference(duplicate_literals_removal,[status(thm)],[f624]) ).
fof(f627,plain,
( xp = sz10
| xp = sz00
| ~ sP0_prd(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f224]) ).
fof(f1554,plain,
( doDivides0(xp,xm)
| sP1_prd(xp,xr)
| ~ doDivides0(xp,sdtasdt0(xr,xm))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(resolution,[status(thm)],[f400,f208]) ).
fof(f1558,plain,
( doDivides0(xp,xm)
| sP1_prd(xp,xr)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(forward_demodulation,[status(thm)],[f205,f1554]) ).
fof(f1559,plain,
( doDivides0(xp,xm)
| sP1_prd(xp,xr)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1558,f56]) ).
fof(f2137,plain,
( ~ aNaturalNumber0(sK12_skl(xp,xr))
| ~ sP1_prd(xp,xr) ),
inference(resolution,[status(thm)],[f234,f213]) ).
fof(f2167,plain,
( doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1559,f2168]) ).
fof(f2168,plain,
~ sP1_prd(xp,xr),
inference(forward_subsumption_resolution,[status(thm)],[f2137,f233]) ).
fof(f2179,plain,
( doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2167,f169]) ).
fof(f3333,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[f2179,f115]) ).
fof(f3336,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(duplicate_literals_removal,[status(thm)],[f3333]) ).
fof(f3337,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f3336,f56]) ).
fof(f3342,plain,
( xr = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f3337,f81]) ).
fof(f3344,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literals_removal,[status(thm)],[f3342]) ).
fof(f3345,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| ~ doDivides0(xp,sdtasdt0(xp,sK8_skl))
| sP0_prd(xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f3344,f195]) ).
fof(f3347,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| sP0_prd(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[f3345,f255]) ).
fof(f3354,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| sP0_prd(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f3347,f168]) ).
fof(f3450,plain,
( xr = xn
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xm)
| sP0_prd(xp) ),
inference(resolution,[status(thm)],[f3354,f202]) ).
fof(f3452,plain,
( xr = xn
| ~ aNaturalNumber0(xn)
| sP0_prd(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f3450,f216]) ).
fof(f3454,plain,
( xr = xn
| sP0_prd(xp) ),
inference(resolution,[status(thm)],[f3452,f167]) ).
fof(f3457,plain,
( xp = sz10
| xp = sz00 ),
inference(backward_subsumption_resolution,[status(thm)],[f627,f3458]) ).
fof(f3458,plain,
sP0_prd(xp),
inference(forward_subsumption_resolution,[status(thm)],[f3454,f199]) ).
fof(f3626,plain,
sz10 != sz10,
inference(backward_demodulation,[status(thm)],[f4020,f184]) ).
fof(f4020,plain,
xp = sz10,
inference(forward_subsumption_resolution,[status(thm)],[f3457,f183]) ).
fof(f4251,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM495+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:38:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 34.43/4.78 % Refutation found
% 34.43/4.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 34.43/4.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.23/4.81 % Elapsed time: 4.432309 seconds
% 1.23/4.81 % CPU time: 34.792570 seconds
% 1.23/4.81 % Total memory used: 267.096 MB
% 1.23/4.81 % Net memory used: 248.198 MB
%------------------------------------------------------------------------------