%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM516+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 : n003.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 01:40:49 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 16 unt; 2 def)
% Number of atoms : 379 ( 100 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 534 ( 233 ~; 234 |; 50 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 75 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f22,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
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(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(f48,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f60,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f63,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f87,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(f89,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f114,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f115,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f118,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,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(f123,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)],[f119]) ).
fof(f144,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(f145,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)],[f144]) ).
fof(f146,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)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f160,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(f161,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)],[f160]) ).
fof(f162,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))],[f161]) ).
fof(f163,plain,
! [X0] :
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f175,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f176,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f177,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f194,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f196,plain,
isPrime0(xr),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f202,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f203,plain,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f204,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f206,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f207,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f215,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f147]) ).
fof(f218,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(destructive_equality_resolution,[status(thm)],[f163]) ).
fof(f235,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[status(thm)],[f218,f60]) ).
fof(f239,plain,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[f118,f207]) ).
fof(f265,plain,
! [X0] :
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtlseqdt0(X0,sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f115,f239]) ).
fof(f280,plain,
! [X0] :
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(resolution,[status(thm)],[f115,f207]) ).
fof(f284,plain,
! [X0] :
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtlseqdt0(X0,sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f265]) ).
fof(f333,plain,
! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(sdtsldt0(xn,xr),xm)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f284,f89]) ).
fof(f335,plain,
! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(sdtsldt0(xn,xr),xm)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f64]) ).
fof(f336,plain,
! [X0] :
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(resolution,[status(thm)],[f280,f89]) ).
fof(f338,plain,
! [X0] :
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f64]) ).
fof(f340,plain,
! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(sdtsldt0(xn,xr),xm)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sdtlseqdt0(X0,sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f64]) ).
fof(f349,plain,
! [X0] :
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f64]) ).
fof(f351,plain,
( sdtpldt0(xn,xm) = sdtpldt0(sdtsldt0(xn,xr),xm)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(resolution,[status(thm)],[f349,f340]) ).
fof(f357,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(duplicate_literals_removal,[status(thm)],[f351]) ).
fof(f358,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f64]) ).
fof(f479,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f177]) ).
fof(f576,plain,
( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(resolution,[status(thm)],[f123,f479]) ).
fof(f582,plain,
( ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(duplicate_literals_removal,[status(thm)],[f576]) ).
fof(f583,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f177]) ).
fof(f675,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(resolution,[status(thm)],[f583,f123]) ).
fof(f678,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f64]) ).
fof(f794,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[f678,f64]) ).
fof(f795,plain,
( sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(resolution,[status(thm)],[f794,f89]) ).
fof(f797,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(duplicate_literals_removal,[status(thm)],[f795]) ).
fof(f798,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[f797,f175]) ).
fof(f801,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[f798,f203]) ).
fof(f802,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(resolution,[status(thm)],[f801,f204]) ).
fof(f805,plain,
~ aNaturalNumber0(sdtsldt0(xn,xr)),
inference(forward_subsumption_resolution,[status(thm)],[f802,f176]) ).
fof(f810,plain,
( ~ doDivides0(xr,xn)
| xr = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[f805,f215]) ).
fof(f811,plain,
( ~ doDivides0(xr,xn)
| xr = sz00
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[f810,f194]) ).
fof(f817,plain,
( ~ doDivides0(xr,xn)
| xr = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[f811,f175]) ).
fof(f818,plain,
xr = sz00,
inference(resolution,[status(thm)],[f817,f202]) ).
fof(f850,plain,
isPrime0(sz00),
inference(backward_demodulation,[status(thm)],[f818,f196]) ).
fof(f884,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f850,f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM516+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 02:38:30 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.16/0.52 % Refutation found
% 0.16/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.54 % Elapsed time: 0.180972 seconds
% 0.16/0.54 % CPU time: 1.137813 seconds
% 0.16/0.54 % Total memory used: 115.071 MB
% 0.16/0.54 % Net memory used: 113.676 MB
%------------------------------------------------------------------------------