TSTP Solution File: NUM498+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:29:24 EDT 2023
% Result : Theorem 13.08s 2.06s
% Output : CNFRefutation 13.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 188 ( 44 unt; 4 def)
% Number of atoms : 529 ( 148 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 561 ( 220 ~; 236 |; 58 &)
% ( 31 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 24 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 95 (; 88 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W0 = sz00
& W1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W0 = sz00
| W1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00
& doDivides0(W0,W1) )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,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 = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f52,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f54,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f69,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f70,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| X0 = sdtasdt0(sz10,X0) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f72,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f73,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f84,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| sdtpldt0(W0,W1) != sz00
| ( W0 = sz00
& W1 = sz00 ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) != sz00
| X0 = sz00 ),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f87,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| sdtasdt0(W0,W1) != sz00
| W0 = sz00
| W1 = sz00 ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sz00
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[status(esa)],[f87]) ).
fof(f89,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f90,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ sdtlseqdt0(W0,W1)
| ? [W2] :
( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f89]) ).
fof(f91,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(sk0_0(W1,W0))
& sdtpldt0(W0,sk0_0(W1,W0)) = W1 ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ) ),
inference(skolemization,[status(esa)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sk0_0(X1,X0)) = X1 ),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f129,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f130,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ doDivides0(W0,W1)
| ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ( doDivides0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(sk0_1(W1,W0))
& W1 = sdtasdt0(W0,sk0_1(W1,W0)) ) )
& ( doDivides0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f135,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f136,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( ( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(NNF_transformation,[status(esa)],[f135]) ).
fof(f137,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ( ! [W2] :
( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ! [W2] :
( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(miniscoping,[status(esa)],[f136]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 != sdtsldt0(X1,X0)
| X1 = sdtasdt0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f151,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f152,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& W1 != sz10
& W1 != W0 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ( aNaturalNumber0(sk0_2(W0))
& doDivides0(sk0_2(W0),W0)
& sk0_2(W0) != sz10
& sk0_2(W0) != W0 ) ) ) ),
inference(skolemization,[status(esa)],[f152]) ).
fof(f156,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0)
| X1 = sz10
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f153]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f168,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f171,plain,
isPrime0(xp),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f172,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f175,plain,
xn != xp,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f178,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f179,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f180,plain,
( ( xk = sz00
| xk = sz10 )
& ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm) ),
inference(pre_NNF_transformation,[status(esa)],[f47]) ).
fof(f181,plain,
( xk = sz00
| xk = sz10 ),
inference(cnf_transformation,[status(esa)],[f180]) ).
fof(f182,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[status(esa)],[f180]) ).
fof(f183,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[status(esa)],[f180]) ).
fof(f184,plain,
( spl0_0
<=> xk = sz00 ),
introduced(split_symbol_definition) ).
fof(f185,plain,
( xk = sz00
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( spl0_1
<=> xk = sz10 ),
introduced(split_symbol_definition) ).
fof(f188,plain,
( xk = sz10
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f181,f184,f187]) ).
fof(f193,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(resolution,[status(thm)],[f70,f52]) ).
fof(f202,plain,
sz00 = sdtasdt0(sz10,sz00),
inference(resolution,[status(thm)],[f71,f51]) ).
fof(f203,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[f73,f168]) ).
fof(f215,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[f55,f166]) ).
fof(f216,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(sz10,X0)) ),
inference(resolution,[status(thm)],[f55,f52]) ).
fof(f220,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(xn,X0)) ),
inference(resolution,[status(thm)],[f57,f166]) ).
fof(f229,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[status(thm)],[f74,f167]) ).
fof(f256,plain,
( spl0_2
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f258,plain,
( ~ aNaturalNumber0(xp)
| spl0_2 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( spl0_3
<=> xp = sz00 ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( spl0_8
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f280,plain,
( ~ aNaturalNumber0(xm)
| spl0_8 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( spl0_9
<=> xm = sz00 ),
introduced(split_symbol_definition) ).
fof(f282,plain,
( xm = sz00
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f294,plain,
( spl0_12
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f296,plain,
( ~ aNaturalNumber0(xn)
| spl0_12 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( spl0_13
<=> xn = sz00 ),
introduced(split_symbol_definition) ).
fof(f298,plain,
( xn = sz00
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f406,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f168]) ).
fof(f407,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f167]) ).
fof(f409,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f410,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f166]) ).
fof(f411,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f472,plain,
( doDivides0(xp,sdtasdt0(sz00,xm))
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f298,f172]) ).
fof(f476,plain,
( ~ doDivides0(xp,sz00)
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f298,f182]) ).
fof(f497,plain,
( spl0_32
<=> xn = sz10 ),
introduced(split_symbol_definition) ).
fof(f498,plain,
( xn = sz10
| ~ spl0_32 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f508,plain,
xm = sdtasdt0(sz10,xm),
inference(resolution,[status(thm)],[f167,f71]) ).
fof(f777,plain,
( spl0_68
<=> xn = xp ),
introduced(split_symbol_definition) ).
fof(f778,plain,
( xn = xp
| ~ spl0_68 ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f982,plain,
sdtasdt0(xn,sz00) = sz00,
inference(resolution,[status(thm)],[f166,f73]) ).
fof(f1121,plain,
( spl0_93
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f1123,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl0_93 ),
inference(component_clause,[status(thm)],[f1121]) ).
fof(f1449,plain,
( xm = sdtasdt0(sz10,sz00)
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f282,f508]) ).
fof(f1450,plain,
( xm = sz00
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f202,f1449]) ).
fof(f1521,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[f168,f70]) ).
fof(f1573,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[status(thm)],[f166,f71]) ).
fof(f1799,plain,
( sz00 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f185,f179]) ).
fof(f1816,plain,
( doDivides0(xp,sz00)
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f229,f472]) ).
fof(f1878,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f1816]) ).
fof(f1879,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f1878]) ).
fof(f1893,plain,
( ~ doDivides0(xp,sz00)
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f1450,f183]) ).
fof(f1927,plain,
( doDivides0(xp,sdtasdt0(xn,sz00))
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1450,f172]) ).
fof(f1928,plain,
( doDivides0(xp,sz00)
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f982,f1927]) ).
fof(f2051,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f1893,f1928]) ).
fof(f2052,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f2051]) ).
fof(f2158,plain,
( spl0_181
<=> aNaturalNumber0(sk0_0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f2161,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sk0_0(xp,xm)) ),
inference(resolution,[status(thm)],[f178,f92]) ).
fof(f2162,plain,
( ~ spl0_8
| ~ spl0_2
| spl0_181 ),
inference(split_clause,[status(thm)],[f2161,f278,f256,f2158]) ).
fof(f2296,plain,
( spl0_183
<=> sdtpldt0(xm,sk0_0(xp,xm)) = xp ),
introduced(split_symbol_definition) ).
fof(f2297,plain,
( sdtpldt0(xm,sk0_0(xp,xm)) = xp
| ~ spl0_183 ),
inference(component_clause,[status(thm)],[f2296]) ).
fof(f2299,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xm,sk0_0(xp,xm)) = xp ),
inference(resolution,[status(thm)],[f93,f178]) ).
fof(f2300,plain,
( ~ spl0_8
| ~ spl0_2
| spl0_183 ),
inference(split_clause,[status(thm)],[f2299,f278,f256,f2296]) ).
fof(f2816,plain,
( $false
| ~ spl0_68 ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f175]) ).
fof(f2817,plain,
~ spl0_68,
inference(contradiction_clause,[status(thm)],[f2816]) ).
fof(f3512,plain,
( xn = sdtasdt0(sz10,sz10)
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f498,f1573]) ).
fof(f3513,plain,
( xn = sz10
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f193,f3512]) ).
fof(f3584,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sk0_0(xp,xm))
| xp != sz00
| xm = sz00
| ~ spl0_183 ),
inference(paramodulation,[status(thm)],[f2297,f85]) ).
fof(f3585,plain,
( ~ spl0_8
| ~ spl0_181
| ~ spl0_3
| spl0_9
| ~ spl0_183 ),
inference(split_clause,[status(thm)],[f3584,f278,f2158,f259,f281,f2296]) ).
fof(f3650,plain,
( doDivides0(xp,sdtasdt0(sz10,xm))
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f3513,f172]) ).
fof(f3651,plain,
( doDivides0(xp,xm)
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f508,f3650]) ).
fof(f3652,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[status(thm)],[f3651,f183]) ).
fof(f3653,plain,
~ spl0_32,
inference(contradiction_clause,[status(thm)],[f3652]) ).
fof(f4669,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(resolution,[status(thm)],[f215,f167]) ).
fof(f4670,plain,
aNaturalNumber0(sdtpldt0(xn,xn)),
inference(resolution,[status(thm)],[f215,f166]) ).
fof(f4685,plain,
aNaturalNumber0(sdtpldt0(xn,xp)),
inference(resolution,[status(thm)],[f215,f168]) ).
fof(f4688,plain,
aNaturalNumber0(sdtpldt0(xn,sz10)),
inference(resolution,[status(thm)],[f215,f52]) ).
fof(f5280,plain,
aNaturalNumber0(sdtpldt0(sz10,xn)),
inference(resolution,[status(thm)],[f216,f166]) ).
fof(f5616,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolution,[status(thm)],[f220,f167]) ).
fof(f5617,plain,
( $false
| spl0_93 ),
inference(forward_subsumption_resolution,[status(thm)],[f5616,f1123]) ).
fof(f5618,plain,
spl0_93,
inference(contradiction_clause,[status(thm)],[f5617]) ).
fof(f7405,plain,
( spl0_718
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f7407,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| spl0_718 ),
inference(component_clause,[status(thm)],[f7405]) ).
fof(f7416,plain,
( $false
| spl0_718 ),
inference(forward_subsumption_resolution,[status(thm)],[f7407,f172]) ).
fof(f7417,plain,
spl0_718,
inference(contradiction_clause,[status(thm)],[f7416]) ).
fof(f8399,plain,
( sz10 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f188,f179]) ).
fof(f9101,plain,
( spl0_847
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,sz10) ),
introduced(split_symbol_definition) ).
fof(f9102,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ spl0_847 ),
inference(component_clause,[status(thm)],[f9101]) ).
fof(f9104,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f139,f8399]) ).
fof(f9105,plain,
( ~ spl0_2
| ~ spl0_93
| spl0_3
| ~ spl0_718
| spl0_847
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f9104,f256,f1121,f259,f7405,f9101,f187]) ).
fof(f9112,plain,
( sdtasdt0(xn,xm) = xp
| ~ spl0_847 ),
inference(forward_demodulation,[status(thm)],[f1521,f9102]) ).
fof(f9345,plain,
( spl0_862
<=> doDivides0(xn,xp) ),
introduced(split_symbol_definition) ).
fof(f9346,plain,
( doDivides0(xn,xp)
| ~ spl0_862 ),
inference(component_clause,[status(thm)],[f9345]) ).
fof(f9348,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| doDivides0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ spl0_847 ),
inference(resolution,[status(thm)],[f9112,f134]) ).
fof(f9349,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_862
| ~ spl0_8
| ~ spl0_847 ),
inference(split_clause,[status(thm)],[f9348,f294,f256,f9345,f278,f9101]) ).
fof(f11549,plain,
( spl0_1088
<=> isPrime0(xp) ),
introduced(split_symbol_definition) ).
fof(f11551,plain,
( ~ isPrime0(xp)
| spl0_1088 ),
inference(component_clause,[status(thm)],[f11549]) ).
fof(f11552,plain,
( ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| xn = sz10
| xn = xp
| ~ spl0_862 ),
inference(resolution,[status(thm)],[f156,f9346]) ).
fof(f11553,plain,
( ~ spl0_2
| ~ spl0_1088
| ~ spl0_12
| spl0_32
| spl0_68
| ~ spl0_862 ),
inference(split_clause,[status(thm)],[f11552,f256,f11549,f294,f497,f777,f9345]) ).
fof(f11582,plain,
( $false
| spl0_1088 ),
inference(forward_subsumption_resolution,[status(thm)],[f11551,f171]) ).
fof(f11583,plain,
spl0_1088,
inference(contradiction_clause,[status(thm)],[f11582]) ).
fof(f12279,plain,
( spl0_1234
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,sz00) ),
introduced(split_symbol_definition) ).
fof(f12280,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl0_1234 ),
inference(component_clause,[status(thm)],[f12279]) ).
fof(f12282,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f1799,f139]) ).
fof(f12283,plain,
( ~ spl0_2
| ~ spl0_93
| spl0_3
| ~ spl0_718
| spl0_1234
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f12282,f256,f1121,f259,f7405,f12279,f184]) ).
fof(f12295,plain,
( sdtasdt0(xn,xm) = sz00
| ~ spl0_1234 ),
inference(forward_demodulation,[status(thm)],[f203,f12280]) ).
fof(f13087,plain,
( spl0_1320
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f13089,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl0_1320 ),
inference(component_clause,[status(thm)],[f13087]) ).
fof(f13120,plain,
( $false
| spl0_1320 ),
inference(forward_subsumption_resolution,[status(thm)],[f13089,f4669]) ).
fof(f13121,plain,
spl0_1320,
inference(contradiction_clause,[status(thm)],[f13120]) ).
fof(f13223,plain,
( spl0_1336
<=> aNaturalNumber0(sdtpldt0(xn,xn)) ),
introduced(split_symbol_definition) ).
fof(f13225,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xn))
| spl0_1336 ),
inference(component_clause,[status(thm)],[f13223]) ).
fof(f13256,plain,
( $false
| spl0_1336 ),
inference(forward_subsumption_resolution,[status(thm)],[f13225,f4670]) ).
fof(f13257,plain,
spl0_1336,
inference(contradiction_clause,[status(thm)],[f13256]) ).
fof(f13359,plain,
( spl0_1352
<=> aNaturalNumber0(sdtpldt0(xn,xp)) ),
introduced(split_symbol_definition) ).
fof(f13361,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xp))
| spl0_1352 ),
inference(component_clause,[status(thm)],[f13359]) ).
fof(f13392,plain,
( $false
| spl0_1352 ),
inference(forward_subsumption_resolution,[status(thm)],[f13361,f4685]) ).
fof(f13393,plain,
spl0_1352,
inference(contradiction_clause,[status(thm)],[f13392]) ).
fof(f13551,plain,
( spl0_1368
<=> aNaturalNumber0(sdtpldt0(xn,sz10)) ),
introduced(split_symbol_definition) ).
fof(f13553,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,sz10))
| spl0_1368 ),
inference(component_clause,[status(thm)],[f13551]) ).
fof(f13584,plain,
( $false
| spl0_1368 ),
inference(forward_subsumption_resolution,[status(thm)],[f13553,f4688]) ).
fof(f13585,plain,
spl0_1368,
inference(contradiction_clause,[status(thm)],[f13584]) ).
fof(f17544,plain,
( spl0_1778
<=> aNaturalNumber0(sdtpldt0(sz10,xn)) ),
introduced(split_symbol_definition) ).
fof(f17546,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xn))
| spl0_1778 ),
inference(component_clause,[status(thm)],[f17544]) ).
fof(f17577,plain,
( $false
| spl0_1778 ),
inference(forward_subsumption_resolution,[status(thm)],[f17546,f5280]) ).
fof(f17578,plain,
spl0_1778,
inference(contradiction_clause,[status(thm)],[f17577]) ).
fof(f18497,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xn = sz00
| xm = sz00
| ~ spl0_1234 ),
inference(resolution,[status(thm)],[f12295,f88]) ).
fof(f18498,plain,
( ~ spl0_12
| ~ spl0_8
| spl0_13
| spl0_9
| ~ spl0_1234 ),
inference(split_clause,[status(thm)],[f18497,f294,f278,f297,f281,f12279]) ).
fof(f18515,plain,
$false,
inference(sat_refutation,[status(thm)],[f190,f407,f409,f411,f1879,f2052,f2162,f2300,f2817,f3585,f3653,f5618,f7417,f9105,f9349,f11553,f11583,f12283,f13121,f13257,f13393,f13585,f17578,f18498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:30:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 13.08/2.06 % Refutation found
% 13.08/2.06 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.08/2.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.08/2.08 % Elapsed time: 1.732335 seconds
% 13.08/2.08 % CPU time: 13.636871 seconds
% 13.08/2.08 % Memory used: 143.717 MB
%------------------------------------------------------------------------------