%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM508+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 : Tue May 5 04:57:37 PM UTC 2026
% Result : Theorem 1.98s 1.91s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 1427 ( 458 equ)
% Maximal formula atoms : 1287 ( 40 avg)
% Number of connectives : 2183 ( 791 ~;1203 |; 181 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 138 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 21 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__2478,hypothesis,
( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2478) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
| doDivides0(xr,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( ( ( X3 != sz00
& X3 != sz10
& ! [X4] :
( ( aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& X3 = sdtasdt0(X4,X5) )
& doDivides0(X4,X3) )
=> ( X4 = sz10
| X4 = X3 ) ) )
| isPrime0(X3) )
& ( ? [X4] :
( aNaturalNumber0(X4)
& sdtasdt0(X1,X2) = sdtasdt0(X3,X4) )
| doDivides0(X3,sdtasdt0(X1,X2)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [X4] :
( aNaturalNumber0(X4)
& X1 = sdtasdt0(X3,X4) )
& doDivides0(X3,X1) )
| ( ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(c_0_8,plain,
! [X112,X113] :
( ~ aNaturalNumber0(X112)
| ~ aNaturalNumber0(X113)
| aNaturalNumber0(sdtpldt0(X112,X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_9,hypothesis,
( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(esk16_0)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),esk16_0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2478])]) ).
fof(c_0_10,plain,
! [X166,X167] :
( ~ aNaturalNumber0(X166)
| ~ aNaturalNumber0(X167)
| X166 = X167
| ~ sdtlseqdt0(X166,X167)
| iLess0(X166,X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
cnf(c_0_11,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),esk16_0) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
| doDivides0(xr,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
| doDivides0(xr,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_15,hypothesis,
! [X194,X195,X196,X199] :
( ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk5_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| aNaturalNumber0(esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| X196 = sdtasdt0(esk5_3(X194,X195,X196),esk6_3(X194,X195,X196))
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| doDivides0(esk5_3(X194,X195,X196),X196)
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != sz10
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| esk5_3(X194,X195,X196) != X196
| X196 = sz00
| X196 = sz10
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X199)
| sdtasdt0(X194,X195) != sdtasdt0(X196,X199)
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| aNaturalNumber0(esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| X194 = sdtasdt0(X196,esk7_3(X194,X195,X196))
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( aNaturalNumber0(esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( X195 = sdtasdt0(X196,esk8_3(X194,X195,X196))
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) )
& ( doDivides0(X196,X195)
| doDivides0(X196,X194)
| ~ iLess0(sdtpldt0(sdtpldt0(X194,X195),X196),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X196,sdtasdt0(X194,X195))
| ~ isPrime0(X196)
| ~ aNaturalNumber0(X194)
| ~ aNaturalNumber0(X195)
| ~ aNaturalNumber0(X196) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])])])])]) ).
cnf(c_0_16,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,hypothesis,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,hypothesis,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
fof(c_0_20,hypothesis,
! [X210,X211] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X211)
| xr != sdtasdt0(X210,X211)
| ~ aNaturalNumber0(X210)
| X210 = sz10
| X210 = xr )
& ( ~ doDivides0(X210,xr)
| ~ aNaturalNumber0(X210)
| X210 = sz10
| X210 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
fof(c_0_21,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_22,negated_conjecture,
! [X216,X217] :
( ( ~ aNaturalNumber0(X216)
| xn != sdtasdt0(xr,X216) )
& ~ doDivides0(xr,xn)
& ( ~ aNaturalNumber0(X217)
| xm != sdtasdt0(xr,X217) )
& ~ doDivides0(xr,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_23,hypothesis,
( doDivides0(X1,X2)
| doDivides0(X1,X3)
| ~ iLess0(sdtpldt0(sdtpldt0(X3,X2),X1),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X1,sdtasdt0(X3,X2))
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_25,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
~ doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
~ doDivides0(xr,xm),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]),c_0_31]) ).
cnf(c_0_33,hypothesis,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_11]),c_0_29])]) ).
cnf(c_0_34,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_11]),c_0_28]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM508+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n021.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:41:25 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.98/1.91 % Version : CSE_E---1.7
% 1.98/1.91 % Problem : theBenchmark.p
% 1.98/1.91 % SZS status Theorem for theBenchmark.p
% 1.98/1.91 % SZS output start CNFRefutation
% See solution above
% 1.98/1.91 % Total time : 1.372s
%------------------------------------------------------------------------------